Group ‘A’Construction of a

Thermodynamic Diagram

August 16, 2002

Lynn LeBlanc Lynn LeBlanc (coordinator), (coordinator),

Chad Kauffman,Chad Kauffman, Greg McFarquhar,Greg McFarquhar,

David Metzler, Pat Parrish,David Metzler, Pat Parrish,

Robert Pasken, Anthony Rockwood, Robert Pasken, Anthony Rockwood,

Jie SongJie Song

Overview

Students will construct (and use) a Skew-T log-P Students will construct (and use) a Skew-T log-P diagram as an aid in understanding and applying diagram as an aid in understanding and applying basic thermodynamic concepts. basic thermodynamic concepts. This will fit in the middle of a standard This will fit in the middle of a standard

thermodynamic course covering the gas laws, thermodynamic course covering the gas laws, 11stst Law of Thermodynamics, hydrostatics, and Law of Thermodynamics, hydrostatics, and water substance in the atmospherewater substance in the atmosphere

Learning Objectives

Students will learn how to apply the Students will learn how to apply the fundamental thermodynamic principles in fundamental thermodynamic principles in the construction of the thermodynamic the construction of the thermodynamic diagram.diagram.

Students will learn how to apply the Students will learn how to apply the thermodynamic diagram to practical thermodynamic diagram to practical problems.problems.

Audience

Intended audience is undergraduate majors Intended audience is undergraduate majors in atmospheric science/meteorology. in atmospheric science/meteorology.

A knowledge of thermodynamics is A knowledge of thermodynamics is essential to understanding why the essential to understanding why the atmosphere behaves the way it does.atmosphere behaves the way it does.

Required Resources

Semi-log paperSemi-log paper Hard-copy Skew-T log-P diagramsHard-copy Skew-T log-P diagrams Java applets for:Java applets for:

Aircraft AltimetryAircraft Altimetry Macromedia FlashMacromedia Flash

p-p- diagrams diagrams Skew-T diagramsSkew-T diagrams

Assessment Plan

Interactive Web-based exercises to test ability to Interactive Web-based exercises to test ability to interpret or analyze thermodynamic diagramsinterpret or analyze thermodynamic diagrams Quantitative submissionsQuantitative submissions Textual submissionsTextual submissions

Student will use the skew-T log-P diagram to Student will use the skew-T log-P diagram to quantify changes in variables during atmospheric quantify changes in variables during atmospheric processes.processes.

Student will sketch a Skew-T log-P diagram as Student will sketch a Skew-T log-P diagram as part of an exam.part of an exam.

Learning Activities Teaching strategy will include lectures, hands-on Teaching strategy will include lectures, hands-on

activities, interactive computer-based instructions.activities, interactive computer-based instructions. Multiple instructional methods seemed to be a Multiple instructional methods seemed to be a

natural fit for this project.natural fit for this project. Because the thermodynamic diagram is a key tool Because the thermodynamic diagram is a key tool

for research meteorologists and operational for research meteorologists and operational weather forecasters, this approach grounds the weather forecasters, this approach grounds the learning of thermodynamic within a professional learning of thermodynamic within a professional application.application. This strategy offers the advantage of providing This strategy offers the advantage of providing

inherent interest in the topic and motivation for inherent interest in the topic and motivation for their learning.their learning.

Discussion/Reflection

All team members plan to use major All team members plan to use major portions of this project in their classrooms portions of this project in their classrooms during the 2002-3 academic year.during the 2002-3 academic year.

Proposed Syllabus Rubric

1.Teach Ideal Gas Law1.Teach Ideal Gas Law-Avagadro’s Principle-Avagadro’s Principle-Partial Pressure-Partial Pressure-Gas constant for dry air-Gas constant for dry air

Plot isotherms on P-alpha diagramPlot isotherms on P-alpha diagramProblems/exercisesProblems/exercises

Plot isosteres on p-T diagramPlot isosteres on p-T diagram(p increasing (p increasing , T increasing , T increasing ) )Problems/exercisesProblems/exercises

Plot isosteres on log p-T diagramsPlot isosteres on log p-T diagramsProblems/exercisesProblems/exercises

Proposed Syllabus Rubric

1.Teach Ideal Gas Law1.Teach Ideal Gas Law-Example Problem-Example Problem

Using Excel Create a PUsing Excel Create a P Diagram by plotting Diagram by plotting the 200K, 300K and 400K isothermsthe 200K, 300K and 400K isotherms

Pressure-Specific Volume

100

200

300

400

500

600

700

800

900

1000

1000110012001300140015001600170018001900200021002200230024002500

Specific Volume

Pre

ssu

re

200

300

400

Syllabus Rubric-Example Problems-Example Problems

What happens to the isotherms as the pressure gets closer to 1000 mb?

Why does that happen?

From the shape of the isotherms what changes to the axis would you suggest to make the isotherms straight?

Syllabus Rubric-Example Solutions-Example Solutions

The isotherms get closer together as the pressure The isotherms get closer together as the pressure increases. Since the function is hyperbolic a Log-increases. Since the function is hyperbolic a Log-Linear graph is more appropriateLinear graph is more appropriate

Pressure-Specific Volume

100

1000

1000110012001300140015001600170018001900200021002200230024002500

Specific Volume

Pre

ssu

re

200

300

400

Syllabus Rubric-Example Problem-Example Problem

Which line in the PWhich line in the P Diagram below indicates an Diagram below indicates an

isobaric change from 200Kisobaric change from 200K to 400 Kto 400 Ka)a) AA

b)b) BB

c)c) CCPressure-Specific Volume

100

1000

1000110012001300140015001600170018001900200021002200230024002500

Specific Volume

Pre

ssu

re

200

300

400

Syllabus Rubric-Example Problem-Example Problem

Which line in the PWhich line in the P Diagram below indicates an Diagram below indicates an

isosteric change from 200Kisosteric change from 200K to 400 Kto 400 Ka)a) AA

b)b) BB

c)c) CC

Pressure-Specific Volume

100

1000

1000110012001300140015001600170018001900200021002200230024002500

Specific Volume

Pre

ssu

re

200

300

400

Syllabus Rubric-Example Problem-Example Problem

Which line in the PWhich line in the P Diagram below indicates an Diagram below indicates an

isothermal change from 200Kisothermal change from 200K to 400 Kto 400 Ka)a) AA

b)b) BB

c)c) CC

Pressure-Specific Volume

100

1000

1000110012001300140015001600170018001900200021002200230024002500

Specific Volume

Pre

ssu

re

200

300

400

Syllabus Rubric2.Teach 12.Teach 1stst Law of Thermodynamics Law of Thermodynamics

Work, Heat, EnergyWork, Heat, EnergyProblems/ExercisesProblems/Exercises on processes, paths on processes, paths (draw by hand)(draw by hand)Problems/ExercisesProblems/Exercises using interactive Java using interactive Java Applets with P-alpha diagram Applets with P-alpha diagram

specifications for design of [Java Applet]specifications for design of [Java Applet]Plot sounding of T-log p diagramPlot sounding of T-log p diagram

Why does it look odd?Why does it look odd?Skew isotherms 45Skew isotherms 45oo

Plot soundingPlot sounding

Syllabus Rubric3.Adiabatic Processes3.Adiabatic Processes

Poisson’s Equation & Hydrostatic EquationPoisson’s Equation & Hydrostatic Equation-Variation as p, alpha with height-Variation as p, alpha with height

Hypsometric Equation, Reduction to sea-levelHypsometric Equation, Reduction to sea-levelAltimetryAltimetry

Java Applet for aircraft flying at constant pressureJava Applet for aircraft flying at constant pressureProblems and ExercisesProblems and Exercises

Derivation of Adiabatic Lapse RateDerivation of Adiabatic Lapse RateStudent calculates and plots lines of constant theta Student calculates and plots lines of constant theta on skew-T log-P diagramon skew-T log-P diagramProblems and exercises using paper diagrams or Problems and exercises using paper diagrams or Java Skew-T applet (TBD)Java Skew-T applet (TBD)

Syllabus Rubric4.Water Vapor in the Atmosphere4.Water Vapor in the Atmosphere

Define variablesDefine variables

Relation between variablesRelation between variables

Variable Gas ConstantVariable Gas Constant

Virtual TemperatureVirtual Temperature

Problems and ExercisesProblems and Exercises

Phase ChangesPhase Changes

Latent HeatsLatent Heats

Students use diagram for applicationStudents use diagram for application

Syllabus Rubric

4. Water Vapor Continued4. Water Vapor ContinuedDerive Claussius-Claperyon EquationDerive Claussius-Claperyon Equation

Students plot lines of constant wStudents plot lines of constant wss on Skew- on Skew-T, log-P diagramT, log-P diagram

Problems/Exercises on paper or AppletProblems/Exercises on paper or AppletDerive Moist Adiabatic Lapse RateDerive Moist Adiabatic Lapse RateStudents plot lines lines of constant Theta-Students plot lines lines of constant Theta-w given critical values at 1000 mb.w given critical values at 1000 mb.

Syllabus Rubric

5.Processes in the Atmosphere5.Processes in the Atmosphere

Parcel process (definition)Parcel process (definition)

Problems/ExercisesProblems/Exercises

Java Applets

P-alpha diagram P-alpha diagram

Draw paths which describe a processDraw paths which describe a process

Display changes in all thermodynamic Display changes in all thermodynamic variables (temperature, pressure, volume, variables (temperature, pressure, volume, internal energy, enthalpy, entropy, work, internal energy, enthalpy, entropy, work, heat)heat)

Java Applets cont’d.

Skew-T log-PSkew-T log-PFollow a parcel as it moves in the Follow a parcel as it moves in the

atmosphere vertically (or change temperature at atmosphere vertically (or change temperature at constant pressure)constant pressure)

Motions controlled by mouse or specific Motions controlled by mouse or specific forcing by synoptic vertical motionforcing by synoptic vertical motion

Display current values of all Display current values of all thermodynamic variable and derived quantities thermodynamic variable and derived quantities (latent heat released, liquid water condensed)(latent heat released, liquid water condensed)

Questions on Adiabatic Processes

1. Assume that in Denver, CO a station 1. Assume that in Denver, CO a station pressure of 850 mb and a station pressure of pressure of 850 mb and a station pressure of 1010°C are measured. Reduce the station °C are measured. Reduce the station pressure of 850 mb to a sea-level adjusted pressure of 850 mb to a sea-level adjusted pressure (assuming a dry atmosphere).pressure (assuming a dry atmosphere). Hint: You can use the U.S. Standard Hint: You can use the U.S. Standard

atmosphere lapse rate of 6.5 K/km in atmosphere lapse rate of 6.5 K/km in your calculation.your calculation.

Adiabatic Processes cont’d.

2. Assume that a beginning aviation student 2. Assume that a beginning aviation student erroneously assumes that the atmosphere is erroneously assumes that the atmosphere is isothermal rather than assuming the standard dry isothermal rather than assuming the standard dry adiabatic lapse rate. What error (%) will be made adiabatic lapse rate. What error (%) will be made in the difference between altitudes calculated in the difference between altitudes calculated assuming an isothermal atmosphere and a U.S. assuming an isothermal atmosphere and a U.S. Standard Atmosphere?Standard Atmosphere?

Assume a dry atmosphere in both Assume a dry atmosphere in both calculations with a temperature of 15calculations with a temperature of 15°C, and a °C, and a surface pressure of 1013.25 mb.surface pressure of 1013.25 mb.

Adiabatic Processes cont’d.

3. Calculate the height at which the 500 mb level 3. Calculate the height at which the 500 mb level occurs for a typical tropical, mid-latitude and Arctic occurs for a typical tropical, mid-latitude and Arctic atmospheres assume a standard Atmosphere lapse atmospheres assume a standard Atmosphere lapse rate of 6.5rate of 6.5 K/km and assuming surface temperatures K/km and assuming surface temperatures of 30°C, 10°C, -10°C. of 30°C, 10°C, -10°C.

Determine the thickness of the layer between Determine the thickness of the layer between 500-100 mb for the same three regions assuming 500-100 mb for the same three regions assuming mean virtual temperatures of 228K, 223K, 210K.mean virtual temperatures of 228K, 223K, 210K.

What is the height of the tropopause for the What is the height of the tropopause for the three regions?three regions?

Web-driven Interaction

Process du = (+), (-), or 0

db = (+), (-) or 0

d = (+), (-), or 0

Undetermined

A to B 

       

B to C 

       

A to C 

       

Questions for diagram points (A G)

Is dIs d for ‘A to C’ >, <, = ‘A to G’ or cannot be for ‘A to C’ >, <, = ‘A to G’ or cannot be determined?determined?

Is dIs dfor ‘A to C’ >, <, = ‘A to G’ or cannot be for ‘A to C’ >, <, = ‘A to G’ or cannot be determined?determined? (Explain or note use of Equation of state to (Explain or note use of Equation of state to

calculate specific volume)calculate specific volume) Does the above process represent compressional Does the above process represent compressional

heating, compressional cooling, expansional heating, compressional cooling, expansional heating, expansional cooling?heating, expansional cooling?

Questions for diagram points (A G)

‘‘B to F’ dB to F’ d, (+), (-), 0, or cannot be , (+), (-), 0, or cannot be determined?determined?

‘‘A to C’ dA to C’ d, (+), (-), 0, or cannot be , (+), (-), 0, or cannot be determined? determined? 

‘‘D to B’ dD to B’ d, (+), (-), 0, or cannot be , (+), (-), 0, or cannot be determined?determined?

Water Vapor Exercises/Problems Given T, TGiven T, Tdd as a function of pressure as a function of pressure

(a) Compute/determine from Skew-T diagram at (a) Compute/determine from Skew-T diagram at 1000 mb.1000 mb.

[w, w[w, wss, e, e, e, ess, T, Tww, RH, q, q, RH, q, qss, T, Tvv, , θ, ρ, θθ, ρ, θee, θ, θww]]

(b) Lift a parcel at 1000 mb to LCL(b) Lift a parcel at 1000 mb to LCLCompute LCL and all above variablesCompute LCL and all above variables

(c) Lift to 6 km (use hypsometric equation to (c) Lift to 6 km (use hypsometric equation to determine pressure level)determine pressure level)Compute all above variablesCompute all above variablesCompute latent heat released (per kg of air)Compute latent heat released (per kg of air)

(d) Redo with Java Applet(d) Redo with Java Applet

Water Vapor Exercise/Problems

Wallace & Hobbs (p. 80) question on lifting Wallace & Hobbs (p. 80) question on lifting parcel over mountainparcel over mountain Perform using a Skew-TPerform using a Skew-T Redo using Java AppletRedo using Java Applet

Water Vapor Exercises/Problems

A closed insulated room is initially at 25A closed insulated room is initially at 25°C, °C, 20% RH. Volume of the room is 400m20% RH. Volume of the room is 400m33.. How much water must be evaporated to How much water must be evaporated to

raise RH to 60%? What is the final room raise RH to 60%? What is the final room temperature (under constant pressure of temperature (under constant pressure of 1000 mb)?1000 mb)?

Validate your answer using your Validate your answer using your constructed thermodynamic diagramconstructed thermodynamic diagram