Download Experiment 2

Physics Laboratory Manual
PHYC 10180
Physics for Ag. Science
2014-2015
Name.................................................................................
Partner’s Name ................................................................
Demonstrator ...................................................................
Group ...............................................................................
Laboratory Time ...............................................................
2
Contents
4
Introduction
Laboratory Schedule
5
Springs
7
Newton’s Second Law
15
An Investigation of Fluid Flow using a Venturi
Apparatus
21
Archimedes’
Measurements
29
Principle
and
Experimental
Heat Capacity
35
Investigation into the Behaviour of Gases
and a Determination of Absolute Zero
43
Photoelectrical Investigations into the Properties of
Solar Cells
53
Using JagFit
65
3
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.
4
Laboratory Schedule
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 and 9
Wednesday 4-6: Groups 2,4,6,8,10 and 11.
Dates
19 - 23 Jan
Semester
Week
1
26 - 30 Jan
2
2 - 6 Feb
3
9 - 13 Feb
4
16 – 20 Feb
5
23 – 27 Feb
6
2 – 6 Mar
7
23 - 27 Mar
8
30 Mar - 3 Apr
9
6 - 10 Apr
10
13 - 17 Apr
11
20 - 24 Apr
12
Science East 143
Springs:
1,2
Springs:
7,8
Heat Capacity:
1,2
Heat Capacity:
7,8
Heat Capacity:
5,6
Heat Capacity:
11
Heat Capacity:
3,4
Heat Capacity:
9,10
Fluids:
1,2
Fluids:
7,8
Fluids:
5,6
Fluids:
11
5
Room
Science East 144
Springs:
3,4
Springs:
9,10
Newton:
3,4
Newton:
9,10
Newton:
1,2
Newton:
7,8
Newton:
5,6
Newton:
11
Solar:
3,4
Solar:
9,10
Solar:
1,2
Solar:
7,8
Science East 145
Springs:
5,6
Springs:
11
Gas:
5,6
Gas:
11
Gas:
3,4
Gas:
9,10
Gas:
1,2
Gas:
7,8
Archimedes:
5,6
Archimedes:
11
Archimedes:
3,4
Archimedes:
9,10
6
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?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
7
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
What features of the graphs do you think are important and why?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
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.
8
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
Position of the top of spring
Position of the bottom of spring
New length of spring
9
Spring 2
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
Disk 1
Disk 2
Disk 3
Disk 4
Disk 5
Total mass
added to the
mass hanger
(g)
30
40
New reference
position (cm)
New spring
length (cm)
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
Disk 1
Disk 2
Total mass
added to the
mass hanger
(g)
30
New reference
position (cm)
New spring
length (cm)
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.
10
Graph representing the length of the two springs for different masses added to the
hanger.
11
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.
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
Work out the slopes of the two lines.
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
What are the two intercepts?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
How can you use the slopes of the two lines to compare the stiffness of the springs?
______________________________________________________________________
______________________________________________________________________
12
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
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?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
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.
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
13
14
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 F  ma , 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
15
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?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
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
s  ut 
1 2
at , where s is distance, u the initial velocity, t is time, and a acceleration.
2
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.
16
mh
(kg)
0.012
mcart
(kg)
0.5
M=
mh+mcart
(kg)
a (m/s2)
M.a (N)
1/a (m-1s2)
s (m)
t (s)
0.012
1.0
s (m)
t (s)
s (m)
0.012
1.5
t (s)
From the numbers in the table what do you conclude about Newton’s second law?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
Analysis and determination of the acceleration due to gravity.
If Newton is correct, F  (mh  mcart )  a
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.
F  (mh  mcart )  a 
m
1 1
 mcart  h
a F
F
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?
17
What value do you get for the intercept?
Create your graph either manually or using Jagfit (see back of manual) and attach your
printed graph below.
18
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.)
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
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/s 2.
How does the accuracy of your measurements affect this comparison?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
19
20
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, called a Venturi apparatus, the
amount of fluid flowing along the channel (volume/time) remains constant but the velocity
and pressure of the fluid vary along the channel. In the Venturi apparatus used here
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 = 𝐴0 𝑣0 = 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.
If the pressure change is due only
to a velocity change (i.e. there is
no change in height, a simplified
version of Bernoulli’s equation can
be used:
𝜌
𝑃 = 𝑃0 − 2 {𝑣 2 − 𝑣02 }
(Eq. 2)
Here  is the density of water:
1000 kg/m3.
The flow rate also depends on the pressure, P0, behind the fluid flowing into the
apparatus (Poiseuille’s law). In this experiment the pump provides the pressure that
makes the fluid flow through the apparatus. The higher the power to the pump the
greater the pressure and the faster the fluid flows.
In this experiment you will use the Venturi apparatus to investigate fluid flow and verify
that equation 2 holds. You will also investigate how the voltage supplied to the pump
affects the pressure and flow rate.
21
Apparatus
The apparatus consists of a reservoir, which is a plastic box, of water connected to a
Venturi apparatus (see picture and figure below) through which the water can flow into a
collecting beaker, itself placed in a box. An electrical pump causes the water flow in the
apparatus.
Wide section.
Narrow section.
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 (A 0) and small (A) crosssections by multiplying the depth by the width for the two sections of the apparatus.
Depth____________ Width (large)______________ Width (narrow) ______________
Area (A0) ______________ Area (A) ______________
.
22
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 apparatus 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”.
Make sure that the eight fixing taps on the Venturi apparatus are all just finger tight. Fill
the reservoir so that the pump is fully submerged in the plastic box. Ensure that the
outlet of the apparatus is in the beaker which is in the box. Turn on the power supply
to the pump and set the voltage to 10V. Remove any air bubbles by gently tilting the
outlet end of the Venturi apparatus upwards.
Measure the time that it takes for 400 ml (0.4l = 4x10-4 m3) of water to flow through the
Venturi apparatus. Be sure to read the water level by looking at the bottom of the
meniscus.
When the flow is steady note the pressures on the four sensors. Enter your data in the
table. Repeat the measurements twice more. Be sure to return all the water to the
reservoir (plastic box). Make sure that the apparatus stays free of air bubbles.
Run
P1
P2
P3
P4
Time
/kPa
/kPa
/kPa
/kPa
/s
1
2
3
Average
23
Calculate the flow rate, Q, volume/time in units of m3s-1, from the average value of the
time taken for 400 ml to flow through the apparatus. Remember 1ml = 1cm3 = 1x10-6 m3.
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
Use equation (1) and the cross-sectional areas that you calculated to work out the
velocity of the water flow in the wide (v0) and narrow (v) sections of the apparatus.
v0=
v=
______________________________________________________________
______________________________________________________________
Which is larger v or v0? Is this what you expected?
____________________________________________________________________
____________________________________________________________________
If the apparatus was not constricted the pressure at point 2 (P 0) would be equal to the
average of the values P1 and P3. Use your average values of P1 and P3 to calculate P0:
P0=1/2(P1+P3) _______________________________________________________
____________________________________________________________________
Use equation 2 and your values for P0,v0 and v to calculate a value for P, the pressure in
the narrow section of the apparatus. The SI unit for pressure is the Pascal (Pa), 1kPa =
1000 Pa = 1000 N/m2 = 1000 kg s-2 m-1.
P= _________________________________________________________________
____________________________________________________________________
____________________________________________________________________
How does your value for the pressure in the narrow section compare to the measured
values P2 and P4? You might consider how precisely you can determine both the
calculated and measured pressures.
_________________________________________________________________
____________________________________________________________________
24
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
Next measure the pressure at a range of different pump supply voltages to the pump.
Complete the table below.
Voltage /V
P1 /kPa
P2 /kPa
P3 /kPa
P4 /kPa
Average
of P1 and
P3 /kPa
Average
of P2 and
P4 /kPa
6
7
8
9
10
11
12
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 two average pressures as a function of pump voltage on the same
graph. Create a graph either manually or using Jagfit (see back of manual) and attach
your printed graph below.
25
26
Comment on your graph, is it consistent with what you expected to happen?
__________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
What can you conclude from this part of the experiment?
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
27
28
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 Galileo 1 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?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
1
Actually, the story is probably apocryphal. However 11 years before Galileo was born, a similar experiment was
published by Benedetti Giambattista in 1553.
29
Experimental Uncertainties
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 245  5
km, 253  1 km, 254.2  0.1 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.
h=

Measure and write down the diameter of the cylinder.
d=

30
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.
r2 =

Finally work out the volume. Estimate how well you can determine the volume.
V=

31
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.
h=

Measure and write down the diameter of the cylinder.
d=

Now calculate the radius.
r=

Calculate the radius squared – with it’s uncertainty!
(Show your workings)
r2 =
Finally work out the volume.
V=

32

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.
_____________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
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.
33
Can you think of any systematic uncertainties that should be considered?
estimate their size?
Can you
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
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 ______________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
34
Name:___________________________
Student No: ________________
Partner:____________________Date:___________Demonstrator:________________
Determination of the Specific Heat Capacity of
Copper and Aluminuim.
Introduction
The heat capacity of a material is a measure of the materials ability to absorb heat, or
thermal energy. As a body becomes hotter, the atoms and molecules that comprise it
begin to move more and more violently. In the case of solids, the atoms or molecules
vibrate about the positions that they occupy in the solid. As the temperature of the
material increases, the vibrations become more energetic, eventually breaking the bonds
that hold the solid together as the solid begins to melt.
The purpose of this experiment is to measure the heat capacity of two metals, copper
and aluminium, by supplying a known quantity of heat and recording the resultant rise in
temperature.
The heat capacity of an object is defined as the energy required to raise the temperature
of the object by 1 K. Clearly the greater the mass of the object the more heat is required,
so a more useful quantity is the Specific Heat Capacity (SHC) of an object. This is
defined as the energy required to raise the temperature of 1 kg of the material by 1 K.
Expressing this mathematically,
Q  mc(T f  Ti )
where Q is the amount of heat required, m is the mass of the object, Ti & Tf are the initial
and final temperatures of the object and c is the SHC, measured in units of Joules per kg
per Kelvin (J kg-1 K-1).
Apparatus:
 1 power supply
 1 12V, 50W Immersion heater
 1 1kg block of copper
 1 1kg block of aluminium
 1 Joule-Watt meter plus 10A shunt
 Laboratory thermometer
 Digital multimeter
35

Stopwatch
Health and Safety:
Switch off apparatus after completion of readings.
Take care when handling the blocks and the heater elements, they are very hot.
Do not place the metal blocks directly on the laboratory bench.
Be sure to place the metal blocks on an insulating material, such as a piece of
wood, before heating them.
Set up:
 Set the power supply to 12V AC.
 Connect cables from the power supply (AC output) to the Joule-Watt meter.
 Connect the immersion heater to the Joule-Watt meter where it says ‘load’.
 Insert the immersion heater into one of the metal blocks.
 Insert a thermometer into the same block.
Figure 1. Specific heat experimental arrangement, be sure to connect the ac output
(yellow) from the power supply to the Joule-Watt meter.
Procedure:
Start with the aluminium block and repeat for the coppper one.



Measure the fraction of the heater, f, inserted in the block.
insert the probes into the cables attaching the heater to the Joule-Watt meter,
make sure everything is turned off, then record the resistance.
From the resistance and the voltage (12 Volts for all the measurements carried
out here) you can work out the electrical power, P, supplied to the block.
Figure 2. Set up for measuring the resistance.
36








Reset the energy display on the Joule-Watt meter.
Record the initial temperature of the block,T1.
Switch on the power supply and start the stopwatch.
Record the temperature and resistance at two minute intervals (one minute
intervals for copper), when it is heating and cooling. Complete the table below.
When the temperature has risen by 20 degrees or after 20 minutes, whichever
comes first, switch off the power supply unit. Note down the energy reading
on the Joule-Watt meter and the electrical heating time (theat).
The temperature will continue to rise for a short period after switching off. Wait
until it reaches maximum, then record the temperature T2.
Stop the stopwatch and record the time, t, and immediately zero and restart the
stopwatch.
Note the temperature, T3, after the block has cooled for t seconds.
Record your temperatures below
Time:
mins
Aluminium
Copper
Heating
Resistance Cooling
Heating
Resistance Cooling
Temp (K)
(Ohm)
Temp (K)
(Ohm)
Temp (K)
1
2
3
4
5
6
7
8
9
10
11
37
Temp (K)
12
13
14
15
16
17
18
19
20
Plot the temperature of both blocks as a function of time on the same graph and
comment on the graphs.
_____________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
Cooling Correction:
The block loses heat during the heating cycle. In the absence of these losses it would
have reached a higher final temperature. The uncorrected final temperature is T2. The
corrected final temperature (T4) may be approximated as:
T2 
T2  T3
 T4
2
This formula assumes the dominant heat loss mechanism is due to convection by
heated air, neglecting the cooling due to radiation and conduction.
The readings should be recorded as follows:
Al
38
Cu
Units
Fraction of the heater inserted in the block, f.
Mass of cylinder, m
Kg
Initial temperature, T1
K
Uncorrected final temperature, T2
°C
Electrical Heating Time, theat
Sec
Temperature after t sec cooling, T3
K
Corrected final temperature, T4
K
Rise in temperature, (T4-T1)
K
Resistance of the Heater, R.
Ω
Voltage, V.
V
Power, P. 𝐏 =
𝐕𝟐
W
𝐑
Energy supplied to heater, J = (P x theat)
J
Energy supplied to the block, E = (J  f)
J
Energy as noted from Joule-Watt meter (J2)
J
Energy supplied to the block, E2 = (J2  f)
J
The specific heat capacity, c, may be calculated from conservation of energy. You
should do a calculation based on the energy reading from the Joule-Watt meter and a
second based on the calculated electrical energy supplied.
Electrical energy supplied  increase in stored thermal energy (accounting for
heat losses)
Thus,
therefore:
Metal
Aluminium
Copper
E = mc(T4 – T1)
E
c
m(T4  T1 )
Joules / ( kg K)
Accepted value
J/(kg K)
960
390
Measured Value
J/(kg K)
Measured Value
J/(kg K)
How do your results compare with the accepted values? Comment on any differences
between your measurements and the accepted values. What are the sources of
uncertainty in the experiment?
39
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
How do your results for the electrical energy supplied to the heater differ from the
reading on the Joule-Watt meter? Give reasons. Did it affect your results significantly?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
40
Radiative Heat Losses:
There are three mechanisms for heat loss - convection, conduction and radiation.
In the above experiment we assume convection losses only and ignored the possibility
of losses by conduction, (due to contact of the block and bench) and radiation. If the
experiment had been performed in a vacuum there would have been no conductive or
convective heat losses, and energy could only be lost by radiation.
According to radiation theory, the rate of heat loss by any object at temperature T to its
surroundings at temperature TS is then given by the Stefan- Boltzmann equation:
E/t=A (T4 – TS4) (Eqn. 1)
where Temperature is measured in Kelvin, A is the surface area of the emitter,
Stefan's constant σ = 5.67 × 10-8W m-2 K-4 and ε is the emissivity of the surface, (ε = 1
for an 'ideal' emitter or black body). In the present case, ε, can be calculated as follows:
The amount of heat lost as the block cools from T2 to T3 in time t sec is given by:
E=mc(T2 –T3) (Eqn.2)
If we assume that this energy is all radiated then, using Eqn. 1,
E=A ([(T2+T3)/2]4 – TS4) t (Eqn. 3)
where (T2 + T3)/2 is taken as the average temperature over the cooling cycle. Therefore,
equating Eqn. (2) and (3) we get:
 mc(T2 - T3 A ([(T2+T3)/2]4 – TS4) t]
Calculate a value of ε for each of the two blocks. Comment on your results and in
particular, if you have obtained a value greater than 1, explain why. What factor(s)
would you have to incorporate to obtain a more realistic value?
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
41
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
42
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.
PV  k .
Thus P  1V or introducing k, a constant of proportionality, P  k V or
This is Boyle’s Law.
43
Similarly you can see that at constant volume, increasing the temperature should
increase the pressure by a proportional amount. So P  T or introducing  , a
constant of proportionality,
P  T
or
P  .
T
This is Gay Lussac’s Law.
These laws can be combined into the Ideal Gas Law that relates all three quantities by
PV  nRT
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.
44

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: P  k V 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.
______________________________________________________________________
______________________________________________________________________
x-axis=
y-axis=
What should the slope of your graph be equal to?
_______________________________
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.
45
Use either the graph paper below or JagFit (see back of manual) and attach your
printed graph below.
46
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?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
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 =
47
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)
48
Pressure of gas
(Nm-2)
Gay Lussac’s Law states P  kT 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 P  k (T  Tzero ) where Tzero is
absolute zero on the centigrade scale.
Compare P  k (T  Tzero ) 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?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
What should the slope of your graph be equal to?
What should the intercept of the graph equal?
How can you work out Tzero?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
49
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.
50
Comment on the linearity of your plot. Have you shown Gay Lussac’s Law to be true?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
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 =
51
52
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.
53
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.
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
Important characteristics of solar cells:
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.
54
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).
PMAX  VMPP  I MPP
Eq. (1)
The efficiency (η) of a solar cell is a measure of the maximum power (Pmax) over
the input power (PLIGHT) (Eq. 3):

PMAX VMPP  I MPP

Plight
Plight
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).
55
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.
56
Method:
1. Use the orange meter to measure the resistance of the load resistor, work out which
connection is which.
2. Use the same meter to measure the open-circuit voltage, VOC, of the solar cell. You
can connect the meter directly to the solar cell.
3. Include the load resistor and check that the voltage you measure varies as you would
expect when you change the resistance.
4. Set the circuit diagram as shown in Figure 4, use the yellow meter to measure the
current.
5. 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.
6. Switch on the halogen light source and allow 2-3 minutes for it to stabilise
7. 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 into the voltmeter and similarly for the ammeter).
8. Slowly increase the resistance of the variable load resistor (from 0 towards max) until
you notice a small change in current. 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.
9. Continue until reaching the maximum resistance of the variable resistor
10. Fill in the table over the page, calculate the power in the table ( P = V * I ).
11. Plot the IV curve (current vs voltage) and indicate the VOC and ISC on the grap
12. Plot the power vs voltage (the power graph); indicate the Pmax in the power curve and
find the corresponding voltage. From this graph identify V MPP and IMPP and show
them on the previous graph too.
Considering that the incident power of the halogen light source (PLIGHT) is 1 W, calculate
from Eq.2 the efficiency of the solar cell.
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
57
Measurement
Voltage
(mV)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Current
(mA)
Power
(mW)
0
0
…
58
IV curve (current vs voltage)
59
Power vs voltage (the power graph)
60
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)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Current
(mA)
Power
(mW)
0
0
…
61
Plot the second IV curve (current vs voltage) and indicate the V OC and ISC on the graph.
62
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 V MPP and IMPP
and show them on the previous graph too.
63
How does the efficiency change when the distance between the light source and the
solar cell is decreased?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
Comment on the ISC and VOC values that you have measured for the 2 distances (in part
1 and in part 2).
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
What relationship between the solar cell efficiency and light intensity can you deduce
from your findings?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
What else do you can conclude from your measurements? You should also comment
on how your experimental results might be improved and also on the uncertainty that
might have been introduced in these measurements.
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
__________________________________________________________________
64
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.



3
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.
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.
65