Physics Laboratory Manual

PHYC 10180 Physics for Ag. Science

2013-2014

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Partner’s Name ................................................................

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Contents

Introduction 4

Laboratory Schedule 5

Springs 7

Newton’s Second Law 15

An Investigation of Fluid Flow using a Venturi Apparatus

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Archimedes’ Principle and Experimental Measurements

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Superconductivity, Resistance and Temperature 33

Investigation into the Behaviour of Gases and a Determination of Absolute Zero

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Photoelectrical Investigations into the Properties of Solar Cells

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JagFit 65

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Introduction

Physics is an experimental science. The theory that is presented in lectures has its origins in, and is validated by, experimental measurement.

The practical aspect of Physics is an integral part of the subject. The laboratory practicals take place throughout the semester in parallel to the lectures. They serve a number of purposes:

• an opportunity, as a scientist, to test theories; • a means to enrich and deepen understanding of physical concepts

presented in lectures; • an opportunity to develop experimental techniques, in particular skills

of data analysis, the understanding of experimental uncertainty, and the development of graphical visualisation of data.

Some of the experiments in the manual may appear similar to those at school, but the emphasis and expectations are likely to be different. Do not treat this manual as a ‘cooking recipe’ where you follow a prescription. Instead, understand what it is you are doing, why you are asked to plot certain quantities, and how experimental uncertainties affect your results. It is more important to understand and show your understanding in the write-ups than it is to rush through each experiment ticking the boxes. This manual includes blanks for entering most of your observations. Do not feel obliged to fill in all the blank space, they are designed to provide plenty of space Additional space is included at the end of each experiment for other relevant information. All data, observations and conclusions should be entered in this manual. Graphs may be produced by hand or electronically (details of a simple computer package are provided) and should be secured to this manual.

There will be six 2-hour practical laboratories in this module evaluated by continual assessment. Note that each laboratory is worth 5% so each laboratory session makes a significant contribution to your final mark for the module. Consequently, attendance and application during the laboratories are of the utmost importance. At the end of each laboratory session, your demonstrator will collect your work and mark it. Remember,

If you do not turn up, you will get zero for that laboratory.

You are encouraged to prepare for your lab in advance.

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Laboratory Schedule

Depending on your timetable, you will attend on either Wednesday 2-4pm or Wednesday 4-6pm. Please consult the notice boards in the School of Physics, Blackboard, or contact the lab manager, Thomas O’Reilly (Science East Room 1.41) to see which of the experiments you will be performing each week. This information is also summarized below. Timetable: Wednesday 2-4: Groups 1,3,5,6,7,9 and 11 Wednesday 4-6: Groups 2,4,6,8 and 10.

Semester Room Dates Week Science East 143 Science East 144 Science East 145

20 - 24 Jan 1 Springs: 1,2

Springs: 3,4

Springs: 5,6

27 - 31 Jan 2 Springs: 7,8

Springs: 9,10

Springs: 11

3 - 7 Feb 3 Fluids: 1,2

Newton: 3,4

Archimedes: 5,6

10 - 14 Feb 4 Fluids: 7,8

Newton: 9,10

Archimedes: 11

17 – 21 Feb 5 Fluids: 5,6

Newton: 1,2

Archimedes: 3,4

24 – 28 Feb 6 Fluids: 11

Newton: 7,8

Archimedes: 9,10

3 - 7 Mar 7 Fluids: 3,4

Newton: 5,6

Archimedes: 1,2

24 - 28 Mar 8 Fluids: 9,10

Newton: 11

Archimedes: 7,8

31 Mar – 4 Apr 9 Gas: 1,2

Solar: 3,4

Superconductor: 5,6

7 - 11 Apr 10 Gas: 7,8

Solar: 9,10

Superconductor: 11

14 – 18 Apr 11 Gas: 5,6

Solar: 1,2

Superconductor: 3,4

21 - 25 Apr 12 Gas: 11

Solar: 7,8

Superconductor: 9,10

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Name:___________________________ Student No: ________________ Partner:____________________Date:___________Demonstrator:________________

Springs What should I expect in this experiment? You will investigate how springs stretch when different objects are attached to them and learn about graphing scientific data. Introduction: Plotting Scientific Data

In many scientific disciplines, and particularly in physics, you will often come across plots similar to those shown here. Note some common features:

• Horizontal and vertical axes; • Axes have labels and units; • Axes have a scale; • Points with a short horizontal

and/or vertical line through them; • A curve or line superimposed.

Why do we make such plots? ______________________________________________________________________

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What features of the graphs do you think are important and why? ______________________________________________________________________

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The equation of a straight line is often written as y = m x + c.

y tells you how far up the point is, whilst x is how far along the x-axis the point is. m is the slope (gradient) of the line, it tells you how steep the line is and is calculated by dividing the change in y by the change is x, for the same part of the line. A large value of m, indicates a steep line with a large change in y for a given change in x. c is the intercept of the line and is the point where the line crosses the y-axis, at x = 0.

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Apparatus In this experiment you will use 2 different springs, a retort stand, a ruler, a mass hanger and a number of different masses. Preparation Set up the experiment as indicated in the photographs. Use one of the two springs (call this one spring 1). Determine the initial length of the spring, be careful to pick two reference points that define the length of the spring before you attach any mass or the mass hanger to the spring. Record the value of the length of the spring below.

Think about how precisely you can determine the length of the spring. Repeat the procedure for spring 2. Calculate the initial length of spring 1. ______________________________________________________________________

Calculate the initial length of spring 2. ______________________________________________________________________

Procedure Attach spring 1 again and then attach the mass hanger and 20g onto the spring. Measure the new length of the spring, using the same two reference points that you used to determine the initial spring length. Length of springs with mass hanger attached (+ 20 g)

Spring 1 Spring 2 Position of the top of spring

Position of the bottom of spring New length of spring

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Add another 10 gram disk to the mass hanger, determine the new length of the spring. Complete the table below. Measurements for spring 1

Object Added Total mass added to the mass hanger

(g)

New reference position (cm)

New spring length (cm)

Disk 1 30 Disk 2 40 Disk 3 Disk 4 Disk 5

Add more mass disks, one-by-one, to the mass hanger and record the new lengths in the table above. In the column labelled ‘total mass added to the mass hanger’, calculate the total mass added due to the disks. Carry out the same procedure for spring 2 and complete the table below. Measurements for spring 2

Object Added Total mass added to the mass hanger

(g)

New reference position (cm)

New spring length (cm)

Disk 1 30 Disk 2

Graphical Analysis Add the data you have gathered for both springs to the graph below. You should plot the length of the spring in centimetres on the vertical y-axis and the total mass added to the hanger in grams on the horizontal axis. Start the y-axis at -10 cm and have the x-axis run from -40 to 100 g. Choose a scale that is simple to read and expands the data so it is spread across the page. Label your axes and include other features of the graph that you consider important.

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Graph representing the length of the two springs for different masses added to the hanger.

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In everyday language we may use the word ‘slope’ to describe a property of a hill. For example, we may say that a hill has a steep or gentle slope. Generally, the slope tells you how much the value on the vertical axis changes for a given change on the x-axis. Algebraically a straight line can be described by y = mx + c where x and y refer to any data on the x and y axes respectively, m is the slope of the line (change in y/ change in x), and c is the intercept (where the line crosses the y-axis at x=0). Suppose the data should be consistent with straight lines. Superimpose the two best straight lines, one for each spring, that you can draw on the data points. Examine the graphs you have drawn and describe the ‘steepness’ of the slopes for spring 1 and spring 2.

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Work out the slopes of the two lines.

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______________________________________________________________________ What are the two intercepts? ______________________________________________________________________

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______________________________________________________________________ How can you use the slopes of the two lines to compare the stiffness of the springs? ______________________________________________________________________

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In this experiment the points at which the straight lines cross the y-axis where x = 0 g (intercepts) correspond to physical quantities that you have determined in the experiment. How well do the graphical and measured values compare with each other? ______________________________________________________________________

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Look at the graphs on page 7, the horizontal and vertical lines through the data points represent the experimental uncertainty, or precision of measurement in many cases. In this experiment the uncertainty on the masses is insignificant, whilst those on the length measurements are related to how accurately the lengths of the springs can be determined. How large a vertical line would you consider reasonable for your length measurements? ______________________________________________________________________

What factors might explain any disagreement between the graphically determined intercepts and the measurements of the corresponding physical quantity. ______________________________________________________________________

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Name:___________________________ Student No: ________________ Partner:____________________Date:___________Demonstrator:________________

Newton’s Second Law. What should I expect in this experiment? This experiment has two parts. In the first part you will apply a fixed force, vary the mass and note how the acceleration changes. In the second part you will measure the acceleration due to the force of gravity. Introduction

Newton’s second law states amF = , a force causes an acceleration and the size of the acceleration is directly proportional to the size of the force. Furthermore, the constant of proportionality is mass. Apparatus The apparatus used is shown here and consists of a cart that can travel along a low friction track. The cart has a mass of 0.5 kg which can be adjusted by the addition of steel blocks each of mass 0.5 kg. String, a pulley and additional masses allow forces to be applied to the carts. Take care to ensure that the track is completely level before starting the experiments

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Investigation 1: Check that force is proportional to acceleration and show the constant of proportionality to be mass. Calculate the acceleration due to gravity.

The apparatus should be set up as in the picture. Attach one end of the string to the cart, pass it over the pulley, and add a 0.012 kg mass to the hook.

The weight of the hanging mass is a force, F, that acts on the cart. The whole system (both the hanging mass mh and the cart mcart) are accelerated. So long as you don’t change the hanging mass, F will remain constant. You can then change the mass of the system, M, by adding mass to the cart, noting the change in acceleration, and testing the relationship F=ma. If F=ma and you apply a constant force F, what do you expect will happen to the acceleration as you increase the mass? ______________________________________________________________________

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______________________________________________________________________ There remains the problem of working out the acceleration of the system. According to kinematics, distance travelled is related to the acceleration by the formula

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21 atuts += , where s is distance, u the initial velocity, t is time, and a acceleration.

If the cart starts from rest write down an expression for ‘a’ . Place different masses on the cart. Using ruler and stopwatch measure s and t and hence the acceleration a. Fill in the following table.

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mh (kg)

mcart (kg)

M= mh+mcart

(kg) a (m/s2)

M.a (N) 1/a (m-1s2)

0.012 0.5

s (m)

t (s)

0.012 1.0

s (m)

t (s)

0.012 1.5

s (m)

t (s)

From the numbers in the table what do you conclude about Newton’s second law? ______________________________________________________________________

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Analysis and determination of the acceleration due to gravity. If Newton is correct, ammF carth ⋅+= )( You have varied mcart and noted how the acceleration changed so let’s rearrange the formula so that it is in the familiar linear form y=mx+c. Then you can graph your data points and work out a slope and intercept which you can interpret in a physical fashion.

Fm

mFa

ammF hcartcarth +=⇒⋅+=

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So if Newton is correct and you plot mcart on the x-axis and 1/a on the y-axis you should get a straight line. In terms of the algebraic quantities above, what should the slope of the graph be equal to? In terms of the algebraic quantities above, what should the intercept of the graph equal? Plot the graph and see if Newton is right. Do you get a straight line? What value do you get for the slope? What value do you get for the intercept?

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Create your graph either manually or using Jagfit (see back of manual) and attach your printed graph below.

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Now here comes the power of having plotted your results like this. Although we haven’t bothered working out the force we applied using the hanging weight, a comparison of the measured slope and intercept with the predicted values will let you work out F. From the measurement of the slope, the constant force applied can be calculated to be From the intercept of the graph you can calculate F in a different fashion. What value do you get? You’ve shown that F is proportional to a and the constant of proportionality is mass. If the force is the gravitational force, it will produce an acceleration due to gravity (usually written g instead of a) so once again a (gravitational) force F is proportional to acceleration, g. But what is the constant of proportionality? Are you surprised that it is the same mass m? (By the way, a good answer to this question gets you a Nobel prize.)

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______________________________________________________________________ So since that force was just caused by the mass mh falling under gravity, F= mhg, you can calculate the acceleration due to gravity to be Comment on how this compares to the accepted value for gravity of about 9.785 m/s2. How does the accuracy of your measurements affect this comparison? ______________________________________________________________________

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Name:___________________________ Student No: ________________ Partner:____________________Date:___________Demonstrator:________________

An Investigation of Fluid Flow using a Venturi Apparatus. Theory When a fluid moves through a channel of varying width, as in a Venturi apparatus, the volumetric flow rate (volume/time) remains constant but the velocity and pressure of the fluid vary. In the Venturi apparatus there are two different channel widths. The flow rate, Q, of the fluid through the tube is related to the speed of the fluid (v) and the cross-sectional area of the pipe (A). This relationship is known as the continuity equation, and can be expressed as

𝑄 = 𝐴!𝑣! = 𝐴𝑣              (Eq.1)

where A0 and v0 refer to the wide part of the tube and A and v to the narrow part. As the fluid flows from the narrow part of the pipe to the constriction, the speed increases from v0 to v and the pressure decreases from P0 to P. The flow rate also depends on the pressure, P0, behind the fluid flowing into the apparatus. In this experiment the pressure can be determined from the (minimum) height difference that the water falls through, calculated from the top of the water in the reservoir, h, using the formula P0 = ρgh, where ρ is the density of water = 103 kg m-3 and g is the acceleration due to gravity.

Apparatus The apparatus consists of a five-litre reservoir of water connected to a Venturi apparatus through which the water can flow into a collecting beaker, itself placed in a box.

Procedure Using the spare apparatus in the laboratory, measure the depth of the channel and the widths of the wide and narrow sections. Calculate the large (A0) and small (A) cross-sections.

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Depth____________ Width(large)______________ Width (narrow) ______________

Area (A0) ______________ Area (A) ______________

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Before putting any water in the apparatus, connect the Venturi apparatus to the Quad pressure sensor and GLX data logger.

1. Connect the tubes from the Venturi apperatus to the Quad Pressure Sensor. Ensure that they are connected in the right order. The one closest to the flow IN to the apparatus is connected to number 1 etc. 2. Connect the GLX to the AC adapter and power it up. 3. Connect the Quad Pressure sensor to the GLX. A graph screen will appear if this

is done correctly. 4. Navigate to the home screen (Press “home” key) and then navigate to ‘Digits’

and press select. Data from two of the four sensors should be visible. 5. To make the data from all four sensor visible press the F2 key. All sensor input

should now be visible. 6. Calibrate the sensors, using the atmospheric pressure reading:

(i) Press “home” and “F4” to open the sensors screen. (ii) Press “F4” again to open the sensors menu. (iii) From the menu, select “calibrate” to open the calibrate sensors window. (iv) In the first box of the window, select “quad pressure sensor”. (v) In the third box of the window, select “calibrate all similar measurements”. (vi) In the “calibration type” box, select “1 point offset”. (vii) Press “F3”, “read pt 1”. (viii) Press “F1”, “OK”.

Ensure that the clamp between the reservoir and the Venturi apparatus is closed and make sure that the eight fixing taps are all just finger tight. Fill the reservoir to the 2 litre mark. Be sure to read the water level by looking at the bottom of the meniscus. Ensure that the outlet of the apparatus is in the beaker which is in the box and that the outlet pipe is as low as possible, then open the clamp so that water flows through the Venturi apparatus. Remove any air bubbles by gently tilting the outlet end of the Venturi apparatus upwards. Close the clamp when there is no air left in the Venturi apparatus. Put all of the water back into the reservoir and check that the level is still 2 litres. Set up the apparatus so that the reservoir is at its minimum height above the Venturi apparatus, lowest position of the lab-jack. Measure the height of the top of the water in the reservoir above the level of the highest point of the outflow pipe. Measure the time that it takes for 400 ml (0.4l = 4x10-4 m3) of water to flow through the Venturi apparatus. When the flow is steady note the pressures on the four sensors, with the clamp open. Enter your data in the table. Repeat the measurements for 4 more different heights of the reservoir, be sure to use the whole range availble. Be sure to return all the water to the reservoir and check that the level is still 2 litres before each measurement.

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Height difference/m

P1 /kPa

P3 /kPa

P2 /kPa

P4 /kPa

Average P /kPa

Time /s

Flowrate Q /m3s-1

Repeat your measurements for 4 litres of water in the reservoir.

Height difference/m

P1 /kPa

P3 /kPa

P2 /kPa

P4 /kPa

Average P /kPa

Time /s

Flowrate Q /m3s-1

When you have finished, allow the reservoir to run empty and tilt the Venturi apparatus to empty water from it. Once the apparatus is empty of water remove the pressure tubes from the sensor by gently twisting the white plastic collars that connected the hoses to the sensor (leave the tubes connected to the underside of the Venturi apparatus). Empty as much water as you can from the apparatus and then all of the water into the sink in the laboratory.

Plot a graph of the flow rate as a function of height difference for both experiments on the same graph.

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Comment on whether your data verifies that flow rate is proportional to height difference and therefore pressure of the fluid flowing into the Venturi apparatus. __________________________________________________________________

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Explain any similarities and differences between the two sets of data.

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Create a graph either manually or using Jagfit (see back of manual) and attach your printed graph below.

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Select one of your readings for the measured flow rate (Q), use equation (1) to calculate the fluid speed in the wide part of the tube (v0) and in the constricted part of the tube (v). ______________________________________________________________________

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What can you conclude from your experiment? ______________________________________________________________________

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Name:___________________________ Student No: ________________ Partner:____________________Date:___________Demonstrator:________________

Archimedes’ Principle and Experimental

Measurements. Introduction All the technology we take for granted today, from electricity to motor cars, from television to X-rays, would not have been possible without a fundamental change, around the time of the Renaissance, to the way people questioned and reflected upon their world. Before this time, great theories existed about what made up our universe and the forces at play there. However, these theories were potentially flawed since they were never tested. As an example, it was accepted that heavy objects fall faster than light objects – a reasonable theory. However it wasn’t until Galileo1 performed an experiment and dropped two rocks from the top of the Leaning Tower of Pisa that the theory was shown to be false. Scientific knowledge has advanced since then precisely because of the cycle of theory and experiment. It is essential that every theory or hypothesis be tested in order to determine its veracity. Physics is an experimental science. The theory that you study in lectures is derived from, and tested by experiment. Therefore in order to prove (or disprove!) the theories you have studied, you will perform various experiments in the practical laboratories. First though, we have to think a little about what it means to say that your experiment confirms or rejects the theoretical hypothesis. Let’s suppose you are measuring the acceleration due to gravity and you know that at sea level theory and previous experiments have measured a constant value of g=9.81m/s2. Say your experiment gives a value of g=10 m/s2. Would you claim the theory is wrong? Would you assume you had done the experiment incorrectly? Or might the two differing values be compatible? What do you think? ______________________________________________________________________

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Experimental Uncertainties 1 Actually, the story is probably apocryphal. However 11 years before Galileo was born, a similar experiment was published by Benedetti Giambattista in 1553.

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When you make a scientific measurement there is some ‘true’ value that you are trying to estimate and your equipment has some intrinsic uncertainty. Thus you can only estimate the ‘true’ value up to the uncertainty inherent within your method or your equpiment. Conventionally you write down your measurement followed by the symbol ± , followed by the uncertainty. A surveying company might report their results as

5245 ± km, 1253± km, 1.02.254 ± km. You can interpret the second number as the ‘margin of error’ or the uncertainty on the measurement. If your uncertainties can be described using a Gaussian distribution, (which is true most of the time), then the true value lies within one or two units of uncertainty from the measured value. There is only a 5% chance that the true value is greater than two units of uncertainty away, and a 1% chance that it is greater than three units. Errors may be divided into two classes, systematic and random. A systematic error is one which is constant throughout a set of readings. A random error is one which varies and which is equally likely to be positive or negative. Random errors are always present in an experiment and in the absence of systematic errors cause successive readings to spread about the true value of the quantity. If in addition a systematic error is present, the spread is not about the true value but about some displaced value. Estimating the experimental uncertainty is at least as important as getting the central value, since it determines the range in which the truth lies. Practical Example: Now let’s put this to use by making some very simple measurements in the lab. We’re going to do about the simplest thing possible and measure the volume of a cylinder using three different techniques. You should compare these techniques and comment on your results. Method 1: Using a ruler The volume of a cylinder is given by πr2h where r is the radius of the cylinder and h its height. Measure and write down the height of the cylinder. Don’t forget to include the uncertainty and the units. Measure and write down the diameter of the cylinder.

h= ±

d= ±

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ow calculate the radius. (Think about what happens to the uncertainty) Calculate the radius squared – with it’s uncertainty! One general way of determining the uncertainty in a quantity f calculated from others is to use the following method..

• From your measurements, calculate the final result. Call this f , your answer. • Now move the value of the source up by its uncertainty. Recalculate the final result. Call this +f . • The uncertainty on the final result is the difference in these values.

Finally work out the volume. Estimate how well you can determine the volume.

V= ±

r2 = ±

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Method 2: Using a micrometer screw This uses the same prescription. However your precision should be a lot better. Measure and write down the height of the cylinder. Don’t forget to include the uncertainty and the units. Measure and write down the diameter of the cylinder. Now calculate the radius. Calculate the radius squared – with it’s uncertainty! Finally work out the volume.

h= ±

d= ±

r= ±

V= ±

(Show your workings)

r2 = ±

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Method 3: Using Archimedes’ Principle You’ve heard the story about the ‘Eureka’ moment when Archimedes dashed naked through the streets having realised that an object submerged in water will displace an equivalent volume of water. You will repeat his experiment (the displacement part at least) by immersing the cylinder in water and working out the volume of water displaced. You can find this volume by measuring the mass of water and noting that a volume of 0.001m3 of water has a mass2 of 1kg. Write down the mass of water displaced. Calculate the volume of water displaced. What is the volume of the cylinder? Discussion and Conclusions. Summarise your results, writing down the volume of the cylinder as found from each method. Comment on how well they agree, taking account of the uncertainties. _____________________________________________________________________

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2 In fact this is how the metric units are related. A litre of liquid is that quantity that fits into a cube of side 0.1m and a litre of water has a mass of 1kg.

±

±

±

± ± ±

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Can you think of any systematic uncertainties that should be considered? Can you estimate their size? ______________________________________________________________________

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Requote your results including the systematic uncertainties. What do you think the volume of the cylinder is? and why? My best estimate of the volume is because ______________________________________________________________ ______________________________________________________________________

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± ± ± ±

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Name:___________________________ Student No: ________________ Partner:____________________Date:___________Demonstrator:________________ Superconductivity, Resistance and Temperature. This experiment is in two parts. In the first part you will investigate the relationship between resistance and temperature for a normal material. In the second part you will observe the behaviour in a superconducting material, where below a certain critical temperature, the resistance goes to zero. Precautions You will be using liquid nitrogen to cool the materials. Liquid nitrogen is at an extremely low temperature and contact with any part of your skin or body must be avoided. Exercise extreme caution. The apparatus must remain behind the safety screen. When handling the flask, wear safety gloves and safety goggles. Do not place liquid nitrogen in any vessel other than those which have been designed for it.

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Part 1: Resistance v Temperature in normal materials You are provided with a power supply, resistor, ammeter, thermometer and a method for cooling the resistor. Write a short report detailing your investigations into the behaviour of resistance with temperature. Take data at various temperatures, graph your results and draw conclusions. In particular, extrapolate your data to lower temperatures and suggest what might happen at absolute zero (0K or –273C).

Introduction: Outline what you are going to investigate and provide any theoretical background that will allow you interpret your results.

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Apparatus and Procedure: Describe the apparatus. In particular, draw the electrical circuit that you are using to measure the resistance. Describe the procedure (what you adjust (and how) and what you measure (and how)).

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Temperature (K) Resistance (Ohm)

Data: Tabulate your data here.

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Affix your graph here

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Conclusions: What have you found out? Extrapolate your graph towards absolute zero and comment on what the value of the resistance might be there.

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Part 2: Resistance in a superconducting material Introduction The resistance of a metal decreases as the temperature of the metal decreases. It was discovered in 1911, by the Dutch physicist Kammerlingh Onnes, that the resistance of mercury absolutely disappeared at temperatures below 4 K. (He was awarded the Nobel Prize in Physics for this discovery in 1913). This phenomenon, which he named superconductivity, allows electrical currents to circulate through the superconducting conductor without any losses. The temperature at which a particular material undergoes the transition from a normal conducting state to a superconducting state is known as the critical temperature, Tc. In 1986, a new form of high temperature superconducting material, a ceramic material, YBa2Cu3O7-Δ, was discovered, the first substance to have a critical temperature higher than the boiling point of liquid nitrogen. The Nobel prize was awarded for this breakthrough. The aim of this experiment is to observe the transition of a high temperature superconductor from its superconducting state to a non-superconducting state. This transition is observed by its effect on the inductance of a coil surrounding the sample. Theory The superconducting sample is placed within an inductance coil. When a current passes through the coil, magnetic field lines are generated and these pass through the centre of the coil and any material present within. At room temperature, the magnetic field lines pass through the sample of material which is in its ordinary state. However, as the temperature is lowered past the critical temperature (Tc) of the ceramic sample the magnetic field lines are excluded, or expelled, from the material. The effect of this flux exclusion is to change the inductance of the coil. This change in the inductance of the coil can be measured directly through measuring the current I and the voltage V, as a function of temperature. When an A/C signal at a frequency, f, is passed through the inductor, the current and voltage are related by

LRIV ω+= 2 (Eq.1)

where ω = 2πf, R is the resistance of the coil and L is the inductance of the coil. Eq.1 is similar to Ohm’s law but it includes an extra term due to the energy required to set up or shut down the magnetic fields associated with the coil. The idea in this experiment is to vary the temperature and calculate L by measuring V and I. However, there are two unknowns in Eq.1: R and L. If however we first measure V and I at a given temperature for a D/C signal (where ω =0), then R can be determined. A second pass with the A/C signal allows L to be found.

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Procedure The inductance coil with the sample of the high-Tc material within it, is buried within a styrofoam container with sand. To cool the coil and sample, liquid nitrogen is poured into the container. The temperature of the coil and sample is measured by means of a thermocouple, the output of which is displayed on a meter. When the liquid nitrogen is poured in, the coil and sample are cooled very rapidly and gradually over a period of some minutes their temperature will increase, ultimately returning to room temperature.

You have already recorded the resistance R, of the coil over the temperature range that will be used in this part of the experiment. The coil itself does not show superconducting properties in this temperature region; however the special material inside it should. In this part of the experiment you cool the coil and sample again with liquid nitrogen. This time, as the apparatus warms up, the frequency generator is used to pass an alternating sinusoidal signal at a frequency of 1 kHz through the induction coil. The voltage, V, across the induction coil and the current, I, passing through the circuit are measured. Enter the data in the table on the next page. To increase your precision on estimating Tc, it is useful to take data points at smaller temperature intervals in the region above and below the transition point The fourth column (Inductance) can be calculated using the graph you have already produced. For each temperature reading, estimate the resistance of the coil from your graph; then calculate the inductance using Eq.1.

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Temperature (K) Voltage (V) Current (I) Inductance (H)

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Graph the Inductance, L, as a function of Temperature T. The change from the superconducting state to the normal state should be clearly seen in this graph. Using the graph, estimate Tc for the superconductor. How precisely can you determine

this temperature?

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Name:___________________________ Student No: ________________ Partner:____________________Date:___________Demonstrator:________________

Investigation into the Behaviour of Gases and a Determination of Absolute Zero

What should I expect in this experiment? You will investigate gases behaviour, by varying their pressure, temperature and volume. You will also determine a value of absolute zero. Introduction: The gas laws are a macroscopic description of the behaviour of gases in terms of temperature, T, pressure, P, and volume, V. They are a reflection of the microscopic behaviour of the individual atoms and molecules that make up the gas which move randomly and collide many billions of times each second. Their speed is related to the temperature of the gas through the average value of the kinetic energy. An increase in temperature causes the atoms and molecules to move faster in the gas. The rate at which the atoms hit the walls of the container is related to the pressure of the gas. The volume of the gas is limited by the container it is in. Using the above description to explain the behaviour of gases, state whether each of P,V,T goes up (↑), down (↓) or stays the same (0) for the following cases.

P V T

A sealed pot containing water vapour is placed on a hot oven hob.

Blocking the air outlet, a bicycle pump is depressed.

A balloon full of air is squashed.

A balloon heats up in the sun.

From the arguments above you can see that at constant temperature, decreasing the volume in which you contain a gas should increase the pressure by a proportional amount. Thus VP 1∝ or introducing k, a constant of proportionality, V

kP = or

kPV = . This is Boyle’s Law.

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Similarly you can see that at constant volume, increasing the temperature should increase the pressure by a proportional amount. So TP ∝ or introducing κ , a

constant of proportionality, TP κ= or κ=TP . This is Gay Lussac’s Law.

These laws can be combined into the Ideal Gas Law that relates all three quantities by

nRTPV = where n is the number of moles of gas and R is the ideal gas constant. Experiment 1: To test the validity of Boyle’s Law

The equipment for testing Boyle’s Law consists of a horizontally mounted tube with a graduated scale (0 to 300 cm3) along one side. The tube is sealed by a standard gas tap (yellow colour) next to which is mounted a standard pressure gauge. The effective length of the air column inside the tube is controlled by altering the position of an inner rubber stopper moved via a screw thread. The volume of the air column can be read of the scale and the corresponding pressure taken from the pressure gauge. Procedure

• Ensure that the yellow gas tap is in its open position (i.e. parallel to the tube). • Move the rubber stopper (located inside the tube) to at least 200 cm3 on the graded

scale by unscrewing the thread knob (anticlockwise movement). • Close the yellow gas tap by turning it 90o clockwise compared to the “open” position. • Observe that initially the pressure reading is at approximately 1.0x105 Pa which is

atmospheric pressure; in the next steps you will increase the pressure of the air column inside the tube from approx. 1.0x105 Pa to the maximum pressure written on the pressure gauge.

• Start compressing the air inside the tube by screwing in the thread knob (clockwise direction).

• At 10 different positions of the screw, take readings of the air pressure and the corresponding air volume. For safety reasons do not exceed the maximum pressure on the pressure gauge scale! On the volume scale, each volume value is read by matching the position of the left extremity of the rubber stopper to the graded scale.

• Tabulate your results below.

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• Once you finished taking readings, depressurize the tube to atmospheric pressure by turning the gas tap 90o anticlockwise.

Air Pressure (Pa) Volume of air (m3) Air Pressure (Pa) Volume of air

(m3)

Compare Boyle’s Law: V

kP = to the straight line formula y=mx+c.

What quantities should you plot on the x-axis and y–axis in order to get a linear relationship according to Boyle’s Law? Explain and tabulate these values below. ______________________________________________________________________

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x-axis= y-axis=

What should the slope of your graph be equal to?

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What should the intercept of the graph equal?_______________________________ Make a plot of those variables that ought to give a straight line, if Boyle’s Law is correct.

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Use either the graph paper below or JagFit (see back of manual) and attach your printed graph below.

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Comment on the linearity of your plot. Have you shown Boyle’s Law to be true? How precisely you can determine the pressures and volumes influence your answers? ______________________________________________________________________

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What is the value for the slope? What is the value for the intercept? Use the Ideal Gas Law to figure out how many moles of air are trapped in the column. (The universal gas constant R=8.3145 J/mol K)

Number of moles of gas =

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Experiment 2: To test the validity of Gay Lussac’s Law

The equipment for testing Gay Lussac’s Law consists of an enclosed can surrounded by a heating element. The volume of gas in the can is constant. A thermocouple measures the temperature of the gas and a pressure transducer measures the pressure.

Procedure Plug in the transformer to activate the temperature and pressure sensors. Set the multimeter for pressure to the 200mV scale and the one for temperature to the 2000mV scale. Connect the power supply to the apparatus and switch on. At the start your gas should be at room temperature and pressure, use approximate values for room temperature and pressure to work out by what factors of 10 you need to divide or multiply your voltages to convert to centigrade and Nm-2. Commence heating the gas, up to a final temperature of 100 C. Immediately switch off the power supply. While the gas is heating, take temperature and pressure readings at regular intervals (say every 5 C) and record them in the table below.

Temperature (C)

Pressure of gas (Nm-2)

Temperature (C)

Pressure of gas (Nm-2)

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Gay Lussac’s Law states kTP = and by our earlier arguments heating the gas makes the atoms move faster which increases the pressure. We need to think a little about our scales and in particular what ‘zero’ means. Zero pressure would mean no atoms hitting the sides of the vessel and by the same token, zero temperature would mean the atoms have no thermal energy and don’t move. This is known as absolute zero. The zero on the centigrade scale is the point at which water changes to ice and is clearly nothing to do with absolute zero. So if you are measuring everything in centigrade you must change Gay Lussac’s Law to read )( zeroTTkP −= where Tzero is absolute zero on the centigrade scale. Compare )( zeroTTkP −= to the straight line formula y=mx+c. What should you plot on the x-axis and y–axis in order to get a linear relationship according to Gay Lussac’s Law? ______________________________________________________________________

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Make a plot of P versus T. Use either the graph paper below or JagFit (see back of manual) and attach your printed graph below.

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Comment on the linearity of your plot. Have you shown Gay Lussac’s Law to be true? ______________________________________________________________________

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What is the value for the slope? What is the value for the intercept? From these calculate a value for absolute zero temperature. Comment on the precision with which you have been able to find absolute zero

Absolute zero =

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Name:___________________________ Student No: ________________ Partner:____________________Date:___________Demonstrator:________________

Photoelectrical Investigations into the Properties of Solar Cells

Introduction Solar (or photovoltaic) cells are devices that convert light into electrical energy. These devices are based on the photoelectric effect: the ability of certain materials to emit electrons when light is incident on them. By this, light energy is converted into electrical energy at the atomic level, and therefore photovoltaics can literally be translated as light-to-electricity. The present experiment investigates: (1) the current-voltage relation known as the I-V curve of a solar cell; (2) the effect of light intensity on the solar cell’s power efficiency. Background Theory: First used in about 1890, the term "photovoltaic" is composed of two parts: the word “photo” that is derived from the Greek word for light, and the word “volt” that relates to the electricity pioneer Alessandro Volta. This is what photovoltaic materials and devices do: they convert light energy into electrical energy, as French physicist Edmond Becquerel discovered as early as 1839 (he observed the photovoltaic effect via an electrode placed in a conductive solution exposed to light). But it took another century to truly understand this process. Though he is now most famous for his work on relativity, it was for his earlier studies on the photoelectric effect that Albert Einstein got the Nobel Prize in 1921 “for his work on the photoelectric effect law”. Theory: Silicon is what is known as a semiconductor material, meaning that it shares some of the properties of metals and some of those of an electrical insulator, making it a key ingredient in solar cells. Sunlight may be considered to be made up of miniscule particles called photons, which radiate from the Sun. As photons hit the silicon atoms within a solar cell, they get absorbed by silicon and transfer their energy to electrons, knocking them clean off the atoms. Freeing up electrons is however only half the work of a solar cell: it then needs to herd these stray electrons into an electric current. This involves creating an electrical imbalance within the cell, which acts a bit like a slope down which the electrons will “flow”. Creating this imbalance is made possible by the internal organisation of silicon. Silicon atoms are arranged together in a tightly bound structure. By squeezing (doping) small quantities of other elements into this structure, two different types of silicon are created: n-type, which has spare electrons, and p-type, which is missing electrons, leaving ‘holes’ in their place.

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When these two materials are placed side by side inside a solar cell, the n-type silicon’s spare electrons jump over to fill the gaps in the p-type silicon. This means that the n-type silicon becomes positively charged, and the p-type silicon is negatively charged, creating an electric field across the cell. Because silicon is a semiconductor, it can act like an insulator, maintaining this imbalance. As the photons remove the electrons from the silicon atoms, this field drives them along in an orderly manner, providing the electric current to power various devices.

Figure 1. The pn junction within a silicon solar cell. Give three examples of devices that use solar cells. ______________________________________________________________________

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There are a few important characteristics of a solar cell: the open circuit voltage (VOC), the short circuit current (ISC), the power (P) output and the efficiency (η).

The VOC is the maximum voltage from a solar cell and occurs when the current through the device is zero.

The ISC is the maximum current from a solar cell and occurs when the voltage across the device is zero.

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The power output of the solar cell is the product of the current and voltage. The maximum power point (MPP) is achieved for a maximum current (IMPP) and voltage (VMPP) product (Eq. 1).

MPPMPPMAX IVP ⋅= Eq. (1)

The efficiency (η) of a solar cell is a measure of the maximum power (Pmax) over

the input power (PLIGHT) (Eq. 3):

light

MPPMPP

light

MAX

PIV

PP ⋅

==η Eq. (2)

Figure 2 shows a typical IV curve from which the above solar cell characteristics can be derived. A similar IV curve graph should be achieved in the first part of the present laboratory.

Figure 2. The IV curve of a solar cell, showing the open circuit voltage (VOC), the short circuit current (ISC), the maximum power point (MPP), and the current and voltage at the MPP (IMPP, VMPP).

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Apparatus The apparatus (Figure 3) consists of a silicon solar cell, one ammeter, one voltmeter, a halogen light source, a variable load resistor, crocodile clips and wires.

Figure 3. Apparatus for measuring the IV curve of a silicon solar cell. Part 1. Measuring the IV curve of a silicon solar cell The apparatus consists of a solar cell, an ammeter and a variable resistor both connected in series with the solar cell, and a voltmeter connected in parallel. The electrical circuit required in this experiment is given in Figure 4.

Figure 4. The solar cell’s IV curve electrical circuit.

By taking current and voltage measurements of a solar cell while using a variable resistor, you determine the current-voltage relation, or what is called the solar cell IV curve. The current and voltage of each reading are multiplied together to yield the corresponding power at that operating point.

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Method:

1. Set the circuit diagram as shown in Figure 4 2. Fix the solar cell vertically on the aluminium rail, facing toward the halogen light

source. Set the distance between the light source and the solar cell to be as large as possible

3. Switch on the halogen light source and allow 2-3 minutes for it to stabilise 4. To quickly test your setup, measure:

- the short circuit current (by setting the variable load resistor to 0); you should get a value of around 30 mA; - and the open circuit voltage (by setting the variable load resistor to maximum – rotate until the other end of the load resistor is reached); you should get around 400 mV Make sure you get the values in the positive range, otherwise reverse the wire connection to get them positive (e.g. if you get - 400 mV, then interchange the wires coming in the voltmeter and similarly for the ammeter)

5. Slowly decrease the resistance of the variable load resistor (from max to 0). For each step, simultaneously record both the current and the voltage. Take readings in small steps of resistance in order to get 20 – 25 measurement points

6. Continue until reaching the minimum resistance of the variable resistor 7. Complete the table below; calculate the power in the table ( P = V * I )

Measurement Voltage (mV)

Current (mA)

Power (mW)

1 0 0 2 3 … 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

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8. Plot the IV curve (current vs voltage) and indicate the VOC and ISC on the graph.

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9. Plot the power vs voltage (the power graph); indicate the Pmax in the power curve and find the corresponding voltage. From this graph identify VMPP and IMPP and show them on the previous graph too.

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Considering that the incident power of the halogen light source (PLIGHT) is 1 W, calculate from Eq.2 the efficiency of the solar cell. ______________________________________________________________________

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Part 2: Characterise the effect of light intensity on the solar cell efficiency Repeat the set of measurements from Part 1 using the same experimental setup and method, only this time by (approximately) halfing the distance between the light source and the solar cell. By doing this you increase the incident light intensity on the solar cell and you have to measure the response of the solar cell to this increase.

Measurement Voltage (mV)

Current (mA)

Power (mW)

1 0 0 2 3 … 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

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Plot the second IV curve (current vs voltage) and indicate the VOC and ISC on the graph.

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Plot the second power vs voltage (the power graph); indicate the second Pmax in the power curve and find the corresponding voltage. From this graph identify VMPP and IMPP and show them on the previous graph too.

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How does the efficiency change when the distance between the light source and the solar cell is decreased? ______________________________________________________________________

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______________________________________________________________________ Comment on the ISC and VOC values that you have measured for the 2 distances (in part 1 and in part 2). ______________________________________________________________________

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What relationship between the solar cell efficiency and light intensity can you deduce from your findings? ______________________________________________________________________

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Using JagFit

In the examples above we have somewhat causally referred to the ‘best fit’ through the data. What we mean by this, is the theoretical curve which comes closest to the data points having due regard for the experimental uncertainties. This is more or less what you tried to do by eye, but how could you tell that you indeed did have the best fit and what method did you use to work out statistical uncertainties on the slope and intercept? The theoretical curve which comes closest to the data points having due regard for the experimental uncertainties can be defined more rigorously3 and the mathematical definition in the footnote allows you to calculate explicitly what the best fit would be for a given data set and theoretical model. However, the mathematics is tricky and tedious, as is drawing plots by hand and for that reason.... We can use a computer to speed up the plotting of experimental data and to improve the precision of parameter estimation.

In the laboratories a plotting programme called Jagfit is installed on the computers. Jagfit is freely available for download from this address: http://www.southalabama.edu/physics/software/software.htm

Double-click on the JagFit icon to start the program. The working of JagFit is fairly intuitive. Enter your data in the columns on the left.

• Under Graph, select the columns to graph, and the name for the axes. • Under Error Method, you can include uncertainties on the points. • Under Tools, you can fit the data using a function as defined under

Fitting_Function. Normally you will just perform a linear fit.

3 If you want to know more about this equation, why it works, or how to solve it, ask your demonstrator or read about ‘least square fitting’ in a text book on data analysis or statistics.