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Project Reports for the ENGR 212-503 Group Project on

Design, implementation, and analysis of a thermal sciences demonstration experiment

Fall Semester, 2003

Instructors: Scott A. Socolofsky, Ph.D. Assistant Professor Department of Civil Engineering Tirtharaj Bhaumik Teaching Assistant Ocean and Coastal Engineering Program Institution: TEXAS A&M UNIVERSITY Dwight Look College of Engineering

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PREFACE This set of proceedings presents the final reports by students in the ENGR 212-503 course titled “Conservation principles in thermal sciences” for the fall semester, 2003, at Texas A&M University. The projects were conducted in groups of about four students each and were directed toward design, implementation, and analysis of a thermal sciences demonstration experiment. The students were asked to think of an experiment that could be done inexpensively in the home that would also demonstrate a concept from the course. A few sample ideas were distributed, but the students also did a good job of coming up with ideas of their own. The students worked on the projects for about five weeks and were required to turn in several progress reports summarizing significant milestones for completing the experiments. The project description is provided in Part I of these proceedings; the student reports are in Part II. Overall, the project provided an important opportunity for students to investigate many of the simplifying assumptions made in class for a real system.

College Station, Scott A. Socolofsky December 2003 Tirtharaj Bhaumik

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CONTENTS

Part I. Project Assignment and Description ENGR 212-503 Group Project: Design, implementation, and analysis of a thermal sciences demonstration experiment S. A. Socolofsky ........................................................................................................................3

Part II. Group Projects Project 1: Experimental calculation of Cv of air A. Abreu, P. K. Katsabas, A. E. Paul, II & J. A. Roddy..........................................................11 Project 2: Application of the ideal gas law to everyday life G. L. Anderson, C. C. Curtis, K. W. Richardson & E. E. Sladecek ........................................15 Project 3: Buoyancy of an egg J. A. Austin, C. R. Ottman, Z. A. Stein, & S. B. Williams......................................................19 Project 4: Mixing chambers E. M. Bahr, M. P. Davis, M. K. Sumrall & J. K. Vaughan .....................................................23 Project 5: Observation and analysis of heat transfer between convection oven and water T. P. Baumgartner, M. T. Burnett, L. A. Hargrove & G. L. Humphrey, Jr. ............................27 Project 6: Volumetric expansion in a closed system due to heat with constant pressure R. J. Bennett, R. G. Hinloopen, B. G. Jimenez & P. J. Kim....................................................31 Project 7: Do you have a hard time blowing up balloons? A. M. Blackburn, H. A. Bowdre, J. W. Honea & P. D. Pepper...............................................35 Project 8: Ideal expansion of air R. R. Bohacek, M. R. Gonzalez, C. J. Hoelscher & E. A. Reed..............................................39 Project 9: Manometer experiment using water and air Z. W. Bujnoch, D. E. McElligott, K. E. Niedzwecki & H. B. Palmer, Jr................................43 Project 10: Agar solutions J. Carter, P. S. Clifford, D. I. Garza, K. L. Golden & C. A. Young ........................................47

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Project 11: Latent heat of fusion of water experiment V. S. Cuellar, J. M. Gustafson, J. M. Juarez & H. Luna..........................................................51 Project 12: Effects of heating an air-filled balloon M. Dominguez, B. P. Lusk, C. T. Millar & T. Morris.............................................................61 Project 13: Relative humidity analysis J. A. Dovalina, Jr., J. D. Grothues, S. D. Ingram & H. H. Sun................................................65 Project 14: Heat transfer between an air-filled balloon and water baths at differing temperatures B. A. Ford, R. D. Goodnight, R. N. Mosher & M. R. Murphey..............................................71 Project 15: Heat exchange between ice and water J. E. Griffin, K. H. LeClair, T. J. Perales & J. A. Sibert..........................................................75 Project 16: Can Charles, Boyle, and Gay-Lussac’s ideal gas equation accurately approximate the behavior of air? M. T. Hiatt, M. C. Morris, M. S. Posey & J. T. Ryan .............................................................79 Project 17: Hydraulics of a draining container D. N. Holub, V. A. Valero & J. T. Varghese...........................................................................81 Project 18: Rate of heat transfer from an apartment J. E. Howson, A. M. Thompson, J. W. H. Trout & J. M. Walling ..........................................87 Project 19: Investigating the fluid dynamics of a draining container J. D. Jurado, J. G. Schulze, S. E. Schulze & C. R. Shaw.........................................................91 Project 20: Buoyancy force and density M. L Lutz, J. Q. Martin, J. S. Sokol, T. N. Stephens & L. M. Strban .....................................97

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PART I: PROJECT ASSIGNMENT AND DESCRIPTION

ENGR 212-503 Group Project:Design, implimentation, and analysis of a thermal sciencesdemonstration experiment

Scott A. SocolofskyCollege of Engineering, Texas A&M University, College Station, USA

ABSTRACT: For this project, teams of four students each will work together to design, construct,conduct, and analyze a thermodynamic demonstration experiment and write a report in the formatconsistent with this project description. Students are free to design their own experiment, or they maychoose from a list of suggestions. The apparatus must be inexpensive or use readily available partsand must demonstrate a concept from the course ENGR 212: Conservation principles in thermalfluid science. Weekly progress reports and milestones will be assigned. The projects will be gradedon neatness, conformation to the style standards, making a “best effort” to obtain quality data, andon the analytical analysis techniques presented. Projectsare due with the individual evaluation formsby December 1st at 5:00 p.m. A document presenting all of the projects together for download willbe made available on the course website.

1 INTRODUCTION

Thermodynamics is an exciting experimentalsubject; indeed, our everyday environment isa complex thermodynamic system that throughthe greenhouse effect and other energy regulat-ing processes maintains a comfortable climatefor our existence. Not only is thermodynamicsan integral part of physics and chemistry, it alsotouches our lives throughout the day as we driveour cars, cook our meals, take our showers, andparticipate in sports and other activities. Despitethe wealth of examples around us, the thermo-dynamics classroom often presents a challeng-ing subject matter in a series of relatively ab-stract, and idealized problem sets. However,these problems could be tied in to our experi-ences with our environment through a simpleset of basic thermodynamic experiments. Thepurpose of this group project is for each teamto identify such an experiment, conduct it, andreport their finding back in the form of a shortwritten article.

In your later careers as engineers, scientists,researchers, business associates, or communitymembers, you will continually be expected towork in teams and to present your results, de-signs, and conclusions in the form of a writtenreport. Moreover, learning to work in teams andto write reports is a skill that must be learnedby practice. The Accreditation Board for En-gineering and Technology (ABET) lists this asone of their evaluation criteria when review-ing engineering curricula around the country(EAC 2003). In addition, recent technical ar-ticles about engineering education emphasizethe need for team, writing, and design skills(Liggett and Ettema 2001; Weiss and Gulliver2001; Tullis and Tullis 2001; Hotchkiss et al.2001). Therefore, this project serves two goals:to acquaint each team with a thermodynamicconcept and to provide an opportunity to learnskills needed to work in a group and communi-cate results.

You should take care in deciding which mem-

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bers to have in your team. Imagine you are theowner of a small engineering consulting com-pany and you are hiring people to work for you.There are several tasks that need to be com-pleted and you want members in your team tospecialize on one or more of these tasks. It isin everyone’s best interest that the teams are asstrong as possible.

The remainder of this document describes thegroup project in more detail and gives guide-lines for preparing the report and submittingprogress reports. The Methods section describesthe types of experiments that are permitted andsets guidelines for the experimental apparatusand the format of the project report. The Resultssection summarizes the content of the project re-port, including a detailed outline of the materialthat each section should present. The Discus-sion section breaks the project down to a man-ageable list of tasks and describes the progressreports that will be due at the end of each weekof the project. The final section, Summary andConclusions, overviews the project and suggestsavenues for obtaining help in completing theproject.

2 METHODSThis group project is designed to challenge yourcreativity and to get you to think analyticallyabout thermodynamic systems that are presentin our everyday lives. The project requires eachteam to define a problem that will be investi-gated experimentally, to build and conduct theexperiment, and finally to present the results ofthe project in the form of a written report.

The experiment that your team will conductmust illustrate a concept from the course ENGR212-503 Conservation principles in thermal sci-ences. The Discussion section presents a set ofguidelines that will help teams in defining theexperiment that they wish to conduct. In ad-dition, the Appendix A presents several ideasthat may also be selected. It is encouraged thateach team discuss their ideas with the instructor.This will help ensure that the experiments arefeasible, that they meet the requirements, andthe instructor’s experience may also help sug-gest variations that will make the experimentsbroader in scope.

Experiments will be conducted in the home,not in a laboratory setting, and should notrepresent a cost burden or danger to the stu-

dents involved. They may make use of regu-lar appliances (stove, oven, cappucino maker,microwave, etc.), dishes (pots, pans, plasticcontainers, recylables, etc.), tools (screwdriver,hammer, pliers, etc.), and measuring devices(stopwatches, measuring cups, thermometers,etc.). Specialized equipment (any of the abovethat you need but do not have) may be pur-chased, but may not exceed a total of $5.00 in-vestment. If your team has a fun idea but cannotthink of an economical way to make a requiredmeasurement, please discuss the issue with theinstructor in the hopes that some satisfactorymethod can be found.

The final reports must all be submitted in therequired format. Each team should downloadthe MS-Word template and style files from thecourse website. The package you download willalso include a style document that explains therequirements for most any special part of the re-port. It is important that your team follow theassigned style since your grade will be affectedby it and because all of the reports will be as-sembled together and posted on the course web-site. Teams that do not follow the style properlywill detract from the esthetic presentation of thefinal report.

3 RESULTS

The group projects will be graded based onthe individual evaluation forms (50%) and theproject content (50%). The project content por-tion will be based solely on the written report.This section details the content of the written re-port.

The project description you are currentlyreading is written in the required format. In yourlater careers as engineers, presentation and con-formation to specifications will be critical fac-tors in your success; therefore, team projectswill be graded harshly for deviations from thepermitted format. This document presents anexample of each element that might be includedin the report. Follow the formatting used herevery carefully. Projects that do not follow thisformat will tarnish the presentation quality ofthe final class report.

Each report will contain five mandatory sec-tions and an abstract. Subsections are permitted.The project page limit is six pages. The contentof these sections is described in the following.

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3.1 AbstractThe abstract is a short paragraph that summa-rizes all of the important parts of the report. It’spurpose is to help readers decide whether theyare interested in reading the complete report.For this project, the abstract should include astatement of the thermodynamic problem inves-tigated, a description of the experimental setupand measurements made, a summary of the re-sults of the experiment, and a comparison be-tween the measurements and analytical solu-tions. The word limit for the abstract is 150words.

3.2 IntroductionIf the reader decides to continue past, or maybeskip, the abstract, the Introduction section isyour chance to get their attention. The Intro-duction should contain three parts. The first partis also the first paragraph. The first paragraphshould begin with a relevant statement that cap-tures the reader’s attention. The subsequent sen-tences should continually narrow the topic untilthe final sentence, which should state preciselywhat the project is about. The second part cancontain several paragraphs and should be a sum-mary of the literature review. For this project theliterature review should present either informa-tion about the problem your team has selected,information about laboratory methods to makethe measurements you will need, or both, as ap-plicable. Each paragraph should focus on onesubject of the literature review and contain refer-ences to more than one paper or book. The thirdpart of the introduction is a single paragraphthat gives a road-map for the rest of the docu-ment. It should tell the reader where to expectto find what types of information. After readingthe Introduction, the reader should know whatyou are studying, how it might have been stud-ied in a detailed laboratory setting, what results,if any, are known from the scientific literature,and where to find the remaining information inthe report.

3.3 MethodsIn the Methods section, you should carefully de-scribe all of the methods used to conduct the ex-periment. It should describe how to assemblethe apparatus, how all the measurements wereconducted and what equipment was used tomake the measurements, and how the data will

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be analyzed (e.g. Excel regressions, or statisticalmeans, etc.). The Methods section should notmake judgments about the quality of the meth-ods used, but rather should detail the methodsso that the readers can form their own opinionsabout the quality of the results to come.

3.4 Results

The results section describes all the impor-tant results collected during the experimentalphase. This section should detail the raw data,free from interpretation and/or modification. Itshould explain what experimental runs weremade. The quantitative results can be presentedin the form of tables or figures or both, as ap-propriate. Figure 1 presents an example figuresummarizing experimental data. When possi-ble, error bars and data points should be pre-sented together with linear regression results.Captions should be short, but should completelydescribe the data presented. Not every datapoint collected must be reported. Instead, thedata needed for the discussion in the next sec-tion should be presented in an unbiased way.

3.5 Discussion

This is the first section where your team’s opin-ion may be reported. The Discussion sectionshould present an analytical solution using themethods we have developed in class as a predic-tion for the type of results to be expected. This

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Table 1: Schedule of progress reports and briefdescription of their contents.

Date Due Progress report

3. Nov. Description of experiment, setup,and measurements to be made

10. Nov. First draft of Introduction, includ-ing literature review

17. Nov. Complete draft of Methods and par-tial draft of Results sections

24. Nov. Complete draft of Discussion andpartial draft of Summary and Con-clusions

1. Dec. Final draft of the report

analytical solution should then be compared tothe measured experimental data. Similaritiesand differences should be pointed out and ex-plained where possible. Explanations can in-clude limitations of the analytical method, devi-ations in the experiments from the idealized sys-tem, and possibly errors or mistakes in collect-ing the experimental data. This section shouldstrive to use physical arguments from the ana-lytical solution to explain the data.

3.6 Summary and ConclusionsThe final section of the report is short and writ-ten in two parts. The first paragraph is a briefsummary of the important points from the previ-ous sections. The second paragraph presents theimportant conclusions that can be drawn fromthe experiment. Neither paragraph should intro-duce new, important information; however, theymay synthesize information to arrive at an im-portant conclusion. If desired, a third paragraphcan suggest steps to take in future investigationson the same subject.

4 DISCUSSIONTo keep the project moving and to prevent prob-lems with meeting the deadline, milestones willbe set for each week and mandatory progressreports will be collected and graded. Table 1presents a schedule for each project report andthe required contents.

In the first week, teams should carefully de-cide what experiment they would like to do.Creativity is encouraged–teams are not requiredto pick an experiment from the list of sugges-tions. Requirements for the experiments are asfollows:

• The experiment must demonstrate a con-cept from the course ENGR 212-503: Con-servation principles in thermal sciences.

• It must be possible to analyze the experi-ment and make predictions about the out-comes using the techniques we have devel-oped in the course.

• Conducting the experiment must lead tosome form of quantitative data. Thiscan include temperature, volume andmass measurements, timing with a stop-watch, pressure estimates using modifiedmanometers, or any other standard mea-sure that does not require expensive labo-ratory equipment.

• Teams should be able to repeat the experi-ment several times to obtain error estimateson the measurements.

• When applicable, the experiments shouldbe run for different initial and boundaryconditions to get a feel for how the chosensystem reacts in different situations.

Simple, every-day activities can be made inter-esting by developing careful experiments andmeasuring some physical quantities. At the endof week one, teams are required to submit astatement describing the thermodynamic systemthey have chosen, the experimental setup theywill use, and the quantitative measurements theywill collect.

During the second week, teams flesh-out theirideas for their project and spend a little time inthe library. The team should especially considerwhat data will be collected and how that datawill be presented in the final report. A shortliterature review should investigate how similarmeasurements are made in careful, laboratorysettings. For instance, if a team’s project re-quires estimating a flow rate with a bucket andstop watch, the literature review could includea summary of more sophisticated ways to mea-sure fluid flow. In addition to the literature re-view, teams should assemble the experimentalapparatus if applicable. The apparatus must bemade from standard things one has around thehouse. If specialized equipment is required, thisequipment must be inexpensive. For instance,straws can be used when tubing is required. Atthe end of week two, teams should submit a

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draft of their Introduction section, which shouldinclude the results of the literature review.

The experiment should be conducted in thethird week of the project. The whole team mustbe present during the experiment. The experi-ment in all its variations should not require morethan two or three hours to complete, includ-ing collecting the data. The third week shouldalso be used to write the Methods section andthe Analysis section of the Discussion. Theprogress report for week three should include adraft of these sections.

In the fourth week of the project, the teamswill compare the measurements to the analyti-cal results, complete the Discussion section, andwork on the Summary and Conclusions. Theexperimental data should be presented and de-scribed in the Results section. The Discussionsection should compare the measurements tothe analytical solution and discuss differencesand similarities. The Summary and Conclusionssection should summarize what was done andlist the important conclusions that can be drawnfrom the project. The final section should notpresent any new material, but rather restate suc-cinctly the important results of the project. Acompleted rough draft is due at the end of weekfour.

By December 1, 2003, each team should turnin one printed copy of the report, a diskette con-taining the MS-Word document of the report,and four individual evaluation forms, one foreach team member.

5 SUMMARY AND CONCLUSIONSThe group project in thermal fluid science de-scribed in this report challenges students tothink critically about a thermal fluid scienceproblem, design an experiment to analyze theproblem, work together in groups, and commu-nicate their results in a strict written format. Theexperiments will be inexpensive, conducted athome, and must generate quantitative as wellas qualitative data. The report will include ashort literature review, a description of the ap-paratus, a presentation of the raw data results,and a comparison of the data results to analyti-cal data. Progress reports will keep the teams ontask and provide important feedback before thefinal project is due.

The open-endedness of this project will re-quire the team to discuss their project in detail

and realistically simulate actual design work.The emphasis on writing will help prepare stu-dents for their later careers and upper-level engi-neering courses. Overall, the project should in-spire creativity, enhance understanding of ther-modynamic systems, and give students a smalltaste of the content of engineering research.

ACKNOWLEDGMENTSYour team may also present a short acknowledg-ments section. The instructor is grateful to the A.A. Balkema Publishers, Rotterdam, Netherlands, fortheir generosity in supplying the MS-Word templateand style sheets for easily creating reports in a stan-dard, journal-quality format.

REFERENCESEAC (2003). Criteria for accrediting en-

gineering programs. Technical report,Engineering Accreditation Commission,Baltimore, Maryland.

Hotchkiss, R. H., M. E. Barber, and A. N. Pa-panicolaou (2001). Hydraulic engineer-ing education: Evolving to meet needs.J. Hydr. Res. 127(12), 1036–1040.

Liggett, J. A. and R. Ettema (2001). Civil-engineering education: Alternate paths.J. Hydr. Res. 127(12), 1041–1051.

Tullis, B. P. and J. P. Tullis (2001). Real-world projects reinforce fundamentals inthe classroom.J. Hydr. Res. 127(12),992–995.

Weiss, P. T. and J. S. Gulliver (2001). Whatdo students need in hydraulic designprojects?J. Hydr. Res. 127(12), 984–991.

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A IDEAS FOR EXPERIMENTSTeams are encouraged to be creative in selectingan experiment for their group project. The ideaspresented here are intended as examples to getthe creative juices flowing. Teams may select todo one of these experiments, a modified versionof these experiments, or an entirely different ex-periment.

A.1 Hydraulics of a draining containerThe following suggestions could cover severalteams’ experiments. In them, we investigate theconservation of mass equation and it’s ability topredict the time required for a reservoir to emptyunder the effect of gravity.

The reservoir could be a milk carton with lid.The outlet might be a straw glued to a hole. Avalve in the straw could be a clothes pin. Mea-sure the time to empty the milk carton with thelid off and with the lid on. Estimate the maxi-mum vacuum pressure the lid can create. Also,measure the time required if the outlet of thestraw is at the same level as the hole in the milkcarton, at higher levels, and at lower levels.

Analyze each experimental set-up using theequations we derived in class. Compare yourtime estimates to the experiments and developa means of including friction loss in your equa-tions. Calibrate the friction coefficient to the ex-perimental data.

A special kind of apparatus for generating aconstant flow rate using gravity forcing alone iscalled a Marriot bottle. Research what this isand include one experiment using these princi-ples. How successful is your apparatus at gen-erating the constant flow rate?

A.2 Relative humidityOne way of estimating the relative humidity isto measure the dew-point temperature. A de-vice that measures the dew-point temperatureis a standard thermometer with the thermome-ter bulb surrounded by a wet cotton swab thatis ventilated by a fan or draft. As air rushesthrough the cotton swab, water evaporates. Ifthe air has 100% relative humidity, no waterevaporates and the temperature will just equalthe ambient air temperature.

Understand how the dew-point thermometerworks, build such a thermometer and find differ-ent environments were you can measure the rel-ative humidity of the air. Such environments in-

clude the air outside, in your house, in the bath-room after taking a shower, etc. Try to think ofa set of experiments that would yield interestingresults. Historical dew-point temperatures forthe United States are also available. These couldbe analyzed and compared to measurements youmake in everyday environments.

A.3 Cooking food and the pressure dynamicsof plastic containers

Have you ever cooked food in a microwave andimmediately covered it with a lid when donecooking? If you do this with a plastic con-tainer, such as a Glad re-usable storage con-tainer, you might have noticed that when thefood is first covered, the container expands dueto some pressure. After a few minutes, the con-tainer returns to normal, and then continues toshrink down under some vacuum pressure.

Perform some experiments to estimate heatlosses at these various states. You can ask theinstructor for a simple means of estimating theamount of vacuum pressure the seal can gener-ate and some guidelines for analyzing the sys-tem analytically.

A.4 Ideal gas lawA simple balloon filled with air at different tem-peratures can investigate the ideal gas law. Isit possible to fill the balloon with pure steam?If so, what will be the behavior as the ballooncools? How can use analyze it since steam isnot an ideal gas? What quantitative data can youobtain?

A.5 Piston devicesSyringes are good examples of piston devices.Can you demonstrate phase changes for closedsystems in piston devices and make calculationsabout the resistance of the syringe piston and thechanges in volume of the system?

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PART II: GROUP PROJECTS

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1. INTRODUCTION

This experiment solves for the Cv of air. In order to accomplish this, the equation Q=m Cv (T2-T1) is utilized. Q is supplied, m is calculated in advance, and change in temperature is measured. This procedure is repeated several times with different values of Q to determine how accurately Cv can be calculated.

The main background information for this experiment is the first law of thermodynamics. This principle provides a sound basis for studying the relationships among the various forms of energy and energy interactions (Cengel & Turner 2001). The original equa-tion for conservation of energy, Q-W=m (∆ke+∆pe+∆u), is first simplified. Knowing that there would be no work interaction, and that the changes in kinetic and potential en-ergy are negligible the equation Q=m(u2-u1) is derived. Then assuming constant specific heats, the final equation Q=mCv(T2-T1) is ob-tained. This equation leaves only one un-known variable that needs to be solved for af-ter all the measurements are collected. The variable m is calculated using the ideal gas

law, PV= mRT. Other formulas that could have been used are m = V/v or m = Vρ know-ing the specific volume or the density of air. The best way to find temperature is simply to measure it.

This report consists of an introduction, methods, results, discussion, summary and conclusion section. The introduction is a ba-sic explanation of the experiment, and the variable being calculated. Following is the methods sections which gives a full descrip-tion of the materials and procedures of the ex-periment. After performing the experiment, the results and conclusions drawn from the re-sults are included. The results and discussion are allocated their own section. The results are just pure data, while the other contains analysis and conclusions drawn from the ex-periment. Final evaluations and comments can be found in the summary and conclusion part of the report.

Project 1: Experimental Calculation of Cv of Air

O. Abreu, P. K. Katsabas, A. E. Paul, II & J. A. Roddy College of Engineering, Texas A&M University, College Station, USA

ABSTRACT: This project presents experimental results to calculate the specific heat, Cv, of air. Us-ing the first law of thermodynamics, conservation of energy, and assuming constant specific heats, we solve for Cv. To accomplish this, we set up a system in which we use a thermometer to measure the change in temperature created by the heat output of a light bulb over the time period of two min-utes. Once all the measurement were recorded and graphed, the slope determined the value of the specific heat of air. The result of the experiment, .721 kJ/kg*K, is very close to the actual value of .718 kJ/kg*K. Differences are attributed to human error or the imperfections of the system, but those appear negligible.

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2. METHODS

A plastic container is used as the system boundary. A thermometer and a stopwatch are used to measure the temperature change over a time period of two minutes. Three different three way bulbs are used to obtain different energy inputs to the system. The bulb is then used as a heating source to create a temperature change. The bulb is connected to a three way switch that is connected to a wire plugged into the wall.

The mass of air is calculated using the for-mula PV=mRT (Assuming air is an ideal gas). Step one consists of measuring and recording the initial temperature of the air and then turn-ing on the light for a duration of two minutes. At this point, the temperature change in the system is measured and recorded. This process is repeated until results are obtained for the nine different power inputs. Using an excel spreadsheet, the Energy input can be found. From the different values of Energy input and ∆T, Cv can be calculated by using the formula: E in = m Cv (T2-T1). 3. RESULTS Table 1: Table of Raw Data

Power watts)

Energy (KJ)

Final Temp (C)

250 0.03 29.0 200 0.024 28.0 150 0.018 27.5 135 0.0162 27.0 100 0.012 26.5 70 0.0084 26.0 50 0.006 25.7 30 0.0036 25.5 15 0.0018 25.2

The energy is calculated by multiplying the wattage of the bulb by the time the bulb is left on. Using the formula P=W*t, energy is found by rearrangement the formula to W=P/t. Using the first bulb with wattages 50, 200 and, 250 watts, the final temperature was 25.7, 28, and 29 degrees Celsius. Using the second bulb with wattages 15, 70 and 135

watts, the final temperature was 25.2, 26, and 27 degrees Celsius. Using the third bulb with wattages 30, 100, and 150 watts, the final temperature was 25.5, 26.5, and 27.5 degrees Celsius. The trend line was calculated using Excel, along with the error bars that have a range of ± 5%. 4. DISCUSSION The results shown above (Figure 1 & 2) are calculated using the formula Q = m Cv (T2-T1). The data is plotted on a graph as energy vs. m*∆T. A trend line is added using Excel with the origin at zero. This produced a trend line with a linear relationship between the two variables related by the equation Cv = .724x. The linear factor is considerably close to the ideal factor of .718. The difference in values can be attributed to the poor seal of the system containing the air being heated. The seal could be improved in future experiments for more accurate read-ings. Also the factor of heat loss from the sys-tem may have led to inaccurate readings. This factor can be decreased by better insulating the system to prevent heat loss. This was dealt with by using a plastic container, since plastic is a poor conductor of heat. Also, since the experiment relies on radiant heat, the light of the bulb is not allowed to directly shine on the thermometer as it would increase the recorded temperature (analogous to why you cannot measure the temperature of the atmosphere by using a thermometer that is directly exposed to sunlight). Since it takes a while for the heat to dissipate through out the system, the final temperature is the max temperature recorded, as the thermometer is placed as far from the bulb as possible. Also, some time is given to let the heat dissipate after the switch is shut off. Outliers in the data points can be attrib-uted to the use of different light bulbs throughout the experiment.

5. SUMMARY AND CONCLUSIONS

The experiment is designed to calculate the value of Cv of air under normal conditions. This is carried out by heating a fixed mass of

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Figure 2: Correlation of Energy input to m*∆T. The points represent energy inputs. Error bars are shown on all data points. The ideal slope is graphed in blue. air in a sealed container with various amounts of energy and measuring the change in tem-perature. Using the relationship Q = mCv (T2-T1), which is derived from the first law of thermodynamics, a graph of Q vs. m(T2-T1) yields a straight line with a slope equal to Cv. In conclusion this experiment shows that the specific heat with respect to constant vol-ume, is equal to .7214 kJ/(kg*K). The actual

value of Cv is equal to .718 kJ/(kg*K). The difference in the two values is minimal and can be attributed to instrumentation error. REFERENCES

Cengel, Y., & Turner, R. (2001). Selected Material From Fundamentals of Ther-mal-Fluid Sciences. New York: McGraw-Hill Primis Custom Publishing

A Graph of Energy vs m*∆T

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1 INTRODUCTION Super-soccer Mom purchases a normal bag of black eyed peas at a local supermarket. She then takes them home and promptly places them into her deep freezer. When she places the bag into the freezer, she notes that the bag is flimsy and the peas have plenty of room to move around. Three days later, while at-tempting to prepare the evening meal, she re-moves the bag of peas from the freezer. She notes that now the plastic bag is stuck to the peas and appears to have had all the air vac-uumed out of the bag. Upset that someone might have tampered with her family’s peas, she checks to see if the bag has any holes or openings that might allow all the air out of the bag; but she finds the bag perfectly sealed. She wonders, like all brilliant people do, if some thermodynamic process is covertly oc-curring in her freezer. Like all moms, she knows everything, and recalls that the bag is just obeying the ideal gas law, which every

good mother can easily quote in normal con-versation. In a closed system, when the temperature of a system decreases and the pressure stays constant, then the volume of the system must decrease. To ensure the safety of her family’s meal, she performs a test with three balloons to determine if the volume of her balloons will decrease with a decrease in temperature.

1.1 Thermometers

For the experiment, temperature must be measured in a room, refrigerator, and a freezer. Our team will use a mercury ther-mometer accurate to the nearest degree, found by the interpretation of the reader, to measure these varying temperatures. In a lab setting, the experiment could be refined by using sev-eral different methods. One can use digital thermometers that measure temperature to the

Project 2: Application of ideal gas law to everyday life G. Anderson, C. Curtis, K. Richardson, E. Sladecek Fighting Aggie Engineering Class of 2006

ABSTRACT: For this experiment, three balloons of varying volume are selected and the pressure is calculated at three varying temperatures in order to test the ideal gas law. Our hypothesis states that the volume will decrease as the temperature decreases and the pressure will remain constant. The methods section gives a brief outline of how the experiment is set up, and how the volumes and temperatures are measured. In the results section, the data is recorded and plotted on a chart. The data recorded plots linearly, thus proving our hypothesis that temperature and volume are di-rectly related and the pressure remains constant. In the discussion and summary and conclusion sections, there is an overview of outside influences that could affect our data, and our team’s opinion on how it was affected.

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nearest hundredth or thousandth. (Tech In-struments 2003). Also, there are new hi-tech thermal analysis devices, such as temperature probes, that are used through a computer sys-tem. Such systems measure temperature with high accuracy and, though expensive, well worth the cost for the very precise calcula-tions (Brown, 1998).

1.2 Volume Volume must also be measured after the bal-loons have reached an equilibrium state at the varying temperatures. We plan to use a tape measure to measure the circumference of the balloon. From the circumference we will cal-culate the radius of the balloon and then the volume. In a lab setting, we realized that no volume measurement would essentially be needed due to the fact that the pressure would be const- ant and one could easily measure pressure. However, we would have access to a caliper which could directly and accurately measure the diameter of the balloon if needed (library book found not cited). For a true reading of volume, modern technology has become crea-tive. Through the use of the ideal gas law, a pressure sensor has been created that will measure volume of a given shape, with a known temperature, and measure pressure from a gauge inserted into the balloon. This device would be much more accurate than our tape measure since it directly knows the pres-sure and applies the law we are proving (Brown 2003). 1.3 Pressure Gauges Pressure is the element that we are solving for therefore we will not directly measure pres-sure. We plan to prove, through the ideal gas law, that the pressure will remain constant. However, in a lab setting pressure can easily and accurately be measured. A barometer should initially be used to measure the atmos-pheric pressure in the room. Then a pressure gauge, following the Bourdon principle, could be used to measure the internal pressure of the balloon (Fawcett, 1946). In addition, a strain-gauge pressure transducer, derived from the piezoelectric effect, could also be used to measure the mechanical pressure inside the

balloon (Cengel, et.al, 2001). The computer device mentioned above that measure the vol-ume could also be switched to precisely measure pressure at a known temperature and volume (Brown 2003).

The body of this report first describes the methods and devices that our team uses to perform our experiment. Next, the report de-scribes all the important experimental data collected and contains a table clearly showing this data. This section contains only raw data with no opinions or outside interpretation of the data. Next, our team discusses our results and states our interpretation of the results. In this segment, our team tells our hypothesis for the experiment and compares it with the ac-tual data. It also states all assumptions, physical limitations, or any errors in meas-urement. The last section of the report briefly summarizes our important points and also draws important conclusions from the ex-periment.

2 METHODS The experiment begins by choosing three bal-loons, each with a slightly different volume. At room temperature, the balloons are filled with air and a temperature reading of the room is made for initial temperature of the gas, which we assume is air, inside the bal-loons. The balloons’ circumferences are then measured by a flexible, incremented tape. The balloons will be considered as spheres, but, for the measurements, we marked a line on the largest diameter of the balloon to take a consistent measurement as the volume de-creased. After taking accurate measurements of the room temperature and the circumfer-ence of the balloons, the three balloons are in-serted into the refrigerator. The thermometer is also inserted into the refrigerator alongside the balloons. The timer is then set to ten min-utes. While the gas is cooling, the radius can be calculated by the following formula:

(a) Radius = Circumference / (2 * π).

The volume of the balloon can then be esti-mated by:

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(b) Volume = (4/3) * π * (Radius)3.

After the time has elapsed, the balloons are measured one by one, and the temperature of the refrigerator is recorded. For an accurate reading of the volume and temperature, the re-frigerator should be opened and shut as quickly as possible while extracting one bal-loon at a time. Next, the balloons and ther-mometer are inserted into the freezer and the same process is repeated as before.

3 RESULTS By following the methods listed above, our team recorded and calculated a unique set of data. To collect the data, we used an alcohol thermometer for temperature and a flexible, standard, incremented tape. The three bal-loons’ initial temperature was 533 Rankine. By use of equations (a) and (b), the initial vol-umes of the red (.203 ft3), blue (.264 ft3), and pink (.226 ft3) balloons were calculated (See Table 1 and Figure 1). We then placed the three balloons in a constant temperature environment of 506 Rankine, a common household refrigerator. After leaving the bal-loons in the colder environment for a time of ten minutes, the temperature of the gases in-side the three balloons was assumed to be the same temperature as the refrigerator. By cal-culating the volumes of the balloons using the same process as stated before, our assumption that the volumes would decrease was con-firmed. The red, blue, and pink balloons re-spective new volumes were .195, .257, .220 feet cubed. The balloons were then placed in a household freezer. The constant temperature of the freezer was 478 Rankine. The balloons were also left in the freezer for ten minutes to be sure that all of the gas would be at the same temperature of the freezer environment. The final volumes of the red, blue, and pink balloons were red, .182, .245, and .215 feet cubed. Our team’s anticipated results were based on our knowledge of the ideal gas law. As shown by the data, when the temperatures of the gases were lowered, the volumes of the balloons decreased.

Figure 1: Plot of Volume Ratio vs. Tempera-ture of each of the three balloons. Table 1: Numerical Results of Measured Cir-cumferences vs. Temperatures and Calculated Volumes vs. Temperatures.

4 DISCUSSION Our experiment was set up to prove the ideal gas law. We measured a change in volume by transferring heat through a closed system which decreased the temperature. We were a little surprised that the balloons did not have a more dramatic decrease in volume. However, we came to the conclusion that if we had used a lighter gas, like helium, the balloons would have had a more emphasized reaction than the mixed air. Also, we attempted to quickly measure the circumferences of the balloons, but in the time it took to measure the balloons, we know the balloons expanded a little so the measure-ments are slightly inaccurate. We initially in-

TEMPERATURE (R) ROOM REF FREEZER

533 506 478 Circumference (in)

RED 27.5 27.125 26.5 BLUE 30 29.75 29.25 PINK 28.5 28.25 28

Volume (ft3) RED 0.203 0.195 0.182

BLUE 0.264 0.257 0.245 PINK 0.226 0.220 0.215

Volume vs. Temperature

0.98

1.00

1.02

1.04

1.06

1.08

1.10

1.12

470 480 490 500 510 520 530 540

Red

Pink

Blue

1.14

Temperature (R)

Volu

me

/ Ini

tial V

olum

e

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tended to prove the pressure was constant in the balloons, but realized we would need a way to measure the pressure to prove the pressure remained constant. We could not find a way to measure the pressure without opening the balloon and releasing some of the air mass inside, thus changing the system. Therefore, we assumed the pressure was con-stant and proved that volume would decrease with a temperature decrease, inadvertently proving the pressure was constant without an actual value for the pressure. 5 SUMMARY AND CONCLUSIONS This experiment is designed to prove the ideal gas law. Through very basic, elementary measurements of volume at varying tempera-tures, we found the volume decreased as the temperature decreased with the assumption of constant pressure.

Overall, we felt that the results from our experiment were accurate. From our data and our knowledge of thermodynamics, we can conclude that there is a direct relationship be-tween volume and temperature while pressure is held constant. Therefore, the Super-Soccer mom was correct in her assumption about the covert activities of the ideal gas law in her freezer. She can now safely serve her family their well balanced meal that includes an un-opened, healthy bag of black-eyed peas. 6 REFERENCES Cengel, Yunus A., Turner, Robert H. (2001)

Selected Material from the Fundamentals of Thermal-Fluid Sciences. McGraw-Hill Custom Publishing. 54

Brown, Lawrence S. (2003) Chemistry 107 Laboratory Manual. Hayden McNeil. 26-27

Tech Instruments. (2003) http://www.tech-instrment.com/DigitalThermometersindex.html.

Fawcett, J. R. (1946). Pressure Gauges. William Morris Press Ltd. 9-11.

Brown, M. E. (1988). Introduction to Thermal Analysis: Techniques and Applications. Chapman and Hall Ltd. 11-118.

Felker, C.A. (1941). Measuring Instruments. The Bruce Publishing Company. 18-21.

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1 INRODUCTION

The world that we know revolves around and relies on the laws of thermodynamics. With-out these principals, engineers would not be able to create and calculate such inventions that allow us to live our everyday lives and to use everyday machines that make our lives easier. Everything from the vehicles we drive, the air conditioners that cool us, and the power plants that provide us with energy are based on the basic laws of thermodynamics. For a large and complicated power plant to function, each smaller system within the over-all power plant system must be accounted for and calculated for basic properties of pressure, heat, density, etc. These large and compli-cated systems can all be separated and re-duced into the very basic principles of ther-modynamics. Our team will attempt to perform an experiment that will relate to one of these very basic principles of thermody-namics.

The experiment we plan to do for our team project deals with buoyancy. The experiment consists of cracking open an egg into a glass of fresh water and cracking open an egg into a glass of salt water. The egg should float in the salt water but not in the fresh water. This

would then prove the force of buoyancy a liq-uid puts on an object is directly proportional to the density of the liquid being used.

The measurements that must be taken in this experiment are rather basic and can easily be preformed, even by a child. To find the density of the water, salt water, and egg, the mass and volume must be recorded. The mass of the different substances can be taken by weighing them on a simple balance scale. In a laboratory, this measurement might be taken on an electronic scale, which will give a read-ing with a greater numbers of significant fig-ures. The volume can be taken by pouring the substances into a graduated cylinder and read-ing the volume measurement. To measure the volume of the egg while it is still in the shell, we will drop the egg into a graduated cylinder full of water and measure the displacement. We can then calculate our error by comparing our recorded values to the values given in our thermodynamics textbook.

There are four other sections that will be included in our experiment dealing with buoyancy. One of these other sections is ti-tled Methods. This section describes how the experiment is preformed and what is and what is not allowed to take place for the experiment to be effective. The Results section reviews

Project 3: Buoyancy of an Egg

J. Austin, C. Ottman, Z. Stein & S. Williams College of Engineering, Texas A&M University, College Station, USA

ABSTRACT: Our team of engineering students, which are enrolled in thermodynamics at Texas A&M University, are experimenting using the laws of physics and thermodynamics. The ex-periment that we are performing deals with the densities of different fluids and the buoyancy that will act on a cracked egg. The laws of physics that we learn from this will in turn help us to bet-ter understand the concepts of thermodynamics in everyday life.

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the information given in the project report, which includes what each section should in-clude. The Discussion section will break the project down into tasks that should be fol-lowed to complete the experiment. The Summary and Conclusion section will include

our final thoughts about the experiment and what we determined to be the reasons for the sinking or floating of the egg.

2 METHODS

The supplies needed to do this experiment are a small kitchen scale, two 500 mL or lar-ger cups, three eggs, water, table salt, and a measuring cup. The two fluids being used are 400 mL of tap water and 400 mL of water with approximately five tablespoons of table salt dissolved into the water. To obtain den-sity measurements for our fluids we will first weigh the 500 mL cups empty and weigh them again while they are full of fluid. The density of the fluids can then be calculated by dividing the mass of the glass of fluid minus the mass of the glass by the volume of fluid in the glass. The density of the egg will be ob-tained by a similar method. The egg will be cracked into a container of known weight and the volume will be measured. The density will be calculated by dividing the egg’s in-nards mass by the egg innards volume. Cal-culations that can be made in this experiment are multiplying the mass of the egg innards by acceleration due to gravity (9.8 m/sec2). The force of buoyancy can then be calculated by multiplying the density of the fluid by acceleration due to gravity and the volume of the egg innards. The experiment is performed by cracking an egg into the cups of salt and tap water and then observing whether or not the eggs float. Then compare the results of the experiment to your calculations.

3 RESULTS

While performing our experiment we ran three trials to receive a greater accuracy in our results. The multiple test trials also allow us to eliminate data that was severely inaccurate

to the related data points. The following table is a record of the initial measurements of the mass and volume of the egg, water, and salt.

From this initial data we are able to calcu-

late the density of the water, saltwater, and egg. The following table is a list of the densi-ties that are calculated using the formula,

Density = Mass / Volume

From the table of densities we can observe

that the density of the egg is greater than the density of the tap water but less than the den-sity of the salt water. This shows why the egg floats in the saltwater but sinks in the unsalted water.

The forces that are involved in this process are the force of gravity acting down on the egg and the force of buoyancy from the water acting up on the egg. In this experiment the density of the liquid is related to the buoyancy directly and therefore the greater the density of the water, the greater the buoyancy force will be acting on the egg. When the buoyancy force is greater than the force of gravity the egg will float. When the opposite occurs, the buoyancy is less than the force of gravity acting on the egg, the egg will sink to the bottom of the glass.

Egg Inards

Salt Water

TRIAL 1 Mass (g) 103 40 399 Volume (mL) 99 - 400 TRIAL 2 Mass (g) 97 45 399 Volume (mL) 94 - 400 TRIAL 3 Mass (g) 97 43 401 Volume (mL) 90 - 400

Egg Inards

Salt Water

Water

TRAIL 1 Density (g/mL) 1.0404 1.0975 0.9975TRAIL 2 Density (g/mL) 1.0319 1.1100 0.9975TRIAL 3 Density (g/mL) 1.0778 1.1100 1.0025

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4 DISCUSSION

After the experimental data had been com-piled, an analytical solution can then be de-termined to back up what we saw in our ex-periment. The following formulas were used to derive the solutions:

FGravity = MEgg * aGravity

(1) FBuoancy = ρFluid * VEgg * aGravity

(2)

Table 3 F(gravity) F(buoyancy)

Egg Salt water Water 1.009 1.065 0.9678

0.9506 1.023 0.9189 0.9506 0.979 0.8842

Using formulas 1 and 2 it can be shown

that in all three trials the FGravity for the egg was less than the FBouancy for the salt water and greater than the FBouancy for the regular water. This confirms what was observed in the ex-periment, where the eggs floated in the salt water and sunk in the regular water. This ex-periment worked because the salt adds mass to the water while adding a nearly unnotice-able amount of volume. This makes the den-sity of the salt water greater than the density of the regular water. These differences in density make the FBouancy for the salt water greater than that of the regular water as seen in the directly proportional relationship be-tween FBouancy and density in equation 2.

5 CONCLUSION

This project taught our group many things about thermodynamics as well as everyday

forces such as gravity. Our first step in the project was to choose one. While we did con-template the ideas that were offered, we searched the internet and found what we thought would be a fun, interesting, and very inexpensive experiment. The project involved very little supplies and did not need lots of equipment to conduct our measurements. The next step was conducting the actual experi-ment. This consisted of taking measurements and placing the egg innards into the different waters. As we discussed in the results section, the difference between the densities of the egg and the type of water determines whether it will sink or float.

The main elements to our project were

density, mass, volume, and the natural gravi-tational force. By calculating these things we were able to explain why egg innards would float in salt water, but not in a glass of every-day household tap water. We are proud of our experiment and the outcome, and feel that this project was an overall success. Our ability to creatively turn two seemingly unrelated sub-stances, eggs and water, into a fun and infor-mative project enhanced our ability to per-form an engineering project and prepare us for the careers ahead of us. Our group functioned well together, which made the process of completing this project rather smooth. Our project helped us understand more thoroughly one of the main aspects of thermodynamics, buoyancy.

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1 INTRODUCTION

Steady flow devices, operating under the same conditions for long periods of time, make up the components of countless modern day ma-chines, both simple and complex. Everything from the nozzle on the end of a garden hose to the turbine used to generate power from a nu-clear reactor power plant is considered a steady flow device. Mixing chamber devices, another simple steady flow device, are an in-tegral part of most people’s everyday life, common throughout any American household. Millions wake up for their morning shower, clean the dishes, and wash their hands thanks to the workings of mixing chamber devices. In the simplest terms, two fluid streams are combined into one, altering their various in-tensive properties such as temperature, spe-cific enthalpy, and density. Knowing the flow rate, density, and temperature of any two of the three streams can allow one to solve for the unknown.

In order to take such measurements, there are many tools available. For measuring flow rate, the simplest method might be to time how long it takes for each stream to fill up a known volume (volume over time is volumet-ric flow rate, multiply by density to find mass flow rate). Accuracy in this method is deter-mined by the accuracy of the timekeeper and

exactness of volume measurements, which can be quite limited. Coriolis mass flow me-ters are available on the market; these are quite expensive, designed for industrial use, and are accurate to .2%. Thermal mass flow meters are also available. Based on a differ-ent design, these can vary in price relative to accuracy, which tends to be around 1.5%.

To measure temperature, the classic ap-proach is to use a simple glass thermometer. These need time to take accurate measure-ments and therefore lead to a phase lag in un-steady experiments, and more heat is lost, making the experiment a non-adiabatic ex-periment. Glass thermometers also tend to be less accurate than other means of temperature measurement. Digital thermometers do not need time to allow for mercury to expand, and thus provide a much more instantaneous result and tend to be much more accurate. Prices vary greatly relative to accuracy.

Effectively, the findings for each stream can be found by direct measurement. Each stream will be studied separately in a system-atic process. Flow rate is tested by measuring the time period required to fill a known vol-ume. Temperature is found and defined as a second property for the substance. Both ex-perimental methods provide a simple ap-proach to finding a relation between the prop-erties of the substance and the process taken.

Project 4: Mixing Chambers

E.M. Bahr, M.P. Davis, M.K. Sumrall & J.K. Vaughan Texas A&M University

ABSTRACT: This is experiment is designed to compare the analytical solution to the measured solution of the properties of a mixing chamber. The apparatus needed to recreate this experiment are inexpensive and readily available. It focuses on the study of the 1st and 2nd Laws of Thermo-dynamics exclusively.

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The remainder of this document will dis-cuss our project in an in-depth manner, and will cover all phases of the experiment. The Methods Section will describe how the ex-periment was conducted, and how it could be set up to be reproduced. The Results Section will give the tabulated values we received from our experiment, as well as a numeric ex-pression of the accuracy of these results as compared to theoretical values. The Discus-sion section will cover our opinion of the data we obtained. Finally, the Summary and Con-clusions section will present and overview of the report as well as the conclusions that can be drawn from our experiment.

2 METHODS

To set up the experiment, three generic paint buckets, one measuring cup, a stopwatch, three digital thermometers, two plastic valves, one plastic mixing-T, and five feet of 1/4” di-ameter plastic, flexible tubing are necessary. Plastic valves need to be secured inside holes drilled at the bottom of two of the buckets. Two feet of tubing is then attached to each valve. The opposite ends of the tubing are then attached to the mixing-T. Finally, one foot of the tubing is attached to the mixing-T for the outward flowing water. For measuring flow rate, one measures the time it takes for each stream to fill up a known volume (vol-ume over time is volumetric flow rate, multi-ply by density to find mass flow rate). Each paint bucket is filled with the same amount of water and the valves are opened to let water flow through the whole system. Once the wa-ter reaches a specified mark, the stopwatch is stopped, the valves are shut, and the volumet-ric and mass flow rates should be calculated. Meanwhile, marks should be made inside the buckets both before and after the water flows through. One should then calculate the individual flow rates of each bucket by measuring the change in height of the water. Now all three flow rates should have been calculated. A container of water should then be brought to near boiling temperatures over a hot stove. Another container should be cooled using ice cubes. The temperature of each liquid is measured using a digital thermometer. These two liquids are poured into each bucket (sepa-rately). The two liquids combine in the mix-

ing-T and flow together out into the third bucket. Temperature should be immediately measured. The actual specific enthalpy at the given temperatures and atmospheric pressure should then be looked up using typical ther-modynamic tables.

The theoretical enthalpy (and therefore tem-perature) can then be calculated using the formula: 332211 *** hmhmhm

•••=+ . Then, com-

pare the actual and theoretical enthalpies and calculate percent error using the formula: (ac-tual – theoretical)/actual.

3 RESULTS

During five separate trial runs, temperature (°C) was measured and both Experimental and Theoretical Enthalpy (kJ/kg) were calcu-lated.

Table 1: All recorded datum.

Measured Tempreture

(°C)

Experimental Enthalpy (kJ/kg)

Calculated Enthalpy (kJ/kg)

Trial 11 82.0 343.312 7.6 31.923 48.5 203.07 261.28

Trial 21 71.6 299.682 4.3 18.043 44.1 184.69 221.23

Trial 31 69.0 288.802 3.2 13.433 41.2 172.58 210.45

Trial 41 66.2 277.082 3.2 13.433 40.0 167.57 202.3

Trial 51 64.3 269.132 3.1 13.013 38.4 160.89 196.46

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Figure 2. Graph of Experimental and Ana-lytical Temperature vs. Enthalpy

4 DISCUSSION

Throughout each of the five trials conducted, we suspect the actual enthalpy value will come out less than the theoretical enthalpy value. This would be due to heat lost into the surrounding environment. After calculating the actual enthalpy values and comparing them to the theoretical values, we find this to be true. In every instance, actual enthalpy values were between 30 and 60 kJ/kg less than the theoretical values for enthalpy. This leads to an average percent error of approxi-mately 21%, as shown in Table 2. This error was obviously due to the fact that heat es-caped into the environment and could be re-duced by using better insulation techniques. This experiment was conducted as a closed system, which does not allow for mass to leave the system, but energy can. Ideally, an isolated system, acting adiabatically, would be best for this experiment and would remove virtually all error. Table 2. Calculated percent error based on measured datum.

Trial Percent Error (%)

1 28.7 2 19.8 3 21.9 4 20.8 5 22.1

5 SUMMARY AND CONCLUSIONS

Mixing Chamber devices and the concepts of Thermodynamics are commonly found in many every day devices. Our experiment was designed to find and calculate enthalpy and therefore temperature values of a simple mix-ing-T device. Five trials were conducted and the enthalpy and temperature values were cal-culated, compared to theoretical values, and an error was determined. Each trial resulted in similar discrepancies between expected and actual values. This was due to a fairly con-stant loss of heat from the system.

From this experiment, one can conclude that a perfect thermodynamically insulated system is not reasonably possible in real-world settings on a limited budget, and there-fore an error will almost always occur. We can also conclude that based on our experi-mental setup, the error we encountered was reasonable. REFERENCE Cengel & Turner (2001), Selected Material

from Fundamentals of Thermal-Fluid Sci-ences, McGraw Hill, New York, 2001.

Van Wylen, Gordon J. and Sonntag, Richard

E., English/SI Version, (3rd ed.) 1986. Fundamentals of Classical Thermodynam-ics. New York: John Wiley & Sons, pp. 635-51.

Temperature vs. Enthalpy

35.0

37.0

39.0

41.0

43.0

45.0

47.0

49.0

51.0

150.00 170.00 190.00 210.00 230.00 250.00 270.00

Entalpy (kJ/kg)

Tem

pera

ture

(°C

)

Experimental Analytical

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1 INTRODUCTION

Have you ever wondered the rate at which your oven transfers heat to an item if you do not open the door? An oven loses a consider-able amount of heat whenever the door is opened which increases the time it takes to complete the heating process. New ovens have a clear glass window, which allows users to see inside it. This clear window can be used to read a thermometer on the inside. Water is a good way to test the rate at which your oven really transfers heat at a set temperature.

To test heat transfer there are many meth-ods, which require a lot of high tech. equip-ment and knowledge that are not available for this experiment. A simple air to water heat exchange experiment in one case that uses a heat transfer test loop. In this procedure the instrument produces all of the needed data electronically. From this data all the needed calculations can be made with more accuracy and precision since human error has been eliminated in the conduction process.

Heat transfer is a process that is present in ever day life and occurs more often than most people think. Fundamentals of Thermal Fluid Sciences explains a simple example of heat transfer as when a cold canned drink is left in

a room it warms up, and then it will cool again when placed in a refrigerator. Also from this book heat transfer is explained as the transfer of energy from warm to cold. Once the temperatures are the same the energy transfer is completed. The main reason for this experiment is to find the rate of heat transfer and the amount of it.

The rest of this document is organized in the following manner. The methods used to complete this experiment are next. This clari-fies any confusion having to do with the proc-esses to acquire data from measurements and achieve calculations as accurate as possible. The results section follows this, and includes all of the data (measurements and calcula-tions) that are found in ways explained in the methods section. This section includes quanti-tative and qualitative data. These results are then thoroughly discussed which includes a group opinion and an analysis of what is found. Finally the project is completely sum-marized and then wrapped up with a conclu-sion on what has been discovered.

Project 5: Observation and Analysis of Heat Transfer Between Convection Oven and Water

T. Baumgartner, M. Burnett, L. Hargrove & G. Humphrey College of Engineering, Texas A&M University

ABSTRACT: The heat transfer between an oven and water is to be observed and analyzed. An experimental setup consisting of a small pan filled with water placed in an electric oven at a con-stant 350°F is to be used. An ordinary kitchen thermometer is placed in the pan to be read through a window in the oven for recording measurements. Temperature is measured at two-minute intervals in order to determine heat transfer over time. Results were consistent with ana-lytical calculations, and provided sufficient evidence that thermodynamic laws tested hold true.

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2 METHODS

2.1 Supplies The materials used to construct the project apparatus are simple, and provide for rela-tively accurate data. A normal household oven was used, one equipped with a digital temperature control to within an accuracy of five degrees Fahrenheit. It also has a working light and a clear window through which the experiment can be observed. A small one-quart metal pan was also used, as well as a normal kitchen thermometer that reads Fahr-enheit. Also, some way to keep close track of time is needed. We used a stopwatch, set to beep at two minute intervals.

2.2 Procedure First, preheat the oven to 350°F, making sure that it is clean inside and the racks are setup to allow space for the pan to fit. Then, take the one quart metal pan and fill it with three cups of room temperature tap water. Allow the wa-ter to settle, and stand the thermometer up-right. Take a starting measurement for the initial temperature of the water. Then, place the thermometer and pan into the oven, being careful not to spill any water. Do it fast enough to minimize the heat loss from the oven to the environment. Start the time, and turn on the oven light. Record the tempera-ture at two minute intervals for the next thirty minutes.

2.3 Data Analysis The data is to be analyzed using the law of conservation of energy. Methods described in Fundamentals of Thermal Fluid Sciences were used in calculations and are further described in the later section entitled discussion. The mass of the water is first calculated using tabulated specific volume data, and the room temperature. Next, constant specific heat is assumed, and the total amount of heat trans-ferred to the water is calculated. Finally, the total heat transferred is divided by the total time to produce an average rate of heat trans-fer for the process. These are the quantities obtained through analysis of the data, and the implications of both measured and calculated

data will be discussed in summary and con-clusions later in the paper.

3 RESULTS

Table 1: The exact data points recorded are shown Time(min) Temperature(F)

0 75 2 82 4 90 6 99 8 109 10 115 12 124 14 131 16 137 18 144 20 149 22 153 24 157 26 161 28 165 30 168

Figure 1: The water temperature rises with a quadratic trend in respect to time.

Presented above are the results from a single experimental run performed to collect data for analysis. The data is as accurate as described in the procedure section and was collected in strict accordance with this method.

Temperature Change of Water

y = -0.0588x2 + 4.9406x + 72.8

020406080

100120140160180

0 10 20 30 40

Time (min)

Tem

pera

ture

(F)

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4 DISCUSSION

We take the pan of water as our closed sys-tem, and assume that no mass enters or leaves our system. Some water will actually evapo-rate, but it is a small enough mass to consider it negligible. With this assumption, we can take the first law of thermodynamics and de-rive an equation for the heat transfer in our system.

PEKEUWQ ∆+∆+∆=− No work goes into the system and kinetic and potential energy changes are negligible so:

UQ ∆= (1) Therefore, the heat transfer to the water is equal to the change in internal energy of the water. Specific heats are related to internal energy by:

TmCU ∆=∆ Therefore:

TmCQ ∆= (2) Taking these equations, and looking at the data, we can determine the heat transfer to the system. First, we must calculate the mass of the water. From Table A-4E the specific vol-ume of water at 75°F is given to be 0.0161 ft3/lbm, therefore the mass of the water is equal to:

3 1 1 ^ 30.0161 ^ 3/ 16 7.48039

Vmv

cups gallon ftft lbm cups gallon

=

⎛ ⎞ ⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠

m = 1.557 lbm Next we take the specific heat of water to be constant and from Table A-3E it is given to be equal to 1.00 Btu/lbm*F. Putting these in equation 2 with the results from our experi-ment we have:

)75168(00.1)557.1( FFlbm

BtulbmQ −⎟⎠⎞

⎜⎝⎛

⋅=

Q = 144 Btu

This gives an average heat transfer rate of:

sBtus

BtudTdQ /08.

1800144 ==

5 SUMMARY AND CONCLUSIONS

From this experiment the planning and carry-ing out of an experiment was accomplished. Even though this was a simple procedure and required little knowledge of technology, a ba-sic knowledge of doing this without an ex-perienced person planning it was acquired. The rate of heat transfer calculation is a com-mon problem in the Fundamentals of Ther-mal-Fluid Sciences text book. The amount of heat transfer was calculated at 144 Btu. The rate of heat transfer of air at 350 F in an oven to water was calculated to be .08Btu/s. This was found using a procedure that could have very likely included some error. The oven may have lost heat whenever it was opened at the beginning in order to place the water in. Also, some of the heat went into the container which the water was in. A last possible source of error may have come from the reading of the thermometer. It was not a digital reading therefore the readings may have been off by a certain factor.

6 ACKNOWLEDGMENTS

We would like to thank the roommates of Luke Hargrove for allowing us to use their home for the conduction of this experiment. We would also like to thank HEB for supply-ing an inexpensive thermometer that was used for recording the temperature of the water.

REFERENCES

Cengel, Yunus A., Turner, Robert H. Fun-damentals of Thermal-Fluid Sciences. McGraw-Hill Primis Custom Publishing

Heaton, Wayne, Keeton, Brandon. Heat

Transfer Laboratory Equipment Design. Mechanical Engineering Department Ar-kansas Tech University

30

31

1 INTRODUCTION

Have you ever seen a hot air balloon lift off the ground and wonder how it is possible? Well, that could never occur unless heat ap-plied to the balloon until the balloon’s volume increased to its maximum volume and then pressure takes over. Our idea is to show how with the application of heat to a system simi-lar to a hot air balloon, will increase the vol-ume of the balloon to a maximum volume let-ting pressure remain constant through out this expansion process.

In order to conduct this experiment you must have prior knowledge of the Ideal Gas Law and the idea behind an Isobaric system. In this type of system there is no pressure change, thus when heat is added, the volume must expand to compensate for the heat. (http://www.ac.wwu.edu). This then leads up to Charles’ Law which states that when the

pressure is held constant, an increase in the temperature of a gas causes a proportional in-crease in volume (http://www.tpub.com). With this knowledge we can perform this ex-periment eliminating many variables.

Throughout the rest of this write up, you will be shown the initial and final measure-ments we took to prove our hot air balloon system. This data will be collected and analyzed to form our idea that the pressure will remain constant as the vol-ume increases to its maximum volume. If done in a lab setting there could be more data pertaining to the water to air ratio and its ex-pansion, possibly more precise measurements including temperature, volume, and pressure, and there could be many different variances in bottle shape, capacity, liquids and the amount of heat applied.

Project 6: Volumetric Expansion in a Closed System Due to Heat with Constant Pressure

Remko Hinloopen, Phillip Kim, Brian Jimenez & Jake Bennett Students, Texas A&M University, College Station, Texas

ABSTRACT: In our experiment our team worked together to design a system to analyze the ef-fects of heat on a closed system containing a known volume. The basis for our experiment is that with the pressure being constant with in the system, that the volume must expand with the appli-cation of heat (Charles’ Law – http://tpub.com). The apparatus used to conduct the experiment included a stove, 2 kitchen pots, a 750 ml glass bottle, latex balloons, thermometer, measuring cup, tap water, a measuring tape and some string. To begin the experiment we first took water and poured it into the glass bottle, with a balloon covering the spout of the bottle, then we placed the system into boiling water and allowed the volume to expand while measuring the expansion of the balloons circumference. With the temperature within the system remaining constant we measured the circumference of the balloon after a constant volume was reached. As the tempera-ture within the system came to a boil the circumference increased thus increasing the volume of the system.

32

Figure 1: 750 mL glass bottle containing 100 mL of tap water with balloon covering the opening.

2 METHODS

In order to conduct this experiment, it is im-perative to take as precise measurement as possible. First, an empty, symmetrical, glass bottle with a volume of 750 mL is found. Then measure 100 mL of tap water in a meas-uring cup. The water is poured into the glass bottle using a funnel. Take a latex balloon and mark it at three different lengths so the average circumference of the balloon can eas-ily be calculated. The open end of the balloon is secured around the opening of the glass bot-tle (Figure 1). Next, approximately 1000 mL of water is brought to a boil in a medium sauce pan and in it, the glass bottle with the attached balloon is placed, this process allows the volume with in the balloon to begin ex-panding (Figure 2). After eight minutes elapses, a piece of string is wrapped around the surface of the balloon and marked (Figure 3). This process is performed at all three marks. Finally, the lengths of the strings are measured with a measuring tape to gain the circumference of the balloon. After the ex-periment is run through several trials, calcula-tions are made. The volume of the balloon is found by first taking the average circumfer-ence, then using the average circumference in the formula: Cave = 2*Π*r, finding the average radius. Once the radius is found it is plugged into V = (4/3)* Π*r^3. Using a variance of the

Ideal Gas Law, (P1*V1)/T1 = (P2*V2)/T2, where P1 = P2.

V1 = 750 ml (no air in balloon) T1 = Room Temperature V2 = 750 ml + volume of balloon following heat application T2 = Boiling Water P = Atmospheric Pressure

So, we are left with the simple formula: V1/ T1 = V2/ T2. This is what will be used to prove that the pressure will remain constant through out the heating process. Figure 2: Balloon begins expanding after be-ing placed within the sauce pan containing the 1000 ml of boiling water.

Figure 3: Bottle is placed in the sauce pan containing 1000 ml of boiling water for eight minutes.

33

Measurements of all 3 radii are shown above to calculate the average circumference.

3 RESULTS

Measurements before inflation: ______________________________ Length (cm) Diameter (cm) Dot 1 7.0 12.5 Dot 2 9.0 14 Dot 3 10.5 15 radius = 2.23 cm volume = 46.45 mL______________

Measurements after inflation:

Trial 1: _____________________ Diameter (cm)___ Dot 1 22.0 Dot 2 25.0 Dot 3 23.0 radius = 3.98 cm volume = 268.9 mL_____ Trial 2: _____________________ Diameter (cm)___ Dot 1 26.0 Dot 2 26.0 Dot 3 23.0 radius = 4.14 cm volume = 296.8 mL_____ Trial 3: _____________________ Diameter (cm)___ Dot 1 24.5 Dot 2 27.0 Dot 3 24.8 radius = 4.30 cm volume = 332.4 mL_____

Trial 4: _____________________ Diameter (cm)___ Dot 1 21.75 Dot 2 26.0 Dot 3 23.75 radius = 4.14 cm volume = 296.8 mL_____

Figure 4: The above graph displays the Vol-ume of the balloon in ml with respect to its trial number Trial V / T

0 1.5 1 1.51 2 1.56 3 1.61 4 1.56

Figure 6: The above graph displays the Vol-ume/Temperature with respect to its trial number.

Volume (ml) per Trial

0

200

400

600

800

1000

1200

0 1 2 3 4 5

Trial #Vo

lum

e (m

l)

Volume (ml)Linear (Volume (ml))

V / T per Trial

11.11.21.31.41.51.61.71.81.9

22.12.22.32.42.5

0 1 2 3 4 5

Trial #

V / T

V / T Linear (V / T)

34

4 DISCUSSION

This experiment demonstrated such concepts as Ideal Gas Law, Charles’ Law, and an Iso-baric Process. The Ideal Gas Law was shown by how the volume to temperature ratio stayed constant. Also, as shown in our results, one can see that as the temperature of the system was increased so did the volume of our sys-tem to act in a way to keep constant pressure. This proves Charles’ Law, which states that in a constant pressure system, as the temperature increases volume does as well.

We expected from this experiment that as the liquid was heated creating a gas that the volume would in fact increase inside the bal-loon because we knew that the pressure would stay constant. The only way to keep constant pressure is to increase volume. Our results show, just as we expected, that our volume did increase with temperature keeping a con-stant pressure.

There were a number of things in the experiment that came as a surprise, as when the balloon started to fill with water vapor. In-stead of the volume of the balloon increasing uniformly, it started to deform as the volume started to increase. We came to the conclusion that because latex rubber weakens as it is heated, the hottest parts of the balloon were inclined to deform first to allow the increase in volume.

In addition, there could have been many er-rors in our measurements, causing a slight variation in what we expected. For example, maybe the seal created by the balloon on the bottle did not completely trap the air, there-fore allowing heat to escape. In turn, if heat escapes from the system it would alter our re-sults somewhat and you may be able to see that in the results section. Possibly adding to the heat loss was a crack that formed in the bottle from rapid transfer to the cold water bath via the hot water bath. Also, there were numerous variables that could have occurred in this experiment yield-ing different numbers, the same result. For instance, a different bottle shape may allow for more volume. The volume of water in the bottle would make it take longer for the water to turn into water vapor, and depending on when the measurements are taken, you may have different numbers. You could use a dif-

ferent balloon which could allow for a faster or slower increase in volume because the ma-terial is more or less elastic than the latex that was used. Also, a different liquid can be used in the system. For example, you could use al-cohol which when heated, turns into vapor much quicker than water. And again, when you take your measurements you could get different numbers, but you should come to the same conclusion.

5 SUMMARY

Our experiment’s purpose is to show that as water is boiled and turned into water vapor, the volume of our system will continue to in-crease until it reaches its maximum volume and in turn the pressure will increase. As the volume increases, however, the pressure will remain constant until that maximum volume is reached. By manipulating the Ideal Gas Law (PV = mRT), we can see that V/T = (mRT)/P = constant. With our results we have found that this is indeed true. Our re-sults did vary a little mainly from errors and impurities of our system such as a deforming balloon and possible leaks. Also, we proved Charles’ Law that states as temperature in-creases, so does volume as long as pressure stays constant. This experiment demonstrated the proper-ties used in hot air balloons and how they are able to fly. It shows you how it is able to fill the balloon with warm air and increase its volume, but also staying at atmospheric pres-sure. This experiment also concludes on the Ideal Gas Law and Charles’ Law which are proved within this experiment and with our results.

REFERENCES

Vanter, Richard. Department of Physics and Astronomy. Western Washington Univesity.http://www.ac.wwu.edu-/~VAwater/Phyicsnet/topics/thermal/Im-portantthermalprocesses.html

Integrated Publishing. http://tpub.com.-content/fc/14104/css/14104.44.html

35

1 INTRODUCTION

Without knowing it we encounter thermody-namic systems in our everyday lives. They are an integral part of both the complex and sim-ple tasks we perform each day: cooking a meal, taking a shower, regulating our thermo-stats, and driving our cars, to name a few. This project has posed us with the task of studying a simple thermodynamic system by designing an experiment that will allow us to trace actual results and compare them with an analytical solution. Although there are nu-merous thermodynamic systems everywhere, many of them are very complex. We decided that a basic and straight-forward system would be ideal to analyze considering our as-signment.

We chose to perform an experiment that would let us measure and analyze a system in which changes in both volume and tempera-ture occur. These changes will be easily ob-served and measured and will allow us to have accurate data. We have decided to ob-serve the changes that dry ice and water go through when put together in a closed system. Our materials will include: dry ice, distilled

water, a thermometer, a beaker, measuring tape, and a rubber band.

This system also undergoes a process that we have chosen not to measure or analyze, and that is the phase change of the dry ice and the water.

The following report will include our methods, results, discussion, and summary of this experiment. The methods section will in-clude our experimental data and analysis. The results portion will focus solely on the nu-merical data obtained. Our discussion will compare our system with an analytical solu-tion to our problem, and our summary will explain what we have learned and taken from this project.

The literature we found was very helpful in performing and analyzing our experiment. We use both our sources to learn things about dry ice so we can calculate the mass and also learn about the reaction it has with water. We can attach a syringe to the water bottle to measure the volume instead of the balloon. This may be more accurate but we won’t be able to use as much dry ice because the sy-ringe is much smaller.

Project 7: Do you have a hard time blowing up balloons?

A. Blackburn, H. Bowdre, J. Honea & P. Pepper BBHP WHOOP Publishers College Station, Texas

ABSTRACT: We set out to find the volume change when dry ice is sublimated in water from the steam that it puts out. We used a balloon to measure this volume. We found that since the bal-loon has elasticity and resists the air from expanding as much as it could, the experiment didn’t work as well as we would have liked. The measured volume change was about half that of what we derived from the ideal gas law.

36

2 METHODS

Our experimental apparatus is very simple, cost-efficient, and suits our project’s purpose. The materials include a 16 oz. water bottle, water, a party balloon, and dry ice.

To set up our device, we measure one cup (8 oz.) of water and pour it into the water bot-tle. Next, we break our dry ice into small pieces and measure one-eighth of a cup. We use pliers to transfer the pieces of dry ice into the balloon as a safety precaution. Then we put the mouth of the balloon over the opening of the water bottle so that it was air-tight. Af-ter the connection is completely sealed, we transfer the dry ice from the balloon into the water bottle.

The dry ice reacts with the water to form a vapor which flows into the empty balloon and causes it to inflate. After the dry ice is com-pletely evaporated, we then measure the circumference of the balloon.

From the circumference, we find the ra-dius, which we then use to find the total vol-ume change of the balloon. We also need to find the empty volume of the water bottle and add it to the balloon’s volume.

This number is the total amount of vapor formed from our reaction. The large volume of vapor compared to the small amount of dry ice demonstrates the properties of a phase change from a solid to a vapor.

3 RESULTS

Table 1: Results for trial 1. Initial conditions

Water 8 oz=0.2337 kg Dry Ice 0.75 oz Circumference of Balloon

0 cm

Volume of Air 251.95 cm3 Final conditions

Water 8 oz=0.2337 kg Dry Ice 0 oz of solid dry ice Circumference of Balloon

63 cm

Volume of Air + Gas

4465.92 cm3

Table 2: Results for trial 2. Initial conditions

Water 8 oz=0.2337 kg Dry Ice 1 oz Circumference of Balloon

0 cm

Volume of Air 251.95 cm3 Final conditions

Water 8 oz=0.2337 kg Dry Ice 0 oz of solid dry ice Circumference of Balloon

73 cm

Volume of Air + Gas

6821.21 cm3

The results we obtained from the experi-ment seem to be accurate when comparing the two trials. We use ¾ oz of dry ice in trial 1and 1 oz in trial 2 and the ratio between these and the final volume of the balloon were close. This means that we had very little error and could do the experiment many times and get the same results. We notice that the balloon takes a small amount of time to blow up. Once the dry ice is dropped in the water, the balloon immediately starts to inflate and it isn’t long after that all the dry ice has sublimated into vapor. The wa-ter and the system are much colder after the entire reaction is over. Figure 1. Watching reaction and measuring circumference. Team listed from left to right: Prissy Pepper, Heather Bowdre, Jim Honea. Photo taken by Amanda Blackburn

37

4 DISCUSSION

We use the ideal gas law to find the analytical results. The temperature and pressure are looked at as constants. With those being con-stant we have the equation V1/m1=V2/m2. The initial mass is the weight of the initial air in the bottle and the final mass is the initial mass plus the mass of the dry ice. We use the vol-ume of the air and the density of air to find its initial mass. We perform the same procedure to find the mass of the dry ice.

We then input our values into the ideal gas law equation from both our trials. This gives us values for V2 that are about twice our measured values. For the first trial the meas-ured value for V2 is 4465.92 cm3 and the de-rived value from the ideal gas law is 8100.86 cm3. The second trial gives us 6821.21 cm3 for the measured and 11028.5 cm3 for the de-rived.

This huge difference in our values is be-cause of the balloons elasticity. In our equa-tion we assume that pressure is constant, but in fact there will be a pressure change because the balloon resists some of the air from ex-panding as much as it can. If the balloon has no elasticity then the measured values will be equal to the derived values.

Figure 2.

5 SUMMARY AND CONCLUSIONS

Our experiment was a success. We did not have a large variation from trial to trial. We

learned that only in world with no friction or resistance could we have made the pressure constant. We set out to find out about the flow from a solid to a gas and what a differ-ence in volume it would be and in the end we learned so much more. The elasticity of the balloon played a big factor in comparing our measured results to the results we derived from the ideal gas law.

REFERENCES

How Stuff Works. 15 Nov. 2003 <http://science.howstuffworks.com >.

Baker, White, Tash. Fundamentals of

Chemistry. New York City: Thompson, 1986.

38

39

1 INRODUCTION

Have you ever wondered why you couldn’t stop that runaway hot air balloon? Thermo-dynamic laws and principles govern the be-havior of hot air balloons. By heating and re-leasing air, the pilot is able to control the altitude and path of the balloon (travel.howstuffworks.com/hot-air-balloon1). Our experiment will show how one can use thermodynamic principles to control the den-sity of the air and as a result, control the be-havior of a hot air balloon. We will be con-ducting an experiment that approximates properties of gases, specifically air, using the ideal gas Law and Archimedes Principle. In our experiment we will be using household items such as a balloon, five gallon metal bucket, water, thermometer and a meter stick. However, if we were to conduct this experi-ment in a laboratory setting we would use a thermocouple to measure temperature, a pres-sure transducer to measure the pressure, and a

calibrated piston cylinder device to measure volume.

Thermocouples are inexpensive devices used to measure temperature accurately and easily. These devices consist of two wires of different materials joined at a point. When there is a temperature change at that point, a current is produced. By measuring the volt-age across these wires, it is possible to deter-mine the temperature at that point (Coyne, 1992).

Pressure transducers use silicon dia-phragms with resistive strain gauges fixed into it a back plate to measure pressure (www.sensorland.com). The piezoresistive strain gauges measure the force applied to them by causing a resistance change. This change is then used to determine the pressure.

A calibrated piston cylinder device is used to measure the volume of air at a given pres-sure and temperature. Measuring the height of the piston and knowing the area of the cyl-inder allows one to calibrate this device.

Project 8: Ideal Expansion of Air

R.R. Bohacek, M.R. Gonzalez, C.J. Hoelscher, E.A. Reed Engineering 212-503: Group #8

ABSTRACT: This report describes the design, construction, results and analysis of a thermody-namic experiment for the ideal expansion of air. We will be using household items such as a balloon, five gallon bucket, water, a meter stick and a thermometer to conduct our experiment. To conduct this experiment, fill three balloons with air at room temperature, using an air pump, and measure the circumference of the balloon. Fill the five gallon bucket with hot water and submerge the balloons, allowing them to expand. Measure the circumference of the heated bal-loons. Now fill the bucket with cold water and submerge the balloons allowing them to contract. Measure the circumference. You can now find the volume of the balloons by assuming the bal-loons to be spherical, and using the circumference. The method used for this experiment con-tained substantial error. The experimental calculations deviated greatly from the analytical cal-culations.

40

The remainder of this document explains in further detail the methods and results of our experiment. The Methods section describes our experiment and the guidelines for its completion. The Results section summarizes our findings from our experiment. The Dis-cussion section provides a comparison of the results to a simple theoretical analysis. The final section, Summary and Conclusions, pro-vides an overview of the experiment and our findings.

2 METHODS

To conduct the experiment, first gather the needed materials: a meter stick, a thermome-ter, a five-gallon bucket, a pulley, string, a permanent marker, a bicycle pump, and bal-loons. After gathering the materials, the appa-ratus must be assembled. The steps to assem-ble the apparatus are as follows. Begin by marking the five-gallon bucket in the desired length increments (centimeters in our case). Next, glue the pulley to the bottom-center of the bucket. After the glue dries, run the string through the pulley.

Now that the apparatus is assembled, it is time to fill the bucket approximately three-quarters of its capacity with water at room temperature. Measure this temperature by us-ing a household-cooking thermometer. Fill the balloon approximately to the size of a tennis ball with air using the bicycle pump. Tie the balloon to the string that runs through the pul-ley. Prior to submerging the balloon, take note of the water level in the bucket. Sub-merge the balloon in the water by pulling the string on the opposite end of the pulley until the balloon reaches the pulley. Measure the displacement of the water by recording the new water level using the calibrated bucket. Determine the volume of the balloon by cal-culating the cross-sectional area of the bucket and multiplying it by the displacement of the water previously recorded. Next, the pressure of the water on the balloon must be accounted for. Begin by calculating the density of water at the current temperature and atmospheric pressure of water, by using water saturation tables. Using the density found, the depth of the balloon in the water, and the gravitational constant, calculate the gauge pressure of the

water on the balloon. Use this to find the ab-solute pressure by summing the atmospheric pressure and the calculated gauge pressure. Use the Ideal Gas Law to find the mass and to find the density of the air, divide this mass calculated by the volume the balloon. Repeat the above steps using water close to freezing temperature. Instead of having the balloon at room temperature, cool the air in-side the balloon by inserting the balloon into a freezer. Create the freezing water by cooling with ice without adding water. Repeat the steps outlined in the first para-graph using water close to the boiling point. Instead of having the balloon at room temperature, heat the inside air by holding it over boiling water. Create the hot water by replacing the water with an equal amount of water close to the boiling temperature. Repeat this experiment using new balloons at least two more times to compare the results. The data will then be analyzed using statisti-cal means by calculating the average volume, the average temperature, and the average pressure. This is done in order to reduce er-ror.

3 RESULTS

Upon conducting the experiment, the follow-ing data describes our findings. HOT (74˚ C)

BalloonString Length r Volume

0 0.38 0.0605 0.000927 1 0.37 0.0589 0.000855 2 0.37 0.0589 0.000855

ROOM TEMP (20˚ C)

BalloonString Length r Volume

0 0.325 0.0517 0.000580 1 0.355 0.0565 0.000756 2 0.33 0.0525 0.000607

COLD (3.5˚ C)

BalloonString Length r Volume

0 0.31 0.0493 0.000503 1 0.34 0.0541 0.000664 2 0.315 0.0501 0.000528

41

For each balloon we calculated the above data. We had three experimental runs and each run had a different mass value. For bal-loon #0, we found a total change in circum-ference from cold to hot was .07 m. For bal-loon #1, we had a total change in circumference of .03 m and for balloon #2 a total change of .055 m. We used the respec-tive circumferences to calculate the radius and finally the volume. We used the volumes and calculated the following ratios. Balloon 0 V(hot)/V(cold) = 1.84 V(room)/V(cold) = 1.15 V(cold)/V(cold) = 1.00 Balloon 1 V(hot)/V(cold) = 1.29 V(room)/V(cold) = 1.14 V(cold)/V(cold) = 1.00 Balloon 2 V(hot)/V(cold) = 1.62 V(room)/V(cold) = 1.15 V(cold)/V(cold) = 1.00

3.1 Analytical specific volumes We also calculated the analytical specific vol-umes using the Ideal Gas Law. We calculated the same ratios and compared them to those found with our volumes. We used this com-parison to calculate our error values. Calculated Values v(hot)/v(cold) = 1.25 v(room)/v(cold) = 1.06 v(cold)/v(cold) = 1.00

3.2 Error Values Balloon 0 V(hot)/V(cold) = 46.8 V(room)/V(cold) = 8.74 V(cold)/V(cold) = 0.00 Balloon 1 V(hot)/V(cold) = 2.69

V(room)/V(cold) = 7.42 V(cold)/V(cold) = 0.00 Balloon 2 V(hot)/V(cold) = 29.1 V(room)/V(cold) = 8.50 V(cold)/V(cold) = 0.00

4 DISCUSSION

Upon conducting the experiment described in the methods section we encountered one main obstacle, the mounting of the pulley to the bottom of the bucket. The glue we used did not fasten the pulley securely enough to counter the buoyancy force exerted by the wa-ter. In order to alleviate this problem we had to make the following adaptations to the ex-periment. Instead of measuring the displace-ment of water to find the volume of the bal-loon, we measured the circumference of the balloon instead. Since we didn’t use a pulley system, we filled a bucket with water at different tem-peratures. We then placed the balloons into the buckets and allowed time for shrinking and expanding. We measured the circumfer-ence as stated above. We used the circumfer-ence values to calculate the volume enclosed in each balloon.

To solve this problem analytically, we used the Ideal Gas Law (Pv = RT). Knowing that the pressure on the balloon is atmospheric pressure, and the experimental temperature we were able to calculate the specific volume of each balloon. We found that the specific vol-ume for the hot temperature (74.0 °C) was 0.986 m3/kg, for room temperature (20.0 °C) it was 0.833 m3/kg, and for the cold tempera-ture (3.5 °C) 0.786 m3/kg.

We compared our experimental volumes against our calculated specific volumes, knowing that the ratio of volumes is equal to the ratio of specific volumes for any given balloon (V=mv, assuming mass remains con-stant).

Using this comparison method we found that our method has high error. This error is partly due to inaccuracies in measuring the temperature, the inability to control heat trans-fer during measuring, the balloons not being perfect spheres. However, the error is mainly

42

Figure 1: Line regressions for analytical ver-sus experimental data. Typical error bars are showed for each balloon.

due to the pressure of the balloon not equaling the atmospheric pressure. Therefore, the elas-ticity of the balloon makes the pressure of the balloon greater than the atmospheric pressure, causing a volume less than previously pre-dicted.

The points on this graph represent the change in volume ratios of the balloons as the temperature varies. The graphs were con-structed using combinations of ratios of vol-umes at hot, cold and room temperatures. The solid line in the graph represents our calcu-lated ratios of volume. Comparing this line to the others produced by the experiment, we can tell that Balloon 0 had the highest error because of its deviation from the calculated line. Balloon 1, however, straddled this line and therefore experienced the least amount of error. This graph describes our ultimate hypothe-sis that temperature affects volume. The data shows as temperature increases so does spe-cific volume. The relationship is a linear one as seen in the above graph.

5 SUMMARY AND CONCLUSIONS

Had the original method been used, the calcu-lations would have been more accurate. Hav-ing to change the method midstream caused great deviations from the analytical data. The

goal of the experiment was to find a relation-ship between temperature and volume (or specific volume). It was found that as tem-perature increases, so does volume. This con-firms the Ideal Gas Law.

The experiment concluded as air is heated the density decreases. In order to have a more accurate calculation or relationship, controls for measuring temperature and volume must be taken into account. The rate of heat trans-fer must also be better controlled. More accu-rate values can be obtained by using our ideal measurement tools as described earlier. REFERENCES

Coyne, G.S. (1992). The laboratory hand-book of materials, equipment, and tech-nique. 137.

Harris, T.

http://travel.howstuffworks.com/hot-air-balloon1.htm.

www.sensorland.com/HowPage004.html.

Ideal Gas Volumetric Ratio

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 20 40 60 80Temperature (C)

V / V

c Balloon 0

Balloon 1

Balloon 2

Calculated

43

1 INRODUCTION

A manometer is a commonly used device to measure the pressure differences of fluids. This obviously does not include the difference in pressure on thermodynamics students be-fore and after their tests. Actually, a ma-nometer typically consists of a glass or plastic U-tube containing one or more fluids (Cengel 51) attached to an open or closed container, never students. Knowing the atmospheric pressure and the densities of the fluids in the manometer, one can deduce the pressure of the fluid in the container by measuring the height differences of each fluid within the tube. An experiment will be set up using a plastic 2-liter bottle, 60-80 cm of 1-2 cm di-ameter plastic tubing, and various fluids. The pressure differences will be measured with the cap on and off of the bottle, thus as an open or closed system. Measurements will also be taken while utilizing different fluids, such as water, air, alcohol, and oil to evaluate the credibility of the experiment. This will serve to illustrate the basic principles of a manome-ter.

The principle of the manometer has been used for centuries in ship building, and even earlier by the Romans in the construction of their aqueducts (mooreandtaber). These tech-niques were done with an open manometer to measure differences in elevation, like a level. Because of its long history, no one really knows who invented it. Current uses incorpo-rate manometers to measure pressures in wind and water tunnels.

Manometers employ the use of Pascal’s law, which allows one to “jump” from one fluid column to the next in manometers with-out worrying about pressure change as long as we don’t jump over a different fluid, and the fluid is at rest (Cengel 52). This principle is what makes the manometer a useful tool. It allows one to determine pressure differences.

Laboratory experiments differ little from the intended experiment described in this pa-per. They involve a closed container or open duct (fluid in a pipe, or air in a wind tunnel) with an attached U-shaped tube where a fluid rests. The height difference of the fluid on opposing sides of the tube is measured accu-rately and interpreted to determine the pres-sure difference. Often liquid mercury is used

Project 9: Engineering 212-503 Group Project: Manometer Experiment using Water and Air

Z. Bujnoch, D. McElligott, K. Neidzwecki & H. Palmer Dwight Look College of Engineering, Texas A&M University, College Station, USA

ABSTRACT: A manometer is a helpful instrument when measuring the pressures of liquids and gases. This is an example of such an experiment using air and water and the data produced from it. This experiment includes common household materials that can be constructed into a simple manometer. Although this experiment only calculated the pressure in two environments (in a cooler and in boiling water) it is up to the creativity of the experimenter to find different environments to calculate more pressures of the air using the equation and methods described.

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because of its high density. Open manome-ters are still used as levels today.

The analysis of this experiment is broken into five sections. The methods section de-scribes the methods used to execute the ex-periment, involving how to assemble the ma-nometer, how measurements were conducted, and the process used to make these measure-ments. The results section focuses on the re-sults accumulated during the experiment and other important observations. This section re-ports the raw data. The fourth section will be the discussion. This includes the team’s in-terpretation of the resulting data as compared to an analytical solution. The final section summarizes the significant points and conclu-sions drawn in previous sections, finalizing the experiment.

To assemble an apparatus, a 2-liter soft drink bottle, a 2-3 ft. long 1 cm diameter plas-tic tube, a metal coat hanger, tape, and epoxy are needed. A hole was drilled in the plastic bottle toward its bottom end somewhat bigger than the diameter of the plastic tube and the tube was placed in the hole. Epoxy was util-ized to secure the tube in place, making sure that it was air tight. Next, the tube was bent so it created two u-shapes (one upside down and the other right side up) with the end of the tube facing upwards. A coat hanger was bent in the same shape as the tube and taped to it for reinforcement.

2 METHODS

The measurements are conducted by modify-ing the apparatus’s temperature. The original level of the water in the u-tube is marked for later reference. The makeshift manometer is placed partially in an ice chest for 20 minutes to cool the air-filled 2-liter bottle while the u-tube remained outside. The change in the wa-ter level is then measured with a shatter resis-tant ruler. Once the water level returns to its original state, the 2-liter bottle is placed in a pot of boiling water. After the water shot out of the u-tube like a geyser, the pot was taken off the burner and the u-tube was refilled. The bottle was again placed in the pot and the water level change was measured after 1 min-ute.

After constructing the manometer and par-tially filling the tubing with water, measure-ments were taken. The height changes of the tap water were measured. The density of air and water now became necessary. The gravi-tational effects on the air and the cross sec-tional area of the tubing are negligible. The equation used was P= Patm + ρgh. The vari-able P is the unknown pressure in the bottle. The variable Patm is the atmospheric pressure of the latent air. The variable ρ is equal to the density of the tap water, known to be 1 kg/L. The variable g is defined as the gravitational acceleration constant, known to be 9.8 m/s2. The variable h is the height of the liquid, which was measured in the experiment. All of the variables are either known or measured. This equation for the pressure is now solv-able.

The data measured from this experiment, i.e. the height values, will be entered into an Excel table including the gravitational, den-sity, and atmospheric pressure constants. A formula based on the equation, P= Patm + ρgh, will exploit the data and provide the pressure, thus solving the unknown, and the problem.

3 RESULTS In our experiment the heights are initially 0 at room temperature. In the cold temperature setting our height in our open air tube dropped about 4 cm, and the measured temperature in our bottle was 298.2 K. In the hot tempera-ture setting our height in our open air tube rose about 5 cm, and the measured tempera-ture in our bottle was 301.0 K. Our measured room temperature is recorded as 299.2 K. Knowing the densities of air and water, the acceleration due to gravity on earth, and the ideal gas constant, R, the following was calcu-lated:

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Table 1. Data and Calculations.

Measured Data

Calculated Pressures

Tempera-ture (K)

Height Change

(cm)

Ideal Gas

(kPa)

Mano- meter (kPa)

room 299.2 0 101.3 101.3 cold 298.2 -4 100.7 100.9 hot 301.0 5 101.6 101.8

Figure 1. Pressure Comparison of Ideal Gas Law and manometer technique.

4 DISCUSSION

The results of the experiment were calcu-lated both with measurements taken and using the ideal gas law as an analytical comparison. The pressure in the bottle differed very little between the two methods. Using the ideal gas law, the pressure in the bottle was found to be 101.6 kPa hot and 100.7 kPa cold. The pres-sure at room temperature was 101.3 kPa. Us-ing our height change measurements and the equation P=ρg(∆h), the pressures calculated were virtually identical with a difference of only 0.2 kPa. This could be a coincidence as the analytical ideal gas law pressures were based on temperatures measured. This could harbor a margin of error, much like the height change measurements. However, the results appear to be reasonable because they rein-forced what is known about the pressure dif-ferences concerning colder and warmer tem-peratures.

5 CONCLUSIONS

By constructing a very simple version of the manometer experiment unknown pres-sures were easily calculated using the gravita-tional and atmospheric pressure constants, and measuring the height changes. We used our apparatus to conduct the experiment and then collected data for our computations. We con-cluded what we already knew before; that the pressure of colder air is less than that of warmer air. We proved this because the pres-sure in the bottle was greater than the atmos-pheric pressure then caused the water in the manometer to rise and vice versa. If we so desired we can continue this experiment with a longer tube and therefore we could try a broader range of temperatures.

REFRENCES

Çengel, Yunus A. and Robert H. Turner, Fundamentals of Thermal-Fluid Sci-ences, McGraw Hill, 2001

http://www.mooreandtaber.com/manometer.htm

100100.2100.4100.6100.8

101101.2101.4101.6101.8

102

Pc Po Ph

P (k

Pa)

Pressure (IGL) Pressure (M)

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1 INTRODUCTION

Engineering is an area of study that is essential to numerous other fields of study. Astronomy can be taken as an example. We would not be able to explore space without spacecraft or high power telescopes, and engineering plays a major role in the production of both. Electricity from power plants, which we use every day of our lives, would not exist without the help from engineering. Even our cars and roads, which we use each day to get to work, would not exist without the presence of engineering. Obviously engineering is important to many aspects of our lives, but today we are just going to use it to increase our knowledge of a nutrient called agar. Agar is popular in most scientific labs and is used as a base for bacterial culture media and also as a stabilizer and thickener in many types of food. Our group plans on evaluating the phase change of liquid agar to solid agar, in order to evaluate certain properties.

Our research is comprised of two parts, the first being the focus on agar, and what information is available on this nutrient. The second part of our research, although limited, focuses on chemistry and thermodynamics so

that we can prove that temperature remains constant during a phase change.

No previous experiments can be found that have been documented on this study.

Agar is derived from red seaweed (Cayce 2003). It is popular settings because it solidifies at a warmer temperature unlike other substances such as water. Agar solidifies at 32-43°C, providing a warmer environment for bacteria to thrive in (Seltmic 2003). Agar is also used in the production of food. It is a thickening agent for many types of sauces and soups. It is also used in the production of toothpaste, cosmetics, and candy. (Cayce 2003)

2 METHODS

The purpose of the experiment is to find the solidifying point of agar. Agar is grounded red seaweed used in common things such as plates and some gelatin products. The equipment we are going to use in the experiment are as follows: 1 mercury thermometer, 1 1-liter milk jug, 1 1-liter beaker, Difco Granulated Agar, dionized water, 1 stop watch, 1 autoclave, 1 graduated cylinder. To start the experiment we had to

Project 10: Agar solutions

J. Carter, S. Clifford, K. Golden, D. Garza & C.Young Group 10 Texas A&M College Station, TX 77840

ABSTRACT: In our project we evaluated that during a phase change temperature remains constant. Using an agar solution, we observed the temperature change from liquid agar to solid agar. In conclusion we proved that temperature remains a constant 37°C during a phase change and found the solidifying point of agar.

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first prepare the solution. Mix 10 grams of agar and 500 mL of dionized water into a milk jug. After that put it in autoclave for 30 minutes at 20 psi and 120 degrees C and then

put it in a hot bath until it cools to around 60 degrees C. Next step is to find the solidifying point of agar. Using a stopwatch, measure the temperature of the solution every minute until the agar solution begins solidifying. The final step is to organize the data. First place the values into a spreadsheet, then compare the group results to the results found on the website. Next, calculate the heat lost and the specific heat. Lastly, show the graphs of the experiment results.

3 RESULTS

In our experiment we analyzed the solidifying point of agar and also observed the temperature change of cooling agar solution. The purpose we were trying to prove is that during a phase change the temperature will remain constant. To minimize errors, the experiment was performed twice.

In both experiments solid crystals were first seen at 37°C. After this point, the temperature remained constant until the entire solution had solidified. When the solution had finished solidifying, the temperature began decreasing again. Since both experiments had the same results, our group concluded that temperature remains constant through a phase change. We also were able to find that at a 2% solution, the agar solidified at 37°C. Below are the graphs that were derived from both of the experiments. The entire process took about 85-95 minutes to occur.

4 DISCUSSION

Before performing the experiment our team had certain expectations of what we thought would occur. First, we expected the agar solution to solidify between 32 °C and 43 °C, as our research of this substance predicted. We also expected to prove that the temperature would remain constant during a phase change. The reason we felt this would occur is because as the agar solution is cooled and allowed to solidify, energy is released from the bonds that are formed as agar molecules become incorporated into the solid agar latticework. This released energy holds the temperature constant until the entire liquid agar has been solidified. Finally, we expected that the entire process for solidification from a temperature of 65 °C would take a little less than an hour. We based this conclusion upon research we conducted about the properties of the substance agar.

In our experiment the agar solution began to solidify at 37 °C and remained at that temperature until all of the solution was a solid. The entire solidification process from 60 °C to 37 °C took about 85-95 minutes to occur.

Our experimental results mirrored what our team initially predicted would happen with little deviation and few surprises. However, we did have difficulty measuring the overall temperature of the substance. We found that as the agar began to cool it solidified in different places in the beaker causing the temperature to differ at various locations in the solution. To solve this problem we stirred

Experiment 2

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the solution every so often to distribute an even temperature throughout the agar. While this may have helped our temperature readings to be more accurate it also may have altered our results slightly because it helped the solution to release heat into the atmosphere, allowing it to cool faster.

After the experiment we realized that there were several other variations that could have been performed which may have obtained different results. For instance, we used a 1000 mL plastic beaker, which caused the agar solution to take longer to solidify because less of its surface area was open to the cooler atmosphere. To compensate, the solution was stirred. To help minimize the effects that these variations would have on our results, two experiments were performed—the first with stirring and second without. Both experiments yielded close to the same results. More experiments could have been performed to obtain even more results, however the preparation time for the agar solution is about two hours and our team had difficulty meeting to perform the experiment a third time.

5 SUMMARY & CONCLUSION

The point of this experiment was to find the solidifying points of agar. In order for us to begin this experiment a wide range of equipment was needed. Some of the equipment used included a stopwatch, thermometer, a sample of the agar solution, and an autoclave. Once everything was in order, we conducted our experiment and recorded the results. Taking into account that there could have been some minor errors, we still believe that our experiment was a success. The research we did before beginning this experiment stated that the agar solution should solidify between 32 – 42 degrees Celsius. Our results proved that our research was correct. When conducting this experiment we expected that the temperature would remain constant during phase changes. The results also verified these expectations to be legitimate.

As this experiment came to a conclusion, we determined that finding the solidifying points of the agar solutions was the most important aspect of this experiment. These points are very beneficial in the sense that they are very helpful for various laboratory purposes and other experiments. From an engineering perspective, we determined that finding the temperature to be constant during a phase change is most important, since it is essential information when dealing with any type of phase change. From this experiment we were able to connect the basis of what we have learned in engineering to a part of biology.

REFERENCES

Cayce, Edgar. “Agar”. 11 November 2003.

Meridian Institute. 11 November 2003 http://www.meridianinstitute.com/echerb/Files/1agar.html

Seltmic. “Algogel”. 11 November 2003 http://www.seltmc.com/produits/english/algogel/algogel_eng.htm

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51

1 INTRODUCTION

The technology and the science of heat began to develop in the first half of the eighteenth century because it became clear that heat could be used to do useful work. The only available means to do significant work at the time was through men, horses, wind, or fal-ling water. Theoretical ideas, which were clearly formulated by the end of the century, began to develop before 1750.

The two most important of these principles were the suggestion that heat might be con-served and there is a distinction between the amount of heat and quality of heat. Quality of heat is what we now call temperature (Did You Know 2003). In our experiment, we measure the time it takes for water to change from one temperature to another in order to show the conservation of heat in a phase change.

The kinds of laboratory measurements for the project we chose can be measured with the

use of a calorimeter. There are many types of calorimeters used in Calorimetry, but for our case the most suitable would be a Liquid (or Mixing) Calorimeter (Fig. 1), for which its main application is for the determination of heat capacities. Here the calorimeter liquid fills a vessel, which is thermally insulated from the surrounding as thoroughly as possi-ble.

For most cases water is the best medium for measurements in room temperature range (Hemminger and Hohne 1984). Similar to our project, a sample liquid, with some tempera-ture T1 is introduced to the calorimeter liquid that initially holds some temperature of TO. Once the mixture reaches an equilibrium tem-perature of TM, the balance of exchanged heat can be formulated as follows: Equation 1: C1 . m1 . (T1 – TM) = C2

. m2 . (TM –

TO)

where all temperatures are measured with an alcohol or mercury thermometer. The vari-

Project 11: Latent Heat of Fusion of Water Experiment

V.S Cuellar, J.M. Gustafson, J.M Juarez & H. Luna College of Engineering, Texas A&M University, College Station, USA

ABSTRACT: BRRRR !!! It’s cold!! For this project, our team worked together to design, construct, conduct, and analyze the time it takes for water to change from one temperature to another in order to show the conservation of heat principle in which thermodynamics is related. We were able to utilize household materials such as a kitchen sink, an alcohol thermometer, ice, and water. Four separate tri-als were executed; the temperature differences found did not match the computed results, for example in trial 1 the final temperature was 21.62 oC, where the experimental data was 17.5oC. The experi-mental values found were compared to computational values achieved with thermodynamics princi-ples our group has encountered. Differences in the data are accounted for by some errors, such as the mass of the water in the sink, and the water temperature may not have been evenly distributed throughout the sink. Despite the fact that none of the experimental final temperatures are identical to the computational values they are considered to be reliable.

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Figure 1: Calorimeter, Hemminger, Wolfgang and Gunther Hohne. Calorimetry: Fundamen-tal and Practice. Weinheim: Verlang Chemi GmbH, 1984. 170-172.

ables and subscripts are noted as C1 being the specific heat capacity of the sample liquid, m1 the sample mass, T1 the initial temperature of the sample, TM the temperature of the calo-rimeter liquid after mixing, C2 the specific heat capacity of the calorimeter liquid, m2 the mass of the calorimeter liquid, and TO the ini-tial temperature of the calorimeter liquid (Hemminger and Hohne 1984).

Another familiar apparatus that is used in laboratory to aid in calorimetric measure-ments is known as a burette (Fig. 2). A bu-rette is an apparatus used for delivering meas-ured quantities of liquid or for measuring the quantity of liquid or gas received or dis-charged.

It consists essentially of a graduated glass tube, usually furnished with a small aperture and stopcock (Coblentz and Vorisek 1912). The glass tubes of uniform caliber are narrow at one end and the straight part of the tube is divided into cubic centimeters with subdivi-sions of fifths or tenths. For our particular experiment, the use of a burette or a similar device will help to accurately dispense and measure the sample fluid.

The following will briefly outline where each portion of the experiment and related in-formation may be found. The Introduction has served to review which project was cho-sen and how it should be performed profes-

sionally. Information on how the group per-formed the experiment without access to a professional lab can be found in the Methods section. The Results section contains the number of trials as well as the collected data from these trials. Data Tables may be found for all trials in Appendix A. Also in the Re-sults section, graphical representations of the data sets are located. Computations derived from thermodynamic formulas are compared with measured and calculated data from the experiment in the Discussion section. Error analysis and proposal of mistakes in experi-ment conduction may also be found in this section. The Summary and Conclusion sec-tion represents two parts. The Summary will reiterate all the significant aspects of the above Results and Discussion sections. The Conclusion presents all conclusions the group has attained from combining knowledge of thermodynamic principles and accumulated experimental data from research. The Ac-knowledgements and References sections give credit to all professional sources that assisted with this project. The Appendices provide data for the basis of the Results, Discussion, and Conclusion.

Figure 2: Burette (www.pelletlab.com/glassware.html) 2 METHODS This detailed procedure description is neces-sary to perform the experiment. In order to achieve the results desired these procedural steps must be followed precisely. They are as follows:

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1. Determine which unknown variable to ob-tain data for in the experiment.

2. Assemble all required apparatus: one rec-tangular sink, one water source, 12 pounds of ice, one small thermometer with degree range between at least 15 and 30oC, one tape measure, and one stopwatch.

3. Then, fill the sink with water. 4. Using a tape measure, measure the area of

the sink containing water. This value will be used in later computations to determine the mass of the water.

5. With the thermometer, measure the room temperature and wait until the water in the sink reaches room temperature.

6. Take an initial temperature reading of wa-ter at room temperature. This value corre-lates with the 0 time value in the data set.

7. For experiment Trials 1 and 2, we use a set ice mass of 2 1/3 pounds. For experi-ment Trials 3 and 4, we use a set ice mass of 3 ½ pounds.

8. The following procedures are for Trials 1 and 2. Trials 3 and 4 follow with indica-tion.

9. Place 2 1/3 pounds of ice and the thermometer into the sink. At the same time, start the stopwatch.

10. At that point we measure and record the temperature inside the sink every minute (1). Do not remove the thermometer nor stir the ice and water mixture.

11. We continue measuring at the minute in-terval until the instant all ice has melted in the mixture.

12. Drain approximately 1 to 2 inches of wa-ter out of the sink. Add water that is warmer than room temperature to the sink until the original area recorded in the sink is obtained.

13. Repeat steps 5 through 11 for Trial 2. 14. Drain approximately 1 to 2 inches of wa-

ter out of the sink. Add water that is warmer than room temperature to the sink until the original area recorded in the sink is obtained.

15. The following steps are for Trial 3 and 4. 16. Wait until the water in the sink reaches

room temperature.

17. Take an initial temperature reading of wa-ter at room temperature. This value corre-lates with the 0 time value in the data set.

18. Place 3 ½ pounds of ice and the ther-mometer into the sink. At the same time, start the stopwatch.

19. At that point we measure and record the temperature inside the sink every minute (1). Do not remove the thermometer nor stir the ice and water mixture.

20. We continue measuring at the minute in-terval until the instant all ice has melted in the mixture.

21. Drain approximately 1 to 2 inches of wa-ter out of the sink. Add water that is warmer than room temperature to the sink until the original area recorded in the sink is obtained.

22. Repeat steps 16 through 20 for Trial 4. 23. Drain the sink and dry off apparatus.

3 RESULTS

Four separate trials were performed. All vari-ables in the experiment were held constant except for the mass of ice added to the sink of water. What follows are the recorded experi-mental values for the four trials outlined in the above Methods section.

3.1 Trials 1 and 2 – 2 1/3 pounds of ice

The initial temperature value for Trial 1 was 27oC. It took seven minutes for the ice mass to completely melt in the ice and water mix-ture. The mixture reached the minimum tem-perature of 17oC. However, this was not the final temperature. In the last minute of the experiment, the mixture’s temperature rose ½ a degree. For Trial 2, the initial temperature was 25oC. The final temperature of 14oC was reached after eleven minutes. Unlike Trial 1, the final temperature was the minimum tem-perature of the mixture. Table 1 displays all interval temperature recordings for both Trial 1 and Trial 2.

Table 1: Experiment conducted with 2 1/3 pounds ice

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Trial 1 Trial 2

Time (min.)

Temp. (oC )

Temp. (oC )

0 27 25 1 22 19.5 2 19 18 3 18 17 4 17 16.5 5 17 15.5 6 17 15 7 17.5 15 8 - 14.5 9 - 14.5 10 - 14.5 11 - 14

3.2 Trials 3 and 4 – 3 ½ pounds of ice

Trial 3 and 4 used a larger mass of ice while maintaining the same area and mass of water as well as starting at room temperature. Trial 3 had an initial temperature of 26oC and it took thirteen minutes to completely melt the ice mass. The minimum temperature recorded during this trial was 11oC.

Trial 4 began at a slightly lower tempera-ture of 25oC and reached a minimum tempera-ture of 10oC. The ice mass in Trial 4 lasted 18.5 minutes. Figure 3 is a graphical repre-sentation of Trial 3 and Trial 4.

Figure 3: Graph of Temperature versus Time for Trial 3 and Trial 4.

Data Tables for all trials as well as corre-sponding Temperature versus Time graphs for the experiment can be found in Appendix A.

4 DISCUSSION

The experiment performed resulted in finding a final temperature in each trial. These ex-perimental values can be compared to compu-tational values using thermodynamic princi-ples and formulas.

4.1 Thermodynamic Formula and Constants

Latent heat of fusion is a constant value equal to the amount of energy released during freez-ing; therefore, it would also be equivalent to the energy absorbed during a melting phase (Cengel and Turner 2001). Latent heat of fu-sion for water (Lice) can be combined with the masses of different phases, in a thermody-namic equation that includes mass of ice, mass of water (mice and mwater), specific heat (Cwater ) and temperature. The equation is as follows:

Equation 2: mwater * Cwater * ( Tf – Ti ) = - mice * Lice

The constants Lice and Cwater are 333.7 KJ/ kg and 4.23 KJ / kg oC respectively. (Cengel and Turner 2001). Knowing the values of both the mass of ice, mass of water, and the initial temperature, the final temperature can be derived from the above equation.

4.2 Derivation of Remaining Variables

Assuming the sink to be rectangular, the mass of water is obtained. By multiplying the area of the water in the sink and water density, the equation provides the unsolved variable. Mass of the ice in the SI system requires a ba-sic conversion factor.

4.3 Computational versus Experimental Fi-nal Temperature

Utilizing the measured values from each trial of the experiment and some researched con-stants, a computational value of final tempera-ture is supplied for each separate trial.

M e ltin g 3 .5 lb s o f Ic e in 1 5 .7 0 k g o f W a te r

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T im e (m in u te s )

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4.3.1 Trial 1 and 2

The final temperature value recorded experi-mentally for Trial 1 was 17.5oC. The compu-tational value for the same trial was 21.62 oC. The computational value is larger than the ex-perimental value by a difference of 4.12 oC, which demonstrations experimental error.

Trial 2 was repeated to verify the results in Trial 1. Trial 2 experimentally achieved a fi-nal temperature of 14 oC. The computational value obtained is 19.62 oC. Comparing the computational value to the experimental value, a difference is reported of 5.62 oC. Both the initial and final temperatures ex-perimentally are higher for Trial 1.

4.3.2 Trial 3 and 4

Trial 3 had a final temperature value of 11.1

oC in the experiment, where the computed value is 17.93 oC. Again the computational value is larger than the experimental by 6.83

oC. Trial 4 repeated the procedure of Trial 3. The experimental final temperature docu-mented for the trial is 10.5 oC. The computa-tional value solved is 16.93 oC. Evaluating the computational and experimental value a difference is shown of 6.43 oC. Both the ini-tial and final temperatures measured are higher for Trial 3.

4.4 Explanation

None of the experimental final temperatures are identical to the computational values. However, the experimental values can be con-sidered reliable. Trial 3 and Trial 4 had initial temperatures only 1 degree apart. The differ-ence between the computational and experi-mental final temperatures for these two trials is less than five tenths. This exhibits that the trials were performed consistently and the ex-perimental data from Trial 3 was reliably re-produced in Trial 4.

Trial 1 and Trial 2 had a slightly larger di-vergence between the differences of the com-putational and experimental value (Fig. 4). However, if you modify the data set from Trial 2 to start at the same initial temperature

as Trial 1, Trial 1 and the Modified Trial 2 are similar in value (Fig. 5).

Figure 4: Trial 1 and Trial 2 without modifi-cation

Figure 5: Trial 1 and Modified Trial 2

Differences in the computational and ex-

perimental data may be accounted for by four events: Some trials took longer than others even when using the same ice mass, mass of the water in each experiment was based on an assumption, mass of ice in each trial was measured without a high degree of accuracy,

Melting 2 1/3 lbs Ice in 15.70 kg of W ater

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and water temperature may not have been evenly distributed in the sink.

In the set of trials done with a small ice mass, Trial 1 took only half as long as Trial 2 to completely melt the ice. Also, Trial 4 took five minutes longer than Trial 3 to melt the larger ice mass. These differences in the time needed to perform the experiment may have slightly biased some of the experimental data.

The mass of water is found with the simple equation of multiplying area by density. To find the area of the water in each trial, the sink was assumed to be rectangular. The sink may have held more water than was assumed using the rectangular area. Also, for each subse-quent trial after Trial 1, the sink was refilled to a height of 4 inches. Subsequent heights my not have actually been exactly at 4 inches. If the area of the water is larger, then conse-quently the mass of the water would be larger. A larger mass of water would produce a smaller final temperature for each trial.

The ice was hard to weigh because it was irregularly shaped and time sensitive. The masses used in each trial may have been less than measured. Less mass than recorded may account for the difference in the trial time intervals. Also, if the mass of the ice is less, then per equation 2, the final temperature would be less.

Finally, the water and ice mixture was not stirred during any of the trials. This may have caused the water nearer the melting ice to be colder than other areas of the sink. Thus the temperature in the sink was not evenly dis-tributed. Also, the placement of the ther-mometer may have affected the results. The thermometer may have been placed in a colder region. Additionally, the experiment was not insulated and heat loss may have oc-curred.

Computations for all trials, as well as deri-vations of additional variables are located in Appendix C. Data sets for the modified Trial 2 and a comparison to Trial 1 can be located in Appendix B.

5 SUMMARY AND CONCLUSIONS

The latent heat of fusion is the amount of en-ergy absorbed during a melting phase and it is equivalent to the amount of energy released during freezing (Cengel and Turner 2001). This experiment measured the latent heat of fusion of water by measuring the water’s tem-perature before and after ice was added into the water.

After the experiment was complete a final temperature was recorded and the data was put into graphs and tables. The experimental values were compared to thermodynamics formulas and concepts, and resulted in that the values found were similar but not exact to the computational values. We realized that many variables could have accounted for the slight errors in the calculations.

What can be concluded from the experi-mental and computational data is the impor-tance of all or any assumptions during compu-tation. As stated in section 4.4, although consistent, our computational data differed from our experimental data.

Looking back at possible interferences, heat transfer from sink to water, temperature of the air surrounding under side of the sink, etc, are all restraints for accurate calculations and measurements. As needed for all other types of research, the experiment done for our pro-ject was important not only for measuring ac-tual temperatures, but to help determine what other assumptions may have been needed or ignored. ACKNOWLEDGEMENTS

The team is grateful to Jessica Juarez’s room-mates for use of their house to complete the experiment. We would also like to thank Dr. Socolofsky for providing the report template and guidance in the experiment.

REFERENCES

Cengel, Yunus A., and Robert H. Turner. Selected Material from Fundamentals of Thermal-Fluid Sciences. New York: McGraw-Hill, 2001. 74, 934.

Coblentz, Virgil and Anton Vorisek. A Manuel of Volumetric Analysis. Phila-

57

delphia: P. Blakiston’s Son & Co., 1912. 11-13.

Did You Know. 2003. Philadelphia In-struments & Controls Inc. 9 Nov. 2003 < http://www.philadelphiainstrument.com/facts.asp?index=2>

Hemminger, Wolfgang and Gunther Hohne. Calorimetry: Fundamental and Practice. Weinheim: Verlang Chemi GmbH, 1984. 170-172.

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APPENDIX A

Trial 1 Trial 2

Time ( min. ) Temp. ( *C ) Temp. ( *C )

0 27 25 1 22 19.5 2 19 18 3 18 17 4 17 16.5 5 17 15.5 6 17 15 7 17.5 15 8 - 14.5 9 - 14.5 10 - 14.5 11 - 14

Trial 3 Trial 4

Time (min.) Temp. (C) Temp. (C) 0 26 25 1 16.5 17 2 14 14.5 3 13 13 4 12 12.5 5 11.5 12 6 11.5 11.5 7 11.5 10.5 8 11 10.5 9 11 10 10 11 9.5 11 11 9.5 12 11 10 13 11.1 10 14 - 10 15 - 10 16 - 10 17 - 10.5 18 - 10.5

18.5 - 10.5

Melting X of Ice in X of Water

0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19

Time (minutes)

Tem

pera

ture

( C

)

Trial 3 Trial 4

Melting 2 1/3 lbs Ice in 15.70 kg of Water

0

5

10

15

20

25

30

1 3 5 7 9 11

Time (minutes )

Tem

pera

ture

( C

)

Trial 1 Trial 2

59

APPENDIX B

Trial 1 Trial 2 Modified Trial 2

Time (minutes)

Temp (*C)

Temp (*C)

Temp (*C)

0 27 25 27 1 22 19.5 21.06 2 19 18 19.44 3 18 17 18.36 4 17 16.5 17.82 5 17 15.5 16.74 6 17 15 16.2 7 17.5 15 16.2 8 - 14.5 15.66 9 - 14.5 15.66 10 - 14.5 15.66 11 - 14 15.12

Melting 2 1/3 lbs Ice in 15.70 kg of Water

05

1015202530

1 2 3 4 5 6 7 8 9 10 11 12

Time (minutes )

Tem

pera

ture

( C

)

Trial 1 Modified Trial 2

60

APPENDIX C Trial 1:

Area of sink = 15.5 * 15.5 * 4 = 961 in3

? kg = 961 in3 * 1 m3 * 997 kg = 15.70 kg

6.1024 x 104 in3 1 m3

? kg = 2 1/3 lb * 0.45359237 kg = 1.058 kg 1 lb

mwater = 15.70 kg mice = 1.058 kg Cwater = 4.18 KJ kg C kg Lice = 333.7 KJ Ti = 27 oC

mwater * Cwater * ( Tf – Ti ) = - mice * Lice

kg * KJ * C = kg * KJ kg C kg

15.70 * 4.18 * (Tf – 27) = -1.058 * 333.7

Tf = 21.62 oC Trial 2:

Area of sink = 15.5 * 15.5 * 4 = 961 in3

? kg = 961 in3 * 1 m3 * 997 kg = 15.70kg 6.1024 x 104 in3 1 m3

? kg = 2 1/3 lb * 0.45359237 kg = 1.058 kg 1 lb

mwater = 15.70 kg mice = 1.058 kg_ Cwater = 4.18 KJ kg C kg Lice = 333.7 KJ Ti = 25 oC

mwater * Cwater * ( Tf – Ti ) = - mice * Lice

kg * KJ * C = kg * KJ kg C kg

15.70 * 4.18 * (Tf – 25) = -1.058 * 333.7

Tf = 19.62 oC

Trial 3: Area of sink = 15.5 * 15.5 * 4 = 961 in3

? kg = 961 in3 * 1 m3 * 997 kg = 15.70 kg 6.1024 x 104 in3 1 m3

? kg = 3.5 lb * 0.45359237 kg = 1.588 kg 1 lb mwater = 15.70 kg mice = 1.588 kg Cwater = 4.18 KJ kg C Lice = 333.7 KJ Ti = 26 oC kg mwater * Cwater * ( Tf – Ti ) = - mice * Lice

kg * KJ * C = kg * KJ kg C kg

15.70 * 4.18 * (Tf – 26) = -1.588 * 333.7 Tf = 17.93 oC Trial 4: Area of sink = 15.5 * 15.5 * 4 = 961 in3

? kg = 961 in3 * 1 m3 * 997 kg = 15.70 kg

6.1024 x 104 in3 1 m3

? kg = 3.5 lb * 0.45359237 kg = 1.588 kg 1 lb mwater = 15.70 kg mice = 1.588 kg Cwater = 4.18 KJ kg C Lice = 333.7 KJ Ti = 25 oC

kg mwater * Cwater * ( Tf – Ti ) = - mice * Lice

kg * KJ * C = kg * KJ kg C kg

15.70 * 4.18 * (Tf – 25) = -1.588 * 333.7 Tf = 16.93 oC

61

1 INTRODUCTION

In this project, an engineering team is to cre-ate a thermodynamic system and analyze dif-ferent physical properties of it. Our team will create a system in which we analyze the ideal gas law to determine certain properties of a balloon filled with air only and a saturated mixture of liquid water and steam. We will measure temperature, volume, size and pres-sure of the balloon to prove the ideal gas law true.

To measure volume we could incremen-tally fill the balloon with measured amounts of water and measure the circumference along a marked region of the balloon. A calibration curve could then be plotted to find a function of circumference vs. volume of the balloon. When we take the measurements of our bal-loon filled with heated liquid and air we would only measure circumference, and make the data point fit our calibration curve to de-termine volume. Specific volume will be used in calculations, however. Specific vol-ume will be obtained using the air temperature tables in the textbook(Table A-17E). These tables are only approximations because they

assume air is an ideal gas, but the error in our calculations will be accounted for in the end.

To measure size of the balloon we will put a string around the circumference of the balloon and assume that it is spherical in shape. In order to have uniformity in meas-urements, we will mark a line around the bal-loon to assure that the measurement point on the balloon is the same for every sample that is collected. We will then measure the length of the string with a ruler to determine circum-ference. From circumference we can deter-mine volume, surface area, radius, and diame-ter using simple commonly accepted formulas.

To measure pressure we will use the ideal gas law. We could also find pressure by using a Bourdon Tube Pressure Gauge. We would simply wrap the opening of the balloon around the input of the pressure gauge and the gauge would tell us the pressure. This device is similar to a barometer, in that it measures pressure.

Temperature can be measured in a vari-ety of ways. We will measure temperature us-ing a simple household mercury or alcohol thermometer. We will take the measurement by placing the thermometer in the water sur-

Project 12: The Effects of Heating an Air Filled Balloon

M. Dominguez, B. Lusk, C. Miller & T. Morris College of Engineering, Texas A&M University, College Station, USA

ABSTRACT: Four engineering students are to design, construct, and implement a thermodynamic system and analyze certain properties pertaining to the system and the reactions which occur within it. The team is then to write a final report which completely outlines and explains the ex-periment and details the results. This team designed a system in which a balloon filled with air will be evaluated when heated in a pot of hot water. Temperature, volume, and size is measured and the ideal gas law is proven true within certain error limitations.

62

rounding the balloon and assume that the temperature of the surrounding water is the same as the temperature inside the balloon. Temperature could also be measured using a thermocouple. Thermocouples are more accu-rate, but they are also more expensive. Our team has determined that the price difference outweighs the increased accuracy that a ther-mocouple could provide, and the increased accuracy in the temperature measurements will not be necessary for our experiment. An-other way temperature could be measured is by using a radiation thermometer. Radiation thermometers work by measuring infrared rays that are given off by any object with a temperature above 0K. Every object gives off infrared rays adequate to their temperature. An infrared ray sensor can detect the amount of infrared rays given off, and the experi-menter could use that to calculate tempera-ture. Infrared thermometers can be used on any substance, and are commonly used on ob-jects in motion such as train wheels spinning and tires. These objects are clearly very diffi-cult to measure temperature of without stop-ping their motion or using an infrared tem-perature sensor.

Our team has determined that in our measurements we will pursue the best combi-nation of accuracy, availability, and ease of measurement. We have made the decisions on the measurement methods based on these cri-teria, and will conduct the measurements and experiment with the highest degree of accu-racy and safety.

More detailed information about the measurements can be found in the “Methods” section of this document, and the correspond-ing results of the measurements can be found in the “Results” section. The team’s opinions and comments on the experiment and meas-urement methods can be found in the “Discus-sion” section, where the results are also com-mented on and analyzed. The “Summary and Conclusions” section is where all final com-ments, opinions, and conclusions can be found that relate to all important topics of the thermodynamic system.

2 METHODS

The apparatus for our thermodynamic system is simply assembled. It consists of a pot filled

with hot water and a balloon filled with air. The water is to be heated to a certain tempera-ture on a stovetop burner and the balloon par-tially filled with air is to be placed in the hot water.

First, the hot water is prepared in the pot. The pot is filled halfway with the hottest wa-ter possible out of the faucet. A team member then blows up a balloon to a small circumfer-ence, which is to be less than 15 inches. The initial circumference is measured and re-corded by marking the balloon on a line around the circumference to reference later, and then measured using a string wrapped around it and a ruler. The pot is then placed on a stovetop burner and the burner is set on high heat. After the water has risen to a tem-perature of approximately 160 degrees Fahr-enheit, the balloon is placed into the hot water and held as far down into the water as possi-ble by a team member. Temperature is meas-ured using a digital meat thermometer, and is held inside the water without touching the metal of the pot. The balloon is left sub-merged for approximately 3 minutes. The balloon is then removed from the water and the new circumference measured to determine expansion of the air. Specific volume is then determined using the reference temperatures in table A-17E in the textbook.

The data is analyzed using simple statis-tical means, and results are evaluated based on each separate trial. Results are not com-bined from the different trials using methods such as averaging and estimation. All conclu-sions will be drawn from analyzing the results from each individual trial.

3 RESULTS

Initial Diameter: 12.5 inches

Rair=0.3704 Table 1: Balloon Properties Measurements Trial Number

Temperature, (R)

Final Diam (in)

Specific Volume (ft3/lbm)

1 625 13.75 100.1652 620 13.5 102.12 3 625 14 100.165

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅Rlbftpsia

m

3

63

vRTP =

Ideal Gas Law: Pv=RairT ∴ Table 2: Pressure Calculations Trial Number Pressure(psia)

1 2.311 2 2.249 3 2.311

Three trials were ran, each at approxi-

mately the same temperature. The reader can note above the measurements of temperature, final diameter, and specific volume of each trial.

4 DISCUSSION

The designed experiment proposed in previ-ous sections of the report is designed to prove the ideal gas law. To predict results for our experiment, the ideal gas law could be used (Pv=RT).

Since the balloon is tied off, we assume that the mass inside the balloon does not change, thus defining a closed system. One would also have to assume that the balloon is a per-fect sphere, which was found to not necessar-ily be the case. This was perhaps the most limiting feature of the designed experiment.

Measuring the circumference allows you to find the radius, which can be used to solve for the volume of a sphere using the equation V=(4/3)*п*r3. Using this data, you can ob-serve that as the temperature rises, the volume of the air inside the balloon will rise. This is exactly the data that was observed using the designed experiment. When the balloon was placed in the hot water for several minutes, the size of the balloon increased, showing an increase in volume and pressure.

While this general trend was observed in the experiment, the exact numbers that would be expected were not observed in practice. This is due to several factors in the experi-ment.

Assuming that the balloon is a perfect cyl-inder is a large assumption that causes a lot of inaccuracies in the calculations. We also did not measure the pressure inside the balloon so you cannot calculate the exact volume of the balloon at an exact temperature. While the

data from the designed experiment was not exact, it did show the expected trend from the ideal gas law. Several limiting factors in the design caused the experimental data to not be exact, but the overall design was good enough to prove the relationship stated in the ideal gas law.

5 SUMMARY AND CONCLUSIONS

In our thermodynamic system, we set up an apparatus in which we evaluated air expand-ing in a heated balloon. We examined many different ways to evaluate the properties of our system and decided on the methods we used after careful deliberation. We put a bal-loon filled with air into a pot of heated water and measured the temperature and expansion of the balloon. We used the information gath-ered in the experiment to find that the ideal gas law is true and works in real world prac-tice, and not just on paper.

From the information gathered during our experiment we determined that the ideal gas law is true. We used the data and plugged it into the equation Pv=RT and the equation worked out within a reasonable error bracket. The expansion of air due to a temperature in-crease does in fact cause an increase in pres-sure and/or specific volume. We also con-cluded that there is usually an easier way to implement certain designs. Initially we planned to use a somewhat more complicated apparatus in order to decrease error, but in-stead we used a more elementary approach and our solutions were still accurate enough to be able to draw an educated conclusion. This experiment could be better conducted in the future if a pressure measuring device was available and used. The experiment could also be conducted easier if the balloon was a perfect sphere to make the volume measurements more accurate. Mass could also be measured if an accurate digital scale or triple beam balance were available. REFERENCES

G.R. Peacock (1997). Infrared Radiation

Thermometer Applications Repository. http://www.temperatures.com/rtapps.html.

64

M. Bellis. The Bourdon Tube Pressure Gauge. http://inventors.about.com/library/inventors/blbourdon.htm.

J.L. Park (1996). The Ideal Gas Law.

http://dbhs.wvusd.k12.ca.us/GasLaw/Gas-Ideal.html.

J. Milligan. Boiling and Vapor Pressure. http://www.ars-chemia.net/dr-milligans-classes/Course_Info/Classes/101/Notes/Liquids_and_Solids.pdf.

65

1 INTRODUCTION

Why does Texas A&M feel so humid all of the time? Does the temperature influence the humidity at all? In the following report we intend to gather an understanding as to how temperature relates to humidity. We will measure the relative humidity and the tem-perature in a few different places and see how they vary. We will also compare our meas-ured data to exact data gathered from more exact instruments with a similar experiment. The method we chose to use and some other ways to do this experiment are as follows.

To obtain accurate data for temperature and relative humidity, we will need to have access to reliable instruments. There are many different types of instruments that will allow us to obtain the data needed, but one problem that we could incur is the price of the instrument. One instrument that is not af-fordable but very accurate is the WMO Refer-ence Psychrometer. This instrument has been used by scientists and engineers for at least the better part of the twentieth century, but it as well as all instruments is not completely accurate. The WMO Reference Psychrome-

ter has an error of approximately one percent in pressure when the relative humidity ap-proaches either 0 or 100 percent, and the in-strument is not operable when the wet element is below zero degrees Celsius (Measurement of Temperature and Humidity).

Another instrument for measuring the rela-tive humidity is the Arten Thermo-Hygrometer. This instrument gives two rela-tive humidity readings, one from a plastic copper spring driven dial, and another from a paper strip as a check on the meter’s accuracy. The Arten Thermo-Hygrometer is also too expensive for our experiment.

Another way that we could conduct this experiment is by using a hair hygrometer. This instrument involves actual hair, and we would have to construct a lever system, which will magnify the extremely small changes in the length of the hair with changes in relative humidity. This does not seem to be a good method for our experiment as we would have to be very tedious to get accurate results. For our experiment we will be using a sling psy-chrometer to determine the relative humidity both indoors and outdoors. The sling psy-chrometer is the simplest form of a hygrome-

Project 13: Relative Humidity Analysis

J. Dovalina, J. Grothues, S. Ingram & H. Sun College of Engineering, Texas A&M University, College Station, USA

ABSTRACT: In this project, teams of four students will work together to design, construct, con-duct, and analyze a thermodynamic demonstration experiment and write a report in the format consistent with the project description. The project topic is RELATIVE HUMIDITY. The engi-neering team will measure the relative humidity with certain tool and compare the measured (experimental) results to the actual results that are collected from weather organization sources. This project report includes different sections with explanations that have the analysis and results serve as guidance.

66

ter. There are two thermometers in the sling psychrometer, one called a wet bulb and the other a dry bulb. The dry bulb simply takes the temperature of the surrounding air, while the wet bulb has a wet cloth over the top and is spun around until the water has evaporated. Once the water has evaporated the tempera-ture of the wet bulb should drop (unless the relative humidity is 100 percent), and the in-strument allows you to calculate the relative humidity. In knowing the temperature and relative humidity, we will calculate the pres-sure as well.

We chose this final method because it is the cheapest and easiest to perform, while the accuracy does not suffer.

In the following sections, a description, analysis, and discussion of the experiment will be given. The methods section will de-scribe the equipment used, the locations of the experiments, and how the data obtained will be analyzed. It will describe how to assem-ble the apparatus, how all the measurements were conducted and what equipment was used to make the measurements. Data from the ex-periments will be placed in an Excel docu-ment and compared to theoretical results. In this report we will also discuss our analytical solution using the methods we come up with as a prediction for the type of the results to be expected. We will also discuss the comparison between the analytical solutions with the measured experimental data and list out the similarities and differences. The limitations of the analytical method will also be addressed. If there the results vary from each other; the errors or mistakes will be explained and dis-cussed as well. The final section of the report will be short and written in two parts. The first part will be a brief summary of the im-portant points from the previous sections. The second paragraph presents the important con-clusion that can be drawn from the experi-ment.

2 METHODS

One of the toughest challenges in this project is to choose the correct and most efficient methods to conduct the experiment.

For our experiment we will be using a sling psychrometer to determine the relative humid-

ity both indoors and outdoors. The sling psychrometer is the simplest form of a hy-grometer. There are two thermometers in the sling psychrometer, one called a wet bulb and the other a dry bulb. The dry bulb simply takes the temperature of the surrounding air, while the wet bulb has a wet cloth over the top and is spun around until the water has evaporated. Once the water has evaporated the temperature of the wet bulb should drop (unless the relative humidity is 100 percent), and the instrument allows you to calculate the relative humidity.

Our instrument costs about $80, but luckily one of our team member works in the air con-ditioning company and he has a possession for one of the psychrometer tools, therefore our cost in this project is reduced down to $0. Only man hours are conducted in this project.

Measurements of dry bulb and wet bulb temperatures were taken on November 15, 2003 in College Station, Texas with a sling psychrometer. The measurements were taken in 2-hour intervals with the initial reading at 9:00 A.M.; the final ready was taken at 11:00 P.M. The data was placed into an excel document and compared with readings ob-tained from the National Weather Service.

We used Microsoft Excel to show the graphical analysis to represent our results. We collected the data, enter it into the spread-sheet, and then generate three line graphs.

3 RESULTS

After we collect the experimental data from different time during the day, we compared it with the actual data that we gathered from the weather channel and do an analysis on the comparison:

67

Table 1: Data Collected fromWeather Chan-nel 11/15/2003 (OUTDOOR)

Time Dew point

(F) Temperature

(F) Relative Humidity

9am 65 71 81% 11am 67 76 74% 1pm 67 80 64% 3pm 69 76 79% 5pm 69 77 74% 7pm 68 74 82% 9pm 70 72 93% 11pm 69 71 93%

Table 2: Data Collected from Outside Meas-urements

Time Dew point

(F) Temperature

(F) Relative Humidity

9am 63 72 61% 11am 71 78 71% 1pm 72 81 65% 3pm 71 75 82% 5pm 73 76 86% 7pm 69 71 90% 9pm 72 74 91% 11pm 70 72 90%

Table 3: Data Collected from Inside Meas-urements

Location

Dew Point (F)

Tempera-ture (F)

Relative Humidity

Living Room 62 73 53%Bath-room 74 75 96%

The above charts are the raw data in which

we collected from measuring the dew point temperature, temperature, and relative humid-ity in different hours during the day. The numbers are consistent with each other and there is only a narrow range or errors.

We then convert the data into graphical analysis:

Figure 1. Time VS Relative Humidity Graph Figure 1 represents the relative humidity level at different times during the day. We measure the data every two hours from 9am to 11pm. We then will compare the actual and dew point temperature at the same times during one day:

Figure 2. Time VS Temperature Graph

Figure 3. Time VS Dew Point Temperature Graph

Figure 2 represent the temperature in the different times during the day. Sometimes is hard to judge the actual temperature and hu-midity from the temperature you watch in the

Time VS Relative Humidity

0%

50%

100%

9am

1pm

5pm

9pm

Time

Perc

enta

ge

ActualRelativeHumidity

MeasuredRelativeHumidity

Time VS Temperature

6570758085

9am

1pm

5pm

9pm

Time

F ActualTemperature

MeasuredTemperature

Time VS Dew Point Temperature

5560657075

9am

1pm

5pm

9pm

Time

F

Actual DewPoint Temp

MeasuredDew PointTemp

68

news and websites. Therefore we also meas-ured the Dew Point Temperature in the same times of the day when we measure the humid-ity and temperature; the graphical result is shown in Figure 3.

There are small variance of error that we have encountered during the experiment, we will analyze and discuss these errors with de-tailed explanations in the discussion section. 4 DISCUSSION

Relative humidity is the ratio of the actual amount of moisture in the atmosphere to the amount of the moisture the atmosphere can hold. Therefore, a relative humidity of 100% means the air can hold no more water (rain or dew is likely), and a relative humidity of 0% indicates there is no moisture in the atmos-phere. Relative humidity is used by meteor-ologists to help predict the weather, by pa-thologists to predict disease development on plants, and by agricultural scientists to esti-mate evaporation of water.

Relative humidity, combined with air tem-perature, can be used to estimate the actual amount of moisture in the atmosphere, some-times referred to as perceptible water. Water vapor acts as a green house gas by trapping infrared radiation reflected from the earth. This explains why desert temperatures can become much lower at night, as there is little moisture in the air to trap the heat.

The equation to calculate the relative humidity as follows:

Relative Humidity = (Actual Vapor Den-sity / Saturation Vapor Density) X 100%

Since actual vapor density cannot be calcu-lated, we have to predict the relative humidity by taking the measurement of dew point tem-perature from the sling psychrometer. Also we will get the data from the national weather service.

In our project we estimate the relative hu-midity with experimental and actual results.

After taking data from the online weather resources and the data from our method analysis, we were able to distinguish several variances and similarities. Our variation be-tween the actual and measured relative hu-midity is small. During the morning hours the humidity is high due to the moisture generated

by the plants overnight. The humidity drops as the day reaches high noon. As the day con-tinues, the humidity rises again as the sun starts to set. Our measured results agree with the actual data; the possible cause for the slight variation is the accuracy of the tool that we are using.

The temperature and dew point tempera-ture are consistent between the measured and actual results as well. Temperature rises and reaches the highest point around 1 pm, and at the lowest around 9 am in the morning and 11 pm at night.

Our experiment also includes the meas-urements on different relative humidity level in different environments. The experiments are:

• First we will take the measurements of

relative humidity, temperature, and dew point temperature inside a bathroom in a private home. The experiment will be conducted when the bathroom is fully moist and humid; condition will be when a person just got out of a hot shower, or when a person is taking a hot bath, both without the air ventila-tion system running to prevent the moisture leaking out of the room. The environment will be a closed system and well insulated from surroundings.

• We will also take the measurement in a

standard indoor environment. Places like Zachry Engineering Center Lobby; a place with constant air conditioning and good ventilation system. The hu-midity is lowering relatively compared to the moist bathroom.

The relative humidity in the steam filled

bathroom is much higher than the standard air atmosphere in the indoor lobby because the high moisture level inside the bathroom. Strong moist air flies inside the closed space and it is well shown on the statistical analysis.

Our limitations have prevented us from measuring the exact values for the relative humidity. Limitations such as the accuracy of the sling psychrometer and the atmosphere pressure in the experimenting environment. The air pressure will change due to the wind; therefore the relative humidity will vary in the

69

different locations, even in the outdoor envi-ronment.

5 SUMMARY/ CONCLUSION

Several instruments were researched to de-termine which would be the most appropriate for this project; the sling psychrometer ap-peared to be the best choice. Several read-ings of outside air-dry bulb and dew point temperatures were taken and used to deter-mine the relative humidity at various times of the day. The calculated relative humidity data was compared to readings taken by the National Weather Servce. Also, additional measurements were taken in a bathroom after a hot shower and in the lobby of the Zachry Engineering Center, these additional meas-urements were plotted and discussed. Our limitations in accuracy are due to the accuracy of the sling psychrometer and the inability to take readings at the same location as the Na-tional Weather Service.

Our results indicate that the measured data

of relative humidity were very accurate with our sling psychrometer. We have decided that the sling psychrometer is a very efficient way to measure the humidity in the air. Our main finding which we have come to comes from our initial question; the “sticky” feeling you get in the air is, in fact, directly related to the temperature outside and the relative hu-midity.

REFERENCES

Wylie, R. G. and T. Lalas (1991). Meas-ure- ment of Temperature and Hu-midity. World Meteorological Organization

“Measuring Relative Humidity.”

http://www.nws.noaa.gov/om/ed/uc/activit/measurrh.htm

“Arten Thermo-Hygrometer.” Benchmark Relative Humidity (Oct. 2002). http://www.benchmarkcatalog.com/main-relativehum.htm

“Method of Test, Determining Relative Humidity With A Sling Psychrometer.”

Iowa Department of Transportation (Oc-tober 3, 2000). http://www.ecl.dot.state.ia.us/Apr_2003/IM/content/382.pdf

70

71

1 INTRODUCTION Power plants make use of large scale heat ex-changers to regulate temperatures of equip-ment to keep them functioning properly. A car radiator is a heat exchanger that has the same purpose, but on a much smaller scale. A heat exchanger is based on the principle of heat transfer. Our experiment will take a close up look at the basic thermodynamics of heat transfer by using the simple experiment of a balloon in a water bath. The measurements to be taken in our ex-periment include volume and temperature. In a laboratory setting, these types of measure-ments would be taken using sophisticated equipment. Measuring the changing volume of a balloon is very tedious and challenging, but instruments such as a dilatometer have been invented to assist in such measurements. A dilatometer measures changes in length of a subject that is contained in a controlled envi-ronment. Its main function is to calculate the coefficient of expansion of the subject (Bud et. al. 1998). In a laboratory setting, this could be used to help define a coefficient of expansion

for a balloon, thus helping us determine an accurate measurement of the volumetric change. Some of the newest laboratories of today implement instruments such as ther-momechanical analyzers, which measure di-mensional changes such as expansion to aid in volumetric measurements (Moynihan 2003).

For temperature measurements, a type of thermocouple would more likely be used in a laboratory setting. A differential thermal analyzer is a thermocouple that measures temperature differences between two materi-als contained in a controlled environment (Bud et. al. 1998). Since our water bath-balloon system will be open to the atmos-phere, there will be a loss of heat transfer to the environment which will affect our calcu-lated rate of heat transfer. In a laboratory, the system could be contained in a well insulated container. This would make all measure-ments extremely accurate as compared to a simple thermometer in an open system. The following contents of this report will include a break down of our experiment in detail as well as the results gathered. The

Project 14: Heat Transfer between an Air Filled Balloon and Water Baths at Differing Temperatures

Bennett Ford, Ryan Goodnight, Robert Mosher, Megan Murphey College of Engineering, Texas A&M University

ABSTRACT: Our project investigates the heat transfer between a balloon filled with air and water when placed in water baths of different temperatures. We find the mass of air in the balloon using Archimedes’ principal to measure the balloon’s initial volume and knowing the density of air. Let-ting the balloon reach thermal equilibrium with a water bath, it will have a loss/gain in temperature due to heat transfer. Temperature will be measured at two states: state 1 – balloon at room tempera-ture and state 2 – balloon at thermal equilibrium with water bath. From our temperature measure-ments, we can directly measure the heat transfer, Q, using the formula Q = mc∆T. By calculating the heat transfer and timing how long it takes the balloon to come to thermal equilibrium with the water baths, we can find the ∆heat/∆time, rate of heat transfer.

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Methods section will describe a step-by-step guide of the conduction of the experiment. The Results section will contain raw data in the forms of tables and charts and experiment runs made. The Discussion section will entail comparisons of predicted results and actual experiment results. The possibility of human error will be introduced within this section. The Summary and Conclusions section will give an overall view of our experiment and what information can be gathered as a result of the experiment. 2 METHODS The materials needed to conduct the experi-ment are a regular rubber balloon, a clear wa-ter-proof container (large enough to contain an inflated balloon), two thermometers, string, tape, pan (shallow, comparable to a frying pan), measuring cup, water, ice, and a heat source (stove).

Prior to conducting the experiment, place the thermometer end within the balloon and in-flate the balloon using regular air. Tie off the balloon using string allowing the thermometer to be contained within the balloon and keeping air from leaking out. Add tape around the opening to reduce any air leakages.

Now you must measure the mass of the air within the balloon. To do so, fill the clear container full with water. Place container with water in a pan. Submerge the balloon into the container allowing excess water to flow over the edge of the container into a pan. Poor wa-ter in pan into a measuring cup and record the amount as the volume of air inside balloon. Now take the volume measured and calculate the mass of the air using the density of air at room temperature. Take the initial tempera-ture of the air within the balloon and record. Heat water to maximum temperature of about 100 0C, boiling temperature, on a stove. Carefully empty container and fill with the heated water. Place container back in the pan. Place balloon in this hot water bath and record initial water temperature with the second thermometer. Allow system to come to ther-mal equilibrium by observing the system for about 2 minutes. Record exact time allowed for the system to come to equilibrium. Take a final volume reading of the balloon by measur-ing the overflow of water in the pan. Record

the volume as well as the final temperature in the balloon. Remove balloon and allow it to cool down to room temperature. Repeat process with various temperature water baths. When using an ice water bath, to measure the volume loss by the balloon, carefully add pre-measured increments of wa-ter in the measuring cup to the container until it is full again after the system is at equilib-rium. Record the amount of added water. This is the volume loss by the balloon. Allow approximately 10 minutes between trial runs to allow balloon to return to initial conditions. To increase accuracy, it is best to repeat volume measurements before each trial run. Record all initial and final temperatures, volume measurements, and time periods. All our data is tabulated in Excel. Heat transfer is calculated using Q = mc∆T, Eq1. It is plotted verse time period for each trial run to obtain the rate of heat transfer.

3 RESULTS Test trials were only run for two different temperatures due to the difficultly of having multiple water baths heating and cooling. A practice trial was run to check experiment set-up and procedure. The first trial was a water bath at 100oC and the second an ice water bath of 10oC. Each trial was repeated in order to give better accuracy. The results obtained from these test trials include volume and temperature changes. Figures 1 and 2 show the values obtained for the hot and cold water baths. The balloon in the hot water bath expanded to a volume of 1030 mL from 350 mL in the first trial and to a volume of 1100 mL in the second. It shrunk to 325 mL in the first trial and 300 mL in the second trial in the cold water bath.

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4 DISCUSSION

In discussing the validity of this experiment it must first be clearly stated that all of the measurements are rough and inaccurate. This is partially due to the lack of precision in the measurement instruments used as well as a fairly large degree of human error. Inciden-tally, the experiment was not conducted at sev-eral different water bath temperatures, but only at two; the experiment is meant, not for precise lab data, but rather to illustrate and give a gen-eral understanding of some basic thermody-namic principles, to cover over a range of water bath temperatures. The discussion may be furthered by comparing predictions to re-sults. Assuming that the pressure is held constant (this assumption is somewhat reasonable be-

cause the boundary of the balloon is allowed to expand somewhat freely), and that air is taken as an ideal gas (also reasonable on comparison with the critical temperature and pressure of air), it can be expected that the volume should vary directly with the tem-perature. This relationship is seen in the ideal gas equation PV = mRT, Eq2. Figures 1 and 2 verify this information. Heat transfer is calculated using Eq1. The change in temperature is measured directly within the experiment via a thermometer. The specific heat, c, of water is known to be 4.23 kJ/kg/oC. Mass of air is found using the formula m = ρV, Eq3. Volume is measured

within experiment using Archimedes’ princi-ple. The density of air at room temperature is 1.186 kg/m3 (Cengel et. al. 2001). Using the conversion factor 1000 kg/m3 = 0.001 kg/mL, a proper answer can be found for heat trans-fer, Q.

The rate of heat transfer, Q, is found from the equation Q = ∆Q/∆t, Eq4. Allowing 2 minutes for the system to come to equilib-rium means the heat transfer took place within those 2 minutes. This makes 2 min-utes the change in time. Figure 3 shows the rate of heat transfer. The hot water bath had a heat transfer rate of 0.132 kJ/min while the cold water bath’s rate was 0.026 kJ/min. More heat was transferred during the hot wa-ter bath trial than the cold water bath trial.

Errors in the experimental data are given by, but not limited to: extra water spilling out of the bowl due to an unsteady hand holding

Figure 2: Correlation of the temperature to volume of the balloon for the cold water bath.

Figure 1: Correlation of the temperature to volume of the balloon for the hot water bath.

Hot Water Bath

0

200

400

600

800

1000

1200

0 50 100 150

Temperature (C)

Volu

me

(mL)

Trial 1Trial 2

Cold Water Bath

290300310320330340350360

0 10 20 30

Temperature (C)

Volu

me

(mL)

Trial 1

Trial 2

Rate of Heat Transfer

00.020.040.060.080.1

0.120.14

0 2

Tine (min)

Hea

t (kJ

)hot

cold

Figure 3: Rate of heat transfer of hot and cold water baths over the time interval of 2 minutes.

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the balloon under the water; the assumption that the pressure of the balloon out of the wa-ter is the same as when it is completely sub-merged (hydrostatic pressure); loss of heat to environment. However, a good understanding of the errors involved in this basic experiment shed light on the meaning of the data obtained.

5 SUMMARY AND CONCLUSIONS

Heat transfer is very useful in many real world applications. It is exhibited in our experiment of an air filled balloon interacting with water baths of differing temperatures. Some of the parameters within this type of experiment, such as volume change, can be difficult to measure but are attainable. There is much room for human error within our experiment procedure. We were able to verify the correlation be-tween volume and temperature of an ideal gas as well as calculate the rate of heat transfer of the balloon in the different water baths. We discovered the balloon to be a good system to observe heat transfer. This is evident in the balloon’s ability to readily expand and/or shrink as the volume of air is in-creased/decreased due to the heat transfer. We find our experiment to be a success in observ-ing and exploring heat transfer. ACKNOWLEDGMENTS We would like to thank Dr. Socolofsky in his guidance during this project from helping us decide on an experiment to how we should proceed with the experiment. REFERENCES

Bud et. al., Eds. 1998. Instruments of Science:

An Historical Encyclopedia. London: Gar-land Publishing, Inc.

Cengal et. al, Eds. 2001. Fundamentals of

Thermal-Fluid Sciences. New York: McGraw-Hill Primis Custom Publishing.

Moynihan, Joan, Ed. 2003. Instruments and

Equipment. Lab Guide: The Premier Direc-tory for all Scientific Laboratories. Cent-com, Ltd. 2003 ed: 162-164.

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1 INRODUCTION

If you are a person who loves a nice cold frosty beverage and I’m going to assume you do, then you know that ice drops the tempera-ture of a liquid it is put into as it melts. This happens due to a temperature difference be-tween the drink and the ice cubes so therefore since the ice is at a colder temperature, heat will transfer from the drink to the ice cubes. This seemed particularly interesting to us in that we think a final temperature for the sys-tem of water, ice and a container can be pre-dicted using experimentation, specific heats and equations for a closed system. We plan on running several tests of adding different amounts of ice to water at different tempera-tures to see if we can get a basic pattern and then predict results from any temperature be-tween 0 and 100 degrees Celsius and any amount of ice added. But before we can be-gin we must analyze some technical informa-tion.

One thing to consider in doing our experi-ment is which type of thermometers to use. There are many different kinds of thermome-ters that are available. They can be divided

into 3 major categories: non-electric contact thermometers, electric contact thermometers, and optical pyrometers. (Michalski et. Al 1991) The first type is the most commonly available. This type consists of mercury-in-glass, liquid filled, and bimetallic thermome-ters. The second type is comprised of resis-tance, fiber optic and ultrasonic thermometers. (Michalski et. Al 1991) (Total radiation, pho-toelectric, and two-color pyrometers are all of the third type. (Michalski et. Al 1991) We will need a thermometer with a useful range between -20 and 120 degrees Celsius and one that is readily available. Luckily for us both of those conditions are met by classic mercury thermometers. We could also use the resis-tance type, but those are less available, so the common mercury will be used.

Now that our plans have been set out, the rest of this project will be described in more detail in order to fully explain our experiment. The methods section describes the methods used to conduct our experiment, the actual setup, and the methods that were used to col-lect our data. The results section describes every important bit of information collected during the experiment. This section is basi-

Project 15: Heat exchange between ice and water

J. E. Griffin, K. LeClair, T. J. Perales & J. A. Sibert Team 15, Conservation Principles in Thermal Fluid Science, Texas A&M University, College Station, USA

ABSTRACT: The purpose of this experiment is to see how accurately the final temperature of a water and ice mixture can be predicted. The materials needed consist of cheap, easily found, common household items. The actual experiment is to be easily conducted in a relaxed, non-laboratory style setting, such as in a kitchen. However, the data should still be collected as accu-rately as possible for these conditions. The results will present the raw data experimentally found. In the discussion section we will calculate the expected values and compare these to the experimentally found values. As well as attempt to explain any discrepancies found.

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cally all the raw data we collected. The dis-cussion section will of course be where we discuss our opinion on the collected data and combine the results with an analytical solution obtained from methods learned in class. The last section, the summary, will consist of two parts, one in which important points from previous sections will be stated, and then the second part will present our conclusions we drew from the experiment.

2 METHODS

This experiment is designed and being con-ducted to collect enough data in order to pre-dict a final temperature of the mixture based on the initial mass and temperature of the ice and water. In order to obtain enough informa-tion for us to accurately predict a final tem-perature, we decided on doing a total of 4 tri-als, with two different temperatures and two different masses of ice.

The experiment will consist of first, setting up equal amounts of water, approximately 300 milliliters in 4 identical cups. We are choos-ing 473 milliliter Styrofoam cups due to the lack of heat transfer that will occur through the walls of the cups, the easy accessibility of them, and easy access of the thermometer into the cups. We will then take two cups and put them into the fridge until a temperature of ap-proximately 17 degrees Celsius is reached. Then we will insert a different amount of ice into each cup (one cube and three cubes) and record the temperature of the mixture every 30 seconds until the ice is completely melted or an unchanging temperature is reached. We will repeat this procedure for a temperature close to room temperature by letting the cups set out for a while. These temperatures were chosen due to their relative closeness to room temperature which should minimize heat transfer to the surroundings. A regular mer-cury thermometer will be used to measure the changing temperatures. The masses of the ice being added will be measured by measuring the difference in the amount of fluid in the glass once the ice has completely melted and the temperature of the ice will be recorded from the freezer the ice is obtained from. The data collected will be recorded in a table then the temperature of each mixture will be graphed over time to make analyzing the data

easier. This data will be used in the conserva-tion of energy equation to attempt to predict the final temperatures obtained. Once the right equation is known, final temperatures of dif-ferent trials will be easily predictable. If for some reason we suspect that something hap-pened during the experiment that might affect the results or the data just does not seem ap-propriate, we will attempt the trial again.

3 RESULTS

Table 1: The effects 3 cubes of ice have on water at different initial temperatures.

3 cubes of ice Time (minutes)

cold (75 mL)

warm (55 mL ice)

0 17 22.70.5 13 18.6

1 10.2 13.41.5 8.5 10.6

2 6.3 8.62.5 5 7.4

3 4 6.53.5 3.4 5.9

4 3 5.54.5 2.7 5.3

5 2.4 5.25.5 2.2 5.2

6 2 5.26.6 1.9 5.2

7 1.8 5.27.5 1.7 5.2

8 1.6 5.28.5 1.5 5.2

9 1.5 5.2

Table 2: The effects 1 cube of ice has on wa-ter at different initial temperatures.

1 cube of ice Time (minutes)

cold (20 mL ice)

warm (25 mL ice)

0 17.5 22.90.5 16.2 20.3

1 14.2 18.21.5 12.9 16.8

2 12 16.22.5 11.5 15.9

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3 11.2 15.93.5 11.1 16

4 11.1 164.5 11.1 16

5 11.1 165.5 11.1 16

6 11.1 166.6 11.1 16

7 11.1 167.5 11.1 16

8 11.1 168.5 11.1 16

9 11.1 16 Each sample had an initial 300 mL of water which comes out to .3 kg for mass of water-initial. The temperature of the freezer was re-corded at -13˚ C which is 260K and that will be used as the initial temperature of the ice.

4 DISCUSSION

After running the experiments we analyzed the data obtained and realized that multiple parts of the experiment will have to be ac-counted for at once; the temperature of the ice changing from -13° C to 0° C, the melting of the ice, the temperature change of the melted water at 0°C to the final temperature, and the temperature change of the original water from the initial to the final temperature. To account for these stages separately but in one equation we use the conservation of energy equation (∆u + ∆pe + ∆ke = q - w ) , which in our ex-periment reduces down to u1 = u2, since we are assuming zero heat transfer in or out of the system, no work is done, and kinetic and po-tential energy equal zero. Then to account for internal energy change in the separate parts of the experiment we use (mass) x (Cp) x (∆T) for each part except for the melting which we use (mass) x (∆h). The change en-thalpy (∆h) for the melting of ice is 334.7 kJ/kg (http://wblrd.sk.ca). By adding these together and setting them equal to zero the equation becomes

(mw)(Cw)(∆Tw) + (mi)(∆hi) + (mi)(Ci)(∆Ti) + (mi)(Cw)(∆Ti) = 0

where w represents water and i represents ice, masses are in kilograms, temperatures are in Kelvin, and Cw and Ci are in KJ/(Kg*K). When we applied this equation to the data we collected we obtained the information in table 3. Table 3: actual and predicted final tempera-tures

warm with three cubes

warm with one cube

cold with three cubes

cold with one cube

CalculatedFinal temp (Celsius) 7.05 15.2 -2.2 11.5Actual Final temp (Celsius) 5.2 16 1.5 11.1

These temperatures are close enough to accu-rately predict final temperatures because it

Water w ith 3 cubes of ice over time

0

3

6

9

12

15

18

21

24

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.6 7.0 7.5 8.0 8.5 9.0

Ti me ( mi nut e s)

cold wat er wit h 75mL ice

warm wat er wit h 55mL ice

Water w ith 1 cube of ice

0

5

10

15

20

25

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.6 7.0 7.5 8.0 8.5 9.0

Ti me ( mi nut e s)

cold water with 20 mL icewarm water with 25 mL ice

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was no more than 1.85˚ C off from what we experimentally obtained. The deviation can be explained by many factors that could have affected our experimental data. For example, there is definitely a small amount of heat loss to the air due to the surface of the water being exposed to a higher temperature during test-ing. We could have possibly minimized it further by using lids on the cups. Second the ice cubes may have not been at the measured temperature when dropped into the water due to exposure to air and hands while transport-ing it to the cup which would make the final temperature be higher. But as you can see two out of four actual temperatures are lower than the predicted temperatures which we did not expect, and the only thing that could make this happen is an error in measuring the initial and/or final volumes of water, which could have easily happened due to the unaccurate-ness of the beaker used to measure. A solu-tion to this would be to use a much more ac-curate beaker and be more careful when measuring the amounts of water. 5 SUMMARY AND CONCLUSIONS

The experiment went quite well and gave us final temperatures close to the ones predicted by the equation we used. The only problem was that the predicted values were actually a little bit higher than the ones obtained from the experiment. This shows that it was most likely an error on our part when measuring the volumes of the water that cause the devia-tions. The equation used accounts for the three stages of the ice and the temperature de-crease in the initial water.

This experiment proves the final tempera-ture of a mixture can be predicted to an ex-tent, but with our equation the temperatures will not be totally accurate because it does not account for heat transfer from the surrounding air. This experiment is good because it shows how to use the conservation of energy equa-tion on problems that have temperatures of water going through the saturation or freezing point and proves that energy is taken to change states while temperature remains at one value. It also proves that heat goes from higher temperatures to lower temperatures un-til it is at equilibrium.

If this experiment is to be conducted again, the heat transfer from the surrounding air could possibly be obtained and put into the equation to obtain a more accurate result. This could be done by recording the tempera-ture of the air and the surface area of the water exposed. REFERENCES

Michalski, L, K. Echersdorf, and J. McGhee. Temperature Measurement. England: Wiley & Sons, 1991

“Molar Enthalpy of Fusion of Ice”

25 November 2003 <http://wblrd-.sk.ca/~bisstchem/modules/module3/lesson4/enthalice.htm

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1 INTRODUCTION

In today’s world speed and efficiency are many people’s top priority. Performing nec-essary work faster generates more free time for pleasure. A prime example of this is trav-eling. Before traveling it is necessary to fill the gas tank, check the engine fluids, and check the tire pressures. However, checking these values and performing necessary main-tenance costs precious time, time which peo-ple would rather spend actually traveling. As a result, the ability to replenish these vital flu-ids faster would be a great benefit to the ge-neric public. This experiment can assist in answering one facet of this problem by allow-ing the public to determine the mass flow rate of air from an air compressor: the larger the flow rate, the faster the air compressor. In order to solve this problem Team 16 util-izes a bicycle tire and a small air compressor. The team utilizes such equipment citing budget concerns. Nevertheless, the science,

logic, and equations used can be applied to a tire and air compressor of any shape or size. One of the properties that is necessary to know is the temperature of the air inside the tire. To obtain the most accurate results, proper instrumentation must be used. One such instrument is a thermistor. Thermistors placed throughout the tire provide an accurate map of temperature changes inside the tire as it is filled with air. The resistance of a ther-mistor is a function of the surrounding tem-perature. Such a relation is given by the mathematical equation:

R = aeb/T where both a and b are known constants for a particular thermistor and R is the measured re-sistance at a temperature T. (Benedict, 1977) Another property measured during the ex-periment is the pressure inside the tire. In or-der to determine the mass flow rate, both ini-tial and final tire pressures must be measured. If the team were given a larger budget a well manometer could be used. Such an instru-

Project 16: Observations of Mass Flow: Can Charles, Boyle, and Gay-Lussac’s Ideal Gas Equation accurately approximate the behavior of air?

M. T. Hiatt, M. C. Morris, M. S. Posey & J. T. Ryan College of Engineering, Texas A&M University, College Station, Texas, USA

ABSTRACT: In 1802 Gay-Lussac and J. Charles observed a stunning relationship between the volume of a gas and its corresponding temperature. Expanding upon Boyle’s discovery 140 years prior, the three men had discovered what is now known as the Ideal-Gas Equation of State. This equation relates the temperature, pressure, volume, and mass of an ideal gas. Unfortu-nately, there is no such thing as an ideal gas. The question becomes: what constitutes an ideal gas? The following is an attempt to show that ambient air behaves ideally by comparing ex-perimental data to the Ideal-Gas Equation of State. If such an approximation is valid, then one can accurately determine the mass flow through a device simply by knowing the change in pres-sure, volume, and temperature.

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ment would negate the need to disconnect the tire from the compressor—a task that could potentially lead to inadvertent air releases. A second hole would have to be cut into the tire for the placement of the manometer. The team could then determine the pressure inside the tire by noting the height change of the fluid inside the manometer. (Jones, 1965)

Thanks to technological advancements, mass flowmeters due exist. One such exam-ple is an axial flow mass flowmeter. This de-vice is placed in a pipe and consists of an im-peller and turbine positioned perpendicular to the flow of the fluid in the pipe. The impeller causes the fluid to rotate within the pipe, thus creating angular momentum. The turbine then straightens the flow of the stream, countering the stream’s angular momentum. The torque exerted on the turbine shaft by the fluid is proportional to the fluid’s mass flow rate. Team 16 does not doubt the validity of de-vices such as axial flow mass flow meters. Rather, the team hopes to prove the validity of thermodynamic laws governing the behavior of such devices. The rest of this report will concern itself with describing the experiment in greater detail. There are several assump-tions that had to be made in order to make ac-curate calculations. This report will outline the reasons why each assumption had to be made and why certain variables—such as changes in tire volume and air temperature—could be accurately neglected. It will deline-ate how each material/instrument was utilized. It will present the team’s data in a clear and concise manner and will conclude with the team’s findings of how this data properly ap-plies to real world efficiency.

2 METHODS

The goal of this experiment is to accurately obtain the mass of air that is entering into a tire. Team 16 utilizes a standard 26-in bicycle tire, with a 2-in tread diameter, bought locally through a bicycle retailer. Using basic ge-ometry, the team calculates the average vol-ume to be 256.61 in3. Team 16 then pumps air into the bicycle tire to give the tire its ini-tial shape. Once the bicycle tire is filled with

the initial amount of air, Team 16 is ready to begin its experimentation.

It is crucial to find out the initial conditions of the air inside the bicycle tire. The team first measures the pressure within the bicycle tire using a digital tire gauge. The tire gauge gives an accurate gage pressure within the tire measured to a tenth of a pound per square inch. Team 16 adds the local barometric pres-sure (which can be obtained from the local daily weather report) to the gage pressure of the tire, which yields the absolute pressure within the tire.

The average volume change within the tire is calculated to be 0.15 cubic feet. However, since the tire contains an initial amount of air, the volume change is always be less than the stated 0.15 ft3. Due to the small change in tire volume, the team feels it can accurately ne-glect volumetric changes.

The other measurement that needs to be taken is the temperature of the air within the tire. However, this value can be accurately assumed to be equal to the temperature of the ambient air surrounding the tire. This as-sumption can be made because given a finite amount of time both bodies will reach thermal equilibrium with each other, as stated by the Zeroeth Law of Thermodynamics.

Lastly, the tire’s initial mass is determined by weighing the tire on a scale. The weight, according to Newton’s second law of motion, is multiplied by the gravitational constant, 32.174 (lbmft)/(lbfs2) and divided by the local gravity, which can be assumed to be 32.174 ft/s2, to yield the tire’s mass.

After the initial conditions are determined, an air compressor is attached to the tire. The team switches the air compressor on and be-gins measuring the time required to fill the tire to a near-maximum air pressure, near 80 psig. When this value is achieved, the com-pressor is switched off and disconnected from the tire. The tire pressure is again measured and the tire is again weighed. The new mass of the tire accounts for the additional air that entered during the experiment.

The change in mass is then divided by the time it took for the compressor to pressurize the tire. This value is the actual mass flow rate. The actual values are weighed against the theoretical values using Microsoft Excel®

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software. The results are plotted and are given in the next section. This value is then compared to the theoretical mass flow rate.

The theoretical flow rate is determined us-ing the Ideal Gas Law, PV = mRT, and the time of the experiment. The ideal gas law is manipulated so that m = PV/RT. For the pur-poses of this experiment T and V are assumed constant, as stated above, leaving the mass, m, as a function solely of P.

3 RESULTS

A total of ten trials were run. During each run the initial and final tire pressures were re-corded. In addition, the tire was weighed both prior and at the end of each run. All data was recorded in a spreadsheet using Microsoft Ex-cel® computer software. The data table A-1, which may be found at the end of this report, shows the data tabulated for each run. As noted, all measurements were made using English units. Pressures were measured in pounds per square inch. Mass was measured in pounds. Temperature was measured in Fahrenheit and subsequently converted to Rankine. Lastly, time was measured in sec-onds. The pressure differences were then en-tered into the Ideal Gas Equation, as previ-ously described. These theoretical values for the change in mass were then compared to the actual values obtained by weighing the tire.

To determine the mass flow rate, the change in mass was plotted versus time. The resulting graph is Figure 1.

Figure 1 shows the graphical comparisons between actual and theoretical mass flow rates. A trendline was added to each set of

data. The slope of the trendline serves as the average mass flow rate. Notice that the ap-proximating trendlines differ in slope by 0.000059.

4 DISCUSSION

Although Team 16 would have liked to have assured itself that there were no ways for error to enter the experiment, the odds of this happening were doubtful. The team had predictions of how the experiment occurred and also recognized some known areas where error could have entered. The team assumed the volume was constant because the overall change in volume was small. The team also assumed a constant air temperature within the tire, which is not true because there is energy being added to the system in the form of work, which translated to heat. This energy was negligible because the overall energy added to the system was small. In addition, since the tire was exposed to an infinitely lar-ger thermal reservoir—that being the ambient air—it was conjectured that any temperature change would be immediately dissipated. However, in reality one cannot neglect the change of any factor involved, be it tempera-ture, volume, or pressure.

Secondly, while connecting and discon-necting the compressor air was inadvertently released. Any air lost during the pressure measurements or while attach-ing/disconnecting the compressor to the tire was assumed to be negligible. This too was another source for error.

Thirdly, and most obviously, the instru-ments utilized during this experiment were only accurate to such a degree that would sig-nificantly limit the accuracy of Team 16’s fi-nal results. Had the scale measured to further decimal places, a mass other than 0.04 lb could have been measured. Unfortunately, the experimental changes in mass were small and the team did not have the equipment nec-essary to measure such changes with any real meaning.

Team 16 assumed that none of these as-sumptions were factors in calculating the data. Team 16 computed a theoretical value for the mass inside the tire during its initial and final

Theoretical and Actual Results

y = 0.0006x

y = 0.0006x

0.03

0.035

0.04

0.045

0.05

55.00 60.00 65.00 70.00 75.00 80.00Time (s)

Mas

s (lb

)

Actual results Theoretical resultsLinear (Actual results) Linear (Theoretical results)

Figure 1.

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condition using the Ideal Gas Law. Using the change in mass divided by the change in time, Team 16 then calculated the tire’s mass flow rate.

When comparing the trial runs to the theo-retical results, Team 16 was pleasantly sur-prised. The results show that Team 16’s aver-age actual mass flow rate differed from the theoretical mass flow rate by only 0.000055 lbm/s. In addition, when one compares the theoretical and actual mass changes, it is ob-served that the difference between the two never differs by more that 0.1 lbm. It becomes strikingly apparent that Team 16 was signifi-cantly hindered by the fact that the scale util-ized was only accurate to the hundredth of a pound.

Nevertheless, the consistency of the ex-periments is strikingly apparent that it is obvi-ous that air does follow the Ideal Gas Laws. As a result, the determination of the mass flow rate can be accurately measured from the change in pressure.

5 SUMMARY & CONCLUSIONS

Thermodynamics attempts to predict the movement of energy throughout a system. It has been observed that certain gases behave in a predictable manner. Equations, such as Boyle’s, Charles’ and Gay-Lussac’s Ideal Gas Equation, accurately approximates the chang-ing properties of a nearly ideal gas. Thus, Team 16 experimented to see whether or not ambient air’s behavior could be approximated using the Ideal Gas Equation. Due to the budget of the project certain assumptions had to be made thus sacrificing the precision of the final data. It is within reason to conjecture that if given a larger budget and better equip-ment, Team 16 would have been able to ob-tain even more decisive results. Nevertheless, the consistency between the actual and theo-retical results emphasizes the fact that ambi-ent air’s properties can be approximated by treating air as ideal. With such an approximation decided, it be-comes possible for devices such as mass flow meters to accurately (within reason) measure the mass flow by simply examining one changing variable—in Team 16’s case, pres-sure changes. With this information on hand

the public can utilize technology with higher flow rates and consequently save time, which as previously illustrated, is one thing that the general public never has enough of.

ACKNOWLEDGEMENTS Team 16 would like to take this opportunity to thank you for investing the time to review this report. We hope that it was clear, concise, and left the reader with a better understanding of the methods behind the derivation of the mass flow rate of air into a tire. We would also like to thank Russell Joffrion for his technical support and supervision while con-ducting our experiments. Lastly, we would like to thank Dr. S. Socolofsky for his lectures concerning thermodynamic principles and his providing us with the opportunity to perform such experiments.

REFERENCES

Benedict, Robert P. Fundamentals of Temperature, Pressure, and Flow: 2nd edition. New York, Wiley. 1977

Jones, E. B. (Ernest Beachcroft). Instru-

ment Technology: 2nd edition. London, Butterworths. 1965

Çengel, Yunus A. and Turner, Robert H.

Selected Material from Fundamentals of Thermal-Fluid Sciences. New York. McGraw Hill. 2000

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1 INTRODUCTION One of the most essential components of thermodynamics is the principle of mass conservation. Without this principle, a whole area of thermodynamics would be impenetrable, thus leading to a lack of luxuries as well as some necessities that are enjoyed today. With this thought in mind, it is vital that students learning thermodynamics understand how the simple principle of conservation of mass works. One way to test this principle is by measuring the various flow rates and pressures in a container as it is drained by gravity. This experiment will measure several parameters: the vacuum pressure created by the lid, the different times it takes to drain the container with the outlet at different heights, and the amount of friction in the valve.

The conservation of mass equation implies that mass is neither created nor destroyed.

Mass flow rate is equal to the density of the liquid times the velocity times the flow area. It is known that in real fluids, the density does not remain fixed as the velocity increases because of compressibility effects (Benson 1). In the laboratory, the change in density has to be accounted for in order to determine the mass flow rate at higher velocities. Density, however, is considered constant for this experiment. The pressure also has an effect on mass flow rate. According to the equation, the mass flow rate should increase as the total pressure is increased. In this experiment, putting a lid on the container will decrease the pressure, and the flow rate proportionately decreases.

While conducting the experiments, it is necessary to take several measurements. There are a few options for measuring the various aspects of the draining container. To measure time, a stopwatch is used. The National Oceanic and Atmospheric

Project 17: Hydraulics of a Draining Container

Delynn Holub, Veronica Valero, Joyce Varghese Team 17

ABSTRACT: In order to analyze conservation of mass as discussed in thermodynamics, the following experiment, Hydraulics of a Draining Container, was performed. This was done by obtaining a container and measuring the time it takes for water to drain completely through a hole that was made near the bottom. This was repeated, but using outlets at different angles to compare the difference in times. Theoretical results were calculated, and these were compared to actual results in order to determine the coefficient of friction. The coefficient of friction was calculated to be 1.496. In the final part of the experiment, a lid was placed on the container, and the vacuum pressure was estimated by measuring the height the water had drained. This pressure was found to be an average of 7.89*10-5, yet analytical results show the pressure should have been much less that this. This is most likely because it is not possible to completely seal the container in this experiment.

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Administration (NOAA) claimed to be accurate to one second when using a stopwatch in similar experiments they conducted. NOAA also took measurements of the height of the liquid in the container using two methods, each depending on the type of liquid used. For a less dense liquid, a ruler was simply glued to the side of the box and the height was deciphered easily. When they used a more dense liquid that might leave a residue, a piece of Styrofoam was kept floating in the liquid to make it easier to decipher the height of the liquid (Simecek-Beatty 7). Since the container and liquid in this experiment are transparent, however, a floating device is not needed. Also, although gluing a ruler to the side of the container is easy to do, it is not viable since it uses a container that is not a perfect cube shape, and this experiment requires the measurement of volume (Boyes 1). Increments (in ounces) are drawn on the container itself, personalized for its shape. Measuring the times it takes for certain volumes of the liquid to drain allows for a better understanding of the velocity of the liquid through time. The remainder of this report describes the actual project and will be divided as follows. The process of this project, including steps taken and apparatus used, will be fully described in the Methods section. The findings of the experiment will be stated under the Results section. The Discussion section will compare the actual results to the expected results and identify sources of error. The Summary and Conclusions section will review the findings of the experiment and draw any important conclusions from the data. 2 METHODS The following describes the methods in order to conduct the experiment. 2.1 Assembly 2.1.1 Materials: Obtain a plastic Gladware™ container with the lid, a flexible straw, measuring cup,

stopwatch, binder clip, screw, superglue, water, ruler, and index cards. 2.1.2 Assembly: After finding all of the materials needed, use the screw in order to make a hole on one side of the container, approximately a half of an inch from the bottom. The straw should be trimmed so that the length from the container to the middle of the bend is two and a half inches. From the bend to the outlet, the length should be one inch. Then insert the straw into the hole, flush with the inner wall of the container. Use superglue on the outside of the container in order to secure the straw. Now attach the binder clip to the straw, as close as possible to the container, so that no water leaks out. In order to make the straw more stable, place index cards under the straw for support. Put as many as needed to make the straw parallel with the table. 2.2 Conducting the Experiment 2.2.1 Preparation Using the measuring cup, add two ounces of water to the container at a time. Make sure to start the markings at the middle of the hole. This is the zero marking. Use a permanent marker, and calibrate the level by marking one side of the container for every two ounces, up to twenty ounces. Be sure to measure the diameter of the straw with the ruler, and record this data. 2.2.2 Collecting the Data for Experiment 1 Fill the container to the highest marked volume. For the first trial, remove the lid. The straw must be straight so that the outlet is at the same level as the hole. Release the valve by taking off the binder clip. As the container is draining, record the time it takes to reach each 2-ounce marking. 2.2.3 Collecting the Data for Experiment 2 In order to measure the vacuum pressure, put the binder clip back on the straw, and again fill the container to the top

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marking. However, before releasing the valve, put the top on the container, and make sure that no air is leaking. When this is done, take the binder clip off, and wait until the water stops draining. At this point, use the ruler to measure the height from the 20-ounce mark to the point where the water stops, and record this value. 2.2.4 Collecting the Data for Experiment 3 Again fill the container to the highest marked volume. Remove the lid. It is removed for the duration of the experiment. Turn the portion of the straw from the bend to the outlet to a 90-degree angle upwards. Release the valve, and record the time it takes for the container to drain every two ounces using the stopwatch. Repeat this, but with the straw bent at a different angle between 0 and 90 degrees. Using the ruler, measure and record the vertical distance from the outlet to the hole. Repeat twice more, but with a 90-degree angle downwards, and one angle between 0 and 90 degrees below the horizontal. 2.3 Analysis 2.3.1 Experiment 1 In Excel, plot the times recorded at the various volumes into graphs representing volumetric flow rates. In the spreadsheet, find mass by multiplying volume and density. Then, plot mass versus time. Find the maximum pressure using the formula P=ρgh where h equals the height of the water after the straw stops leaking. 2.3.2 Experiment 2 Calculate the maximum pressure with the lid sealing the container using the height that was recorded. 2.3.2 Experiment 3 Measure the times required to drain the container with the straws at different levels. Compare these results. 2.3.3 Coefficient of Friction

To find the coefficient of friction, calculate the theoretical value of the time required to drain the container by using m=ρvA. Compare this theoretical value to the actual result in order to obtain the coefficient of friction. 3 RESULTS

The following are the results gathered while conducting experiments testing the hydraulics of a draining container. Table 1 represents the time required to drain the container with the outlet the same level as the hole. Table 2 represents the height at which the water stopped draining with the lid on the container. It also shows the vacuum pressure calculated at each height. Figure 1 compares the time taken to drain a container with the outlet at various heights above and below the hole. With respect to the horizontal, height was 1.25” for Trial 1, .825” for Trial 2, -1.25” for Trial 3, and -.825” for Trial 4.

Straight Straw, Lid Off Trial 1 Trial 2 Trial 3

Volume, oz Time (s) Time (s) Time

(s) 20 0 0 0 18 7.9 3 4 16 14 7 7 14 18 10 11 12 23 13 14 10 26 18 18 8 32 22 22 6 39 28 27 4 48 34 34 2 59 42 42 0 84 56 57

Table 1: Time recorded at changing volumes during Experiment 1.

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4 DISCUSSION 4.1 Experiment 1 In Experiment 1, the time it took for the container to drain with the lid off is recorded at every two ounces. Using the information in Table 1, the volumetric flow rate was found by dividing the change in volume over the change in time at every two ounces. The volumetric flow rate was then multiplied by the density of water to obtain mass flow rate. The mass flow rate at every two ounces was then averaged for each trial and the three trials were averaged together to obtain an overall average mass flow rate of .0026 lbm/s. Using analytical methods, the theoretical velocity of water was found to be 1.831 ft/s using the formula Vt=sqrt(2gh), where g is gravity and h is the initial height of the water. The theoretical mass flow rate was then found to be .00389 lbm/s using the formula mout,a=(ρVA), where ρ is the density of water, V is the velocity and A is the area of the outlet. This evidence essentially shows that the theoretical mass flow rate is greater than the actual mass flow rate, which would be correct since any friction would slow the actual mass flow rate down. By assuming a constant actual mass flow rate, the actual and

theoretical flow rates can be compared to find a coefficient of friction. Setting the two flow rates equal to each other using the formula mat=kmtt, where ma is actual mass flow rate, mt is the theoretical mass flow rate, k is the coefficient of friction and t is time, the coefficient of friction becomes 1.496. 4.2 Experiment 2 In Experiment 2, the height at which the water stopped draining was recorded in order to find the maximum vacuum pressure the lid created. Using the information from Table 2, the vacuum pressure was found to be an average of 7.89(10-5) psia. Using analytical means, if the lid sealed the container perfectly, the maximum vacuum pressure would have been 2.35(10-5).

Table 2: Pressure calculated from results of Experiment 2.

Straight Straw, Lid On h (from bottom) (in) P=pgh (psia) Trial 1 2.09375 7.88585E-05 Trial 2 2.125 8.00355E-05 Trial 3 2.0625 7.76815E-05

Outlet Above and Below Hole, Lid Off

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80 90 100

Time (s)

Vol

ume

(oz)

Figure 1: Comparison of results of Experiment 3. Diamonds represent Trial 1; squares represent Trial 2; triangles represent Trial 3; crosses represent Trial 4.

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However, since the container used was Gladware™, it was not possible to completely seal the container. 4.3 Experiment 3 In Experiment 3, the time required to drain the container was measured with the outlet at different levels above and below the hole. The results displayed in Figure 1 show that when the outlet is above the hole, the water stops draining at approximately the height of the outlet. When the outlet is below the hole, no matter how far below the hole it is, the water will still drain faster than if it were at the same height. The water will also drain at approximately the same rate at any distance below the outlet. 5 SUMMARY AND CONCLUSIONS 5.1 Summary An important concept in thermodynamics is mass conservation. One way to investigate this principle is to measure the hydraulics of a draining container. First, a calibrated container is used to find the time required for the water to drain every two ounces. The second part of the experiment measures the height that was drained when the lid was on the container. The third part of the experiment again measures the time, but with the outlet at different angles, both above and below the hole. Theoretical values are calculated and compared to actual results. Any differences in values are due mainly to the coefficient of friction. The data from the first experiment is used in order to find the coefficient of friction, and the second experiment is conducted to find maximum vacuum pressure. 5.2 Conclusion This experiment displays the effects of gravity on the time it takes for a liquid to drain from a container. In Experiment 3 the liquid drains slower when the outlet is above the hole because it fights gravity and friction to leave the container. When the outlet is below the hole, however, the liquid drains faster because gravity works with it. This is all

compared to results in Experiment 1. Friction also helps delay draining time since it can be seen that the coefficient of friction calculated is not negligible. In Experiment 2, vacuum pressure is not as much as it should be ideally, probably because it is not possible to have an absolute airtight seal on the container. Overall, despite such lacking in having an ideal situation with this experiment, the effects of pressure, gravity and friction are still clearly visible. REFERENCES

Benson, Tom. “Compressible Mass Flow Rate”. Glenn Research Center. 9 Nov2003.<http://www.grc.nasa.gov/WWW/K-2/airplane/mflchk.html>.

Boyes, Walt. “When Do You Measure

Mass Flow?”. M.R. Francechini, Inc. July 2003: pages (1). 18 Nov. 2003.<http://www.mrfpr.com/Article-Mass-July.pdf>.

Simecek-Beatty, Debra, William J. Lehr,

and Jeffrey F. Lankford. “Leaking Tank Experiments With Orimulsion™ and Canola Oil”. National Oceanic and Atmospheric Administration. December 2001: pages (30). 9 Nov. 2003. <http://response.restoration.noaa.gov/oilaids/pdfs/tank.pdf>.

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Project 18: Rate of Heat Transfer from an Apartment Jonathan E. Howson, Andrea M. Thompson, Jennifer M. Walling Department of Civil Engineering, Texas A&M University, College Station, USA John W. Trout Department of Mechanical Engineering, Texas A&M University, College Station, USA ABSTRACT: This experiment will attempt to calculate the heat flow out of an air-conditioned apartment. The setup of this experiment is as follows: First, all electrical devices in the apartment are unplugged; second, block off the back room of the apartment due to a large temperature difference brought about by the sun; third, remove the vent covers to allow unrestricted air flow. The measurements include the initial and final electric meter readings, the outside air temperature, the initial air temperature in the apartment, the air temperature exiting the vents, the air temperature in the apartment every ten minutes once the air-conditioner is turned on, and the time it takes for the air-conditioner to turn back on once the room reaches a temperature of 65°F. The heat flow into the apartment is 21600kJ. The heat flow out of the apartment is 28800kJ. 1 INTRODUCTION Life today is not what it used to be. Today we take for granted what people a hundred years ago didn’t even dream of. We get into our 120°F car and within five minutes have it down to a nice 75°F, or we step from the sweltering afternoon heat to the cool confines of our home. This is made possible by the invention of air-conditioners. However, air-conditioners use electricity, and in today’s market electricity is expensive, so naturally consumers want more efficient air-conditions so their electric bills won’t be as high. What they don’t realize is that better insulating of their homes would drastically reduce their electric bills without the purchase of a more efficient air-conditioning unit. The cold air in a house leaks out around doors, through windows, and also through walls and ceilings. The more insulation that is installed in the home, the slower the heat flow is out of the house. In this experiment

we are attempting to find the heat flow out of an apartment.

Through research it is discovered that the proper way to perform this test is to use an ammeter and a voltmeter in a lab setting. The ammeter measures the change of amperage in the air-conditioner. The voltmeter measures the total voltage in the given time period. Multiply these two together and the power output is given. A wind sensor measures the velocity of the air entering and exiting the air conditioner. The air ducts are level with no bends. Also, the temperature is measured with digital temperature gauges at specific time intervals and at various locations throughout the system. The temperature entering the air-conditioner is regulated and there is no warming of the air do to the sun and no wind.

In this document the next four sections are the methods, results, discussion and summary. The Methods section entails the actual steps of the procedure. The Results section is a record of the data found when the experiment was performed. The

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Discussion section relates the team’s assessment of the results found during the experiment to the analytically calculated results. The summary portion gives our personal opinions on the results of the experiment.

2 METHODS To begin our experiment we first decide to block off parts of the apartment. The back bedroom is chosen because it is in direct sunlight and is considerably warmer than the rest of the apartment. We block the vent in that room by using a plastic bag with tape. This kept all of the cold air from traveling into that room. Then the door was shut and a towel is placed at the base of the door to prevent any cold air from leaking into the other rooms. The vent covers are removed from all vents for two reasons: first, so the area of the vents can easily be taken, and second, so there is no restriction to the airflow exiting the vents. Inside we turn off every electrical device. All the windows are shut and the curtains are closed, to block out any sunlight.

Outside, the electric meter is read and the temperature is taken with a thermometer. The electric meter is not moving at this point in time. This proves that all the electrical devices inside the apartment are successfully turned off.

The temperature is taken inside before the experiment began. Then the temperature is set on the thermostat to 50˚F. Next, find the velocity of air exiting each vent. Now find the exiting air velocities by using a cotton ball, a ruler, and a stopwatch. The first person holds the cotton ball at the top of the vent, just within the air stream. The second person holds the ruler at the base of the vent, measuring the distance the cotton ball travels. The third person holds the stopwatch, starting it when the cotton ball is released and stopping it as the cotton ball crosses the ruler. The exiting air velocity of each vent is found by the above method three times and then averaged for a final

velocity. During this experiment find the temperature in two different places approximately every ten minutes. One place is in the living room and the other place is in the hallway on the thermostat.

Three people are inside the apartment as the experiment is conducted. Halfway through the experiment an outside person reads the meter. The temperature takes 81 minutes to drop from 81˚F to 65˚F. Then waite six minutes for the air to come back on.

Once this is finished go outside to read the meter again. Find the temperature outside to see if it has varied.

3 RESULTS

Table 1 is a listing of the temperatures recorded by the thermostat and the thermometer, and the times that they were recorded. Table 2 lists all relevant data collected before and after the experiment was run. Table 1: Measurements taken during the experiment.

Time (min)

Thermostat (F)

Thermometer (F)

1:34 75 79 1:44 74 76 1:54 71 74 2:04 69 72 2:14 68 71 2:24 67 70 2:28 65 70 2:36 65 70 2:44 65 69 2:53 65 69 2:55 65 69

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Table 2: Significant Data taken. Measured Data

Meter reading prior to experiment

16671 kWh

Meter reading after the experiment

16673 kWh

Temperature of outside 84.00 (F) Original temp. of house 81.50 (F) Velocity of Living room 1.58 ft/sec Area of vent (living room) 82.5 in2 Velocity of kitchen air 1.9 ft/sec Area of vent (kitchen) 55 in2 Velocity of Bathroom 1.51 ft/sec Area of vent (bathroom) 38.25 in2 AC cut off time 81 min Temp. at cut off time 65 (F) Time for AC to come back on

6 min

Only one trail was run do to the time constraints. Also, the experiment would have gotten different readings each time it was run to variations in the outside temperature, wind velocity, cloud cover, etc.

Figure 1 shows the plot of the data in Table 1 with the linear interpolation line and equation graphed over the two data sets.

Temperature vs. Time

y = -160.5x + 87.23

y = -186.35x + 86.0960

65

70

75

80

85

1:30 1:44 1:58 2:13 2:27 2:42 2:56

Time (min)

Tem

pera

ture

(F)

Thermostat Thermometer

Linear (Thermometer) Linear (Thermostat) Figure 1: Linear interpolation lines for the thermostat and thermometer points.

4 DISCUSSION

The assumptions made for this experiment were:

• The three humans occupying the apartment during the time of the experiment produce zero heat.

• No heat transferred into the measured rooms from the blocked off room.

• No stored heat flowed into the room from the objects in the room.

• No heat or air-conditioning came from the apartment below or beside our test apartment.

• The air flow out of the vent was uniform across the vent

• The system is a non-steady state system

• The apartment cooled at a constant temperature through out the apartment

• The apartment was free standing with equal outside temperature surrounding it

We came up with three steps to solve for the heat flow out of the apartment. Step 1: Find the coefficient of performance (COP) for the air-conditioner.

The COP for the air-conditioner was found by calling up the company and asking them for it. The unit is a CLJ 24-1, 12 seer, 2 ton split AC unit. The COP given to us by the company was 3.00. With this information we are able to move on to step two. Step 2: Find QL from COP = QL/Win

From this equation we can calculate the heat flow into the apartment by solving the equation for QL:

QL= COP * Win QL= 3.00*2 kWh *(3600kJ/kWh) QL= 21600kJ

Step 3: After you have QL find QH from COP = 1/ ((QH/QL) -1)

We did not believe this was a Carnot cycle so the COP could not be calculated from the reversible form of the above equation. However, this equation can now be used to calculate the heat flow out of the apartment. COP = QL/(QH – QL)

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QH – QL = QL/COP QH = QL/COP + QL QH = 21600kJ/3 + 21600kJ QH = 28800kJ 5 SUMMARY AND CONCLUSIONS For an average size one bedroom apartment using a CLJ 24-1, 12 seer, 2 ton split AC unit and cooling the rooms with out the bedroom it takes approximately 81 minutes. The coolest temperature we were able to reach was 65 ˚F. The heat flow from the air conditioner into the apartment, QL, was found to be 21600kJ. QH, the heat flow out of the apartment into the environment, was found to be 28800kJ.

The lowest temperature the air conditioner can actually reach is 50 ˚F; however, the temperature would only reach 65˚F. After considering this for quite some time we came to the conclusion that this is the equilibrium temperature for this apartment with this air conditioning system. This also meant that an enormous amount of heat loss must occur on a regular basis.

To reconstruct this project with less error the assumptions used should be corrected. First, there should be no people in the room. The area should be completely sealed with no extra objects that might contain heat. The air conditioner needs to be attached to the measured area by a single duct. The room should have an outer controlled environment, with no direct sunlight. There must be no other rooms attached to the outside of the room. Next, the equipment used to measure the temperatures should be accurate up to the thousandth place. Finally, the power that is measured should be found with something other than the electric meter box.

The project solved the problem of finding the heat transfer out of the apartment, however; this could have been more accurately found with fewer assumptions.

REFERENCES

Althouse; Braccion; Turnquist. Modern Refrigeratin and Air Conditioning. Goodheart Willcox Company. 2000, pg. 1045.

Technology Division Simulation & Testing Laboratory. August 30, 1994. Report No. F63D400-4-06.

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1 INRODUCTION

The process of water draining through a hole at the bottom of a container may seem simple and straightforward, but upon closer inspec-tion it has a dynamic and complex nature that fluid mechanics can help illustrate. Situations similar to this arise everyday, such as water draining from a bath tub or emptying a tanker filled with gasoline into an underground res-ervoir. This experiment will specifically ana-lyze the time required to drain a pitcher filled with water. These results will allow us to make general assumptions for other systems such as those stated above. The experiment will be run with different initial states to gain a full understanding of the effect of height on drain time.

If this experiment were performed in a pro-fessional laboratory, more advanced equip-ment would be available and higher accuracy

could be obtained. Lasers, precision scales, and time-lapse photography are just a few ex-amples of the quality of equipment available on the professional scale. Devices used to measure fluid flow could also be used in order to accurately measure the velocity of the exit stream.

This experiment could be slightly modified to allow for these devices. Pitot tubes, orifice meters, and venturi meters could all be incor-porated into the container to allow for these measurements (Hardy 2001; Upp 2002). The velocity could be measured at different time intervals and then integrated to obtain more accurate results.

Lasers coupled with a chronograph could be used to obtain very accurate time readings. The lasers could be placed at each height in-crement at which the time is to be recorded. When the water level falls below that height, the laser would then trigger a chronograph

Investigating the fluid dynamics of a draining container

James Schulze, Steven Schulze, Chris Shaw, Juan Jurado Students, Texas A&M University, College Station, TX, USA

ABSTRACT: The simple process of a fluid draining from the bottom of a tank is readily observed in everyday activities. This experiment is intended to investigate and describe the fluid dynamics involved in the draining of water from a container. Water is observed draining from a plastic household pitcher and the time is recorded at specific intervals. Initial heights of 5, 10, 15, and 20 cm are used to present a broad range of data. An analytical solution is provided using fluid me-chanic principles; however, friction was not factored into this solution. It is expected that friction would cause the observed times to be longer than the calculated times. The observed time to drain was faster than the calculated time because the cross section of the container used in the experi-ment was not uniform. The bottom centimeter was curved rather than straight and therefore skewed the results. Ignoring the last centimeter of the container the results are exactly what is to be expected when friction is present.

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that would precisely record the time (Rinkevi-chius 1998). This would require no human input and would significantly reduce the error involved in this portion of the experiment.

The remainder of this document describes the experiment conducted in more detail, gives a summary of the results obtained, and discusses the conclusions that can be drawn from them. The Methods section describes the procedure to perform this experiment, as well as how to construct the apparatus and how the measurements were taken. The Re-sults section contains a summary of the data obtained during the experiment. In the Dis-cussion section, an analytical solution using mathematics and fluid mechanics can be found. In this section, the predictions using the analytical solution and the measured re-sults will be compared and any discrepancies will be discussed. And finally the Summary and Conclusions section will summarize the major results obtained as well as conclusions formulated from this experiment. 2 METHODS

This experiment was not conducted in a labo-ratory setting; all the materials can be found in a typical home setting or at a local super-market. A four liter plastic pitcher was used as the reservoir for the liquid that would be drained. It is important to use a pitcher with a uniform cross sectional area so that for a given change of height, the change in volume will be the same, no matter where the change of height occurred. The pitcher should either be transparent or translucent so that the height of the level of the liquid can be seen outside of the pitcher. A ruler is used to place mark-ings at equal increments on the pitcher and a precision stopwatch is used to measure the change in time. The formulas presented in this report are formed on the basis that water is the liquid to be drained.

First, drill a 4 mm diameter hole on the side of the container as close to the bottom as pos-sible. The results may deviate from the ana-lytical solution if the hole is not drilled as close to the bottom as possible and therefore great care should be taken in this step to drill the hole correctly. This is because the ana-lytical solution assumes that the container

completely drains. Make sure the hole is free of obstructions and that water flows steadily out from it. Use a ruler and a sharpie to place markings at increments of one half of a cen-timeter on the pitcher, starting at the bottom. These markings will be used to calculate the change in height of the water level for a given time period.

Next, plug the hole at the bottom so that none of the water will drain and fill the pitcher with water to a specified level and re-cord the initial height. Make sure none of the water leaks out. Precisely start the stopwatch when the hole at the bottom of the container is unplugged. Now, record the time it takes for the water level to drop in one centimeter in-crements until the water has completely drained. Also record the time when water has ceased to drain out of the hole. Smaller height increments may be used, such as half or quarter a centimeter, in order to achieve more precise results. Repeat the process mul-tiple times for the same water level height to help reduce some of the errors that are not factored into the analytical solution.

Graph the data obtained with time on the abscissa and water level on the ordinate. Next, use Excel to average each trial and then to normalize the data. This should be done by dividing each recorded height level by the ini-tial height and the time at each individual height by the total time. Finally, compare the results obtained to the analytical solution pre-sented in the Discussion section of this report. This process should be repeated multiple times but with each successive trial starting with a different initial water level height. 3 RESULTS

This experiment was performed with four dif-ferent initial water level heights: 20 cm, 15 cm, 10 cm, and 5 cm. The process was re-peated three times for each initial level and the time was recorded at one centimeter dec-rements and when the water stopped draining. The data from the three trial runs for each setup was averaged to obtain a set of data for each initial height. Figure 1 displays the av-erage of the three trial runs for each initial setup on a normalized height versus time graph.

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Figure 1: Normalized height versus time. Each set of data is an average of the three trial runs performed for each height setup.

In order to compare each initial height setup

with one another, the time was also normal-ized and graphed. Figure 2 presents this graph. This graph shows how consistent our data is when it is compared to the other trials.

Figure 2: Normalized height versus normalized time. Each set of data is an average of the three trial runs per-formed for each height setup.

Table 1 displays the total time required for the water to drain from the initial height. The observed time is an average of the three trial runs performed. The calculated time is de-termined from the analytical solution pre-sented in the Discussion section of this report. The percent error for each setup is also re-ported. The percent error is reported as nega-tive because the observed time was less than the calculated time.

Table 1: Total time for water to drain from the con-tainer at different initial water level heights. The calcu-lated time was found using fluid mechanic principles. This data was obtained using a 15.6 cm diameter pitcher and a 4 mm diameter hole.

Initial Height (cm)

Calculated Time

(s)

Observed Time

(s)

Percent Error (%)

20 307.17 305.16 -0.65 15 265.98 254.49 -4.32 10 217.17 201.98 -6.99 5 153.57 128.38 -16.40

4 DISCUSSION

The purpose of this experiment is to calculate the time required for water to drain from a container. The analytical solution to this problem is rather straight forward and is pre-sented in this section. First, the exit velocity of the water is given by the equation:

z g 2 e =V where g is the acceleration due to gravity and z is the height of the water level. Next, the mass flow rate of water leaving the tank is de-termined. The mass flow rate, outm , equals the density of water, ρw, multiplied by the exit velocity given above, Ve, and the area of the hole, Ah. Therefore,

outm = wρ eV hA The mass of the system is given by:

sysm = wρ sysV and the volume of the system is given by Vsys= At z. Conservation of mass gives the equation:

inm - outm = dtdm

but inm is zero. Now, substituting the equa-tions for outm and sysm the equation becomes:

- wρ eV hA = dtVd sysw )( ρ

The density of water is constant and therefore can be canceled from both sides of the equa-tion. Substituting Ve and Vsys into the equa-tion results in we get the differential equation:

z g 2 - hA = tA dtdz

After putting this equation in a form that can be integrated, we obtain the equation:

∫2

1

t

tdt =

hAAt−

g 21∫

2

1

h

h zdz

Height v. Time

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00

Time (s)

Hei

ght (

h / h

)

20 cm15 cm10 cm5 cm

Height v. Time

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.20 0.40 0.60 0.80 1.00

Time (t / t )

Hei

ght (

h / h

)

20 cm15 cm10 cm5 cm

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But the left side is just the change in time and after integrating the right side we get:

t∆ = hA

At−g 2

1 ( )( )122 hh −

Therefore, to calculate the time required for the water level to drop from h1 to h2 simply substitute the values for h1 and h2 along with the calculated cross-sectional areas of the tank and hole into the equation above and solve for ∆t.

This experiment was performed with initial heights of 20 cm, 15, cm, 10 cm, and 5 cm. Table 1 in the Results section gives the calcu-lated and average observed times for water to drain for each of these setups. The percent er-ror is also reported in this table. For a height of 20 cm, it took 305.16 seconds to drain. Solving the above equation for an initial height of 0.20 m draining to a height of 0.00 m, the time is calculated to be 307.17 seconds. This results in a -0.65% error. It is clear that the observed time is shorter than the calcu-lated time. However, the observed time is ex-pected to be longer than the calculated time due to friction. The same is true for the other height setups, and the percent error becomes larger for smaller initial heights.

The reason for this disagreement is due to the fact that the container used had a major flaw in it. It was rounded in the bottom cen-timeter instead of having a sharp corner. When the height is compared to the time for each trial run, it is obvious that the data be-comes distorted when the water level drops below one cm. The curve is consistent with what is expected until this point in which it moves below the ‘measured’ line of best fit. Before this point, the system behaves in a way that it is expected. The time recorded at each height level is slightly longer than what the analytical solution predicts.

This flaw in the container significantly af-fected the data because it was at the bottom of the container. Since the container was curved, this caused the volume of the last cen-timeter to be smaller than if it were square. Therefore, the observed time for the last cen-timeter to drain is expected to be less than the calculated time. The equation stated above predicts a time of one minute nine seconds for the last centimeter to drain. This time ac-counts for approximately 22% of the total

time to drain from a height of 20 cm and this fraction increases as the height decreases. The last centimeter significantly affects the total time to drain and therefore this flaw caused the total time to be considerably less than the predicted time.

Figure 2 demonstrates the consistency of our data when it is compared to the different setups. The normalized height is compared to the normalized time for each setup. It is ob-vious from the graph that the data from each setup agrees with the data from the other set-ups. The 5 cm line slightly deviates from the rest of the lines because the time for the last centimeter to drain accounted for approxi-mately 45% of the total time.

Even though our container was not perfect, the results were very consistent on each trial run. Any deviations between the trials were small and were due to human error in the re-cording of the time. There may also be devia-tions due to the presence of a meniscus at the surface of the water. The time may have been recorded at slightly different heights because it was sometimes unclear when the water dropped to a certain level. This is more ap-parent when the water level is low because the height is decreasing at a slower rate and there is more room for error. 5 SUMMARY AND CONCLUSIONS

The experiment described in this report ana-lyzes the draining of water through a hole at the bottom of a container. Many systems in society can be modeled as a simple container with a draining fluid released from the bottom of the container. Using fluid mechanics and basic calculus an analytical solution was pre-sented. An experiment was prepared and conducted to test the solution and observe de-viations, limitations, and similarities to the analytical solution. The water level in the container as a function of time was observed when conducting the experiment. Using an Excel spreadsheet the data was analyzed and plotted.

The results indicated that the analytical so-lution closely approximates the experiment conducted. It can not be a perfect model for the draining of the fluid without a correction factor to account for frictional forces. Our

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data supported this statement because the ac-tual time to drain to a certain level was longer than the calculated time. Because friction is present throughout the entire container, the force was compounding upon itself, making the deviation from the analytical solution greater the longer the experiment ran. How-ever, the measured times for the container to empty was shorter than the calculated value. This is because the apparatus used had a flaw in which the bottom centimeter was curved, changing the dynamics of the flow. Ignoring the last centimeter in the container, the results were exactly what was expected when friction is present. REFERENCES

Hardy, Jim E. (2001). Flow Measurement Methods and Applications. John Wiley & Sons, Inc. New York. 4 – 9.

Rinkevichius, B.S. (1998). Laser Diagnos-

tics in Fluid Mechanics. Begell House Inc. Publishers. New York. 12 – 13.

Upp, E. L. (2002). Fluid Flow Measure-

ment: A Practical Guide to Accurate Flow Measurement. 2nd Edition. Gulf Publishing Company. Boston. 169 – 179.

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ABSTRACT: The purpose of this project is to explore experimental ways to determine the den-sity of an unknown object using the Buoyancy Force. Buoyancy forces are present on any body in a fluid. This force is dependent on the density of the fluid and the volume of the object’s dis-placement in that fluid. 1 INTRODUCTION

Have you ever been swimming and wondered how you were able to float in water? When you are submerged in water, the densities of your surroundings are much greater than when you are in air. Why do some things float in water and while some do not? A he-lium-filled balloon floats in air, is there some relation between your body floating in water and the helium-filled balloon in air. Does this depend on shapes or weights? Does the com-position of the object contribute to this spec-tacle?

The act of floating is caused by a phe-nomenon called the buoyant force. The force that tends to lift the body is called the buoyant force. When an object is submerged in fluid, there are forces from the fluid that act on the submerged object. This buoyant force is caused by the increase in pressure in a fluid with depth; the further submerged an object is the greater the pressure exerted on the object becomes (Cengel, 437). The two forces we are interested in are the forces acting perpen-dicular to the centroid on the top and bottom of the object. The force on the top of the ob-ject is due to the pressure, and acts in a downward direction. The same is true for the force acting on the bottom of the object ex-

cept the force is slightly greater due to the in-crease in depth and the force acts in an up-ward direction. The difference in the two forces is the buoyant force, and acts in a net upward direction (McGraw-Hill 2001). The buoyant force is a relation between the den-sity of the fluid, the object’s depth and the surface area of the object parallel to the fluids surface. In order to float, the buoyant force must be greater than the force due to the ob-ject’s mass. That means the net difference in the forces is in an upward direction.

There is significance beyond merely caus-ing an object to float which makes buoyancy important. After the necessary calculations are made, it becomes clear that the buoyant force is equal to the weight of the fluid dis-placed by the object. This observation is known as Archimedes’ Principle. The princi-ple further states that the buoyant force acts through the centroid of the object (Cengel, 438).

Using this knowledge, our experiment will determine the density of a roll of quarters by submerging the object in water and compar-ing the weights of the roll in and out of the water. To find the overall density of our roll of quarters, we will use a hanging scale. The detailed steps can be found in the methods section. The hanging scale will be used to

Project 20: Buoyancy Force and Density M. Lutz, J. Martin, J. S. Sokol, T. N. Stephens & L. M. Strban Students, Texas A&M University, College Station, Texas, USA

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measure mass of the object in and out of wa-ter. Once the masses are determined, the av-erage density can be determined. Another method to find the density of an object would be to measure the volume of water it dis-places when submerged and divide the known mass by this volume (Kreith).

2 METHODS

First the proper materials must be gathered, please see Table 1 below.

Table 1: List of Materials Needed Materials Needed One roll of quarters with plastic wrapper One roll of monofilament string One 5 gallon bucket One hanging spring scale Water to fill the bucket Pencil and Paper

Once the proper materials have been con-

gregated, the experiment may begin. Begin by first taking the roll of quarters and securely at-taching a piece of monofilament string to it. The monofilament string should be at least 50 cm. Once the roll of quarters is firmly attached to string, measure the mass of the roll of quar-ters by using the hanging scale. Once the mass is determined, record the data in a table. Now determine the mass of the roll of quarters while submerged in water. Make sure the roll is touching neither the sides nor bottom of the container. The measured masses must be con-verted into forces. Their equivalent forces would be weight. The buoyancy force is de-termined by taking the difference between the weights in air and in water. Repeat the process several times to reproduce the results and get more accurate results.

3 RESULTS

Both weight and buoyancy force act on the centroid of the object. If the buoyant force is equal to the weight of the quarters, the quar-ters will float. But by using common intui-tion, it is known that a roll of quarters will sink. To determine the average density of the

roll of quarters, the following variables and equations are used (Cengel). Table 2. Definition of Variables

Symbol Variable Name V Volume ρW Density of Water ρQ Density of Quarter g Gravitational Constant FT,air Weight in air FB Buoyancy Force FT,water Weight in water π Pi r Radius of quarter h Height of Roll of Quarters m Mass of Roll of Quarters

To find the volume of the roll of quarters,

the following equation is used. Equation 1. Volume of a cylinder

V = πr2h

To find the weight of an object, the follow-ing equation is used: Equation 2. Weight

W = FT, air = ρQgV = mg This can also be written:

ρQ = F T,air / (gV)

Equation 3. Buoyant Force relation to Vol-ume

V = FB / (ρWg)

Equation 4. Buoyant Force FB = FT, air - FT,water

The results were calculated by using an

excel spreadsheet to process the data. The complete spreadsheet can be seen in appendix A. Measurements were taken of the masses of the roll of quarters both in air and under water. From there the data was converted from US Customary units to SI units. The

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masses were then converted into forces using the gravitational constant. From there it was simply a matter of utilizing equations 2, 3, and 4. The percent error for all ten trials was 17.07%. Considering that trial one data can be considered an outlying data point percent error can be determined without that point. That leaves the percent error as 5.94%. This shows the data was fairly accurate and that the experiment went well. The tabulated re-sults can be seen below in Table 4. Table 3. Experimental Results

Calculated Quarter Density ρQ (mg/mm3) % Error

3.801 117.21 1.796 2.61 1.727 1.29 1.966 12.33 1.662 5.03 1.813 3.63 1.675 4.27 1.89 7.98 2.013 15.04 1.727 1.29

Average (All Trials) 17.07 Average (Tr. 2-10) 5.94

4 DISCUSSION

Also, basic properties of quarters are listed in the following table. These values were used for comparison and to determine percent error for the experiment (USmint.gov).

Table 4. Common Properties of Quarters Common Properties of Quarters Composition Cupro-Nickel 8.33

% Ni Balanced Cu Mass 5.670 g Diameter 24.26 mm Thickness 1.75 mm Volume 3235.7 mm3 Density 1.75 mg/mm3 The found densities in the experiment were compared to the density listed in Table 4, to configure a percent error. By viewing the

percent errors found in Table 3, one can see that some results were very close to the actual density and some were not. This can be be-cause of the hanging scale that was used. The digital pound force measuring device was only accurate to two significant digits. More than two significant digits need to be ob-tained for a more accurate reading. The larg-est percent error encountered was 117.21 per-cent, relative to the 3.801 quarter density calculated, which was way above any of the other results. This may be due to the device not being utilized in quite some time. Overall the calculated results were fairly accurate to the US Mint’s listed density of a quarter, or for our case, a roll of quarters.

5 SUMMARY AND CONCLUSION

Our group chose to do an experiment on the measurements of Buoyancy forces and densi-ties of objects in water. Put more simply, we wanted to know why some objects float in water and why some do not? By using Ar-chimedes’ Principle, which states that buoy-ant force is equal to the weight of the fluid displaced, we were able to attain accurate measurements on a roll (40) of quarters. By using quarters we were able to compare our weights and densities to the already calibrated coins. The data gathered from the submerged quarters is compared to the weights in air, and thus the density can be achieved. Our data was recorded into a spreadsheet that calcu-lated weight, buoyant force, and the meas-urement weight in water.

Because of the simplicity of the methods that we used, this project will be very easy to replicate. The main idea behind the theory is that a large body of water has to be used to get a more accurate buoyant force. By using the spring scale we took a reading of the mass of the roll of quarters in the water allowing us to calculate the density. Accounting for dif-ferences caused by the real world, we accept the fact that our calculations will not be exact, however, our calculations are very close to the actual. Common properties of the quarter help us determine how accurate and precise our results are.

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REFERENCES

Cengel, Yunus A.. Fundamentals of Ther-mal-Fluid Sciences. New York: McGraw-Hill Primis Custom Publlish-ing,2001.

Munson, Bruce R.. Fundamentals of Fluid

Mechanis. John Wiley &sons, Inc., 2002.

Kreith, Frank. The CRC Handbook of Me-chanical Engineering. Fluid Mechanics, 3-7. New York: CRC Press, 2001.

http://usmint.gov/about_the_mint/index.cf

m?flash=yes&action=coin_specifications

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APPENDIX

Mass in Air (lbm)

Mass in Wa-ter (lbm)

Mass in Air (kg)

Mass in Water (kg)

FW

(N) FTW (N)

FB

(N) V (m3) ρQ

(mg/mm3) % Error

Trial 1 0.40 0.30 0.181 0.136 1.811 1.334 0.476 4.773E-05 3.801 117.21 Trial 2 0.51 0.23 0.231 0.104 2.309 1.023 1.286 1.288E-04 1.796 2.61 Trial 3 0.42 0.18 0.191 0.082 1.901 0.801 1.101 1.103E-04 1.727 1.29 Trial 4 0.44 0.22 0.200 0.100 1.992 0.979 1.013 1.015E-04 1.966 12.33 Trial 5 0.37 0.15 0.168 0.068 1.675 0.667 1.008 1.010E-04 1.662 5.03 Trial 6 0.46 0.21 0.209 0.095 2.082 0.934 1.148 1.151E-04 1.813 3.63 Trial 7 0.39 0.16 0.177 0.073 1.766 0.712 1.054 1.056E-04 1.675 4.27 Trial 8 0.48 0.23 0.218 0.104 2.173 1.023 1.150 1.152E-04 1.890 7.98 Trial 9 0.41 0.21 0.186 0.095 1.856 0.934 0.922 9.238E-05 2.013 15.04 Trial 10 0.42 0.18 0.191 0.082 1.901 0.801 1.101 1.103E-04 1.727 1.29

Average (All Trials) 17.07 Average (Tr. 2-10) 5.94