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The University of the West Indies

PHYS 0412INTRODUCTION TO OSCILLATIONS & HEAT

Department of Physics

(Revised 2011)

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CONTENTS

AIMS ...................................................................................................................................................... iii

GUIDELINES ........................................................................................................................................... iii

TIPS ........................................................................................................................................................ iv

Format for Writing a Lab Report: .......................................................................................................... iv

Straight Line Graphsv

EXP. 1 Introductory Experiment ......................................................................................................... 1

EXP. 2 Simple Harmonic Motion ........................................................................................................ 2

EXP. 3 The Spiral Spring ...................................................................................................................... 4

EXP.4 Calorimetry .............................................................................................................................. 6

EXP. 5 Methods of Heat Transfer ..................................................................................................... 11

EXP. 6 Gay-Lussacs Law and Boyles Law ........................................................................................ 14

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iii

AIMS

The Phys0411 Lab Course has several aims.

a) It is designed to train you to perform an experiment and to record and analyze the results inan orderly scientific manner.

b) It will teach you to use scientific instruments.

c) The experiments will, in some cases, give you further insight into the physical laws governing

the processes you are investigating.

GUIDELINES

1)

A list would be posted in your notice board (outside Room 121) showing the experiment youwould be doing any week as well as the location of that experiment. Hence, you can read

the manual ahead of time.

2) Sign up the attendance sheet when you come into the lab. This sheet would be removed 30minutes after the scheduled start of the lab. Latecomers will lose 1 or 2 points on that days

experiment. Those who come more than 30 minutes late will not be allowed to do the

experiment.

3) The lab would start on time and finish on time. Learn the art of punctuality. It would helpyou a lot in life.

4) To help you to maximize your concentration in the Lab & to minimize distractions, no food,drink, cell phone conversations or visits by friends will be allowed during the lab period.

5) Lab reports will be written only in a Physics Lab Notebook, which is available in theBookshop. Write your name & lab day inside & outside at the bottom.

6) You will complete all your work in the lab and place your report on the table, according toyour experiment number.

7) Anyone doing cheating or copying of any kind will get zero for that experiment & further willhave to take the Practical Exam. Bringing lab reports from the previous years to the lab or

having any write-up in your lab manual (other than what is already printed) would be

considered as cheating. You may find it helpful to bring your textbook to the lab for

consultation purposes.

8) Your overall score for Phys0411 is as follows: 70 points from the final exam + 10 points fromthe first test + 10 points from the second test + 10 points from the Lab.

9) Those who fail the lab will have to take the Practical Exam. In this case, the practical examcontributes 20% to the lab grade while the remaining 80% comes from the earlier lab work.

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TIPS

1. Read your lab manual ahead of time and come prepared to start the experiment. This wouldhelp you to enjoy your lab work, complete the experiment on time and get a good grade. (The

lab time is not meant for reading the Lab Manual)

2. Write your experimental data in pen and only in your lab notebook and not in rough papers.This would help you to develop care & self-confidence. Attach the appropriate units to all your

data.

3. Get at least one set of your data verified and signed by one of your lab staff. This would helpyou to avoid systematic & serious errors.

4. Your lab partner & you would work together in taking the data. Rest of the work would be doneindividually. This would help you to profit more from your experiment.

5. In general, it would be wise to spend about 2 hours in taking the data and one hour in analyzingyour data. The 10 points for the experiment are distributed roughly as follows:-

DATA (quality & quantity, neat tabulation & units) 3

GRAPHS (whenever possible, with proper scales & labels) & CALCULATIONS 4

DISCUSSION (of the results & errors) & ANSWERS to questions 3

Format for Writing a Lab Report:

Date

Your Name & Your Partners Name

Experiment Number & Title

Aim of the Experiment

Procedure: Simply write the following: As in the Lab Manual. (Nothing else needed)

Data in Tabular Form

Graphs

Calculations

Discussion of the Results

Answers to Questions

Conclusion

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STRAIGHT LINE GRAPHS

Usually, we have two variables in a Physics experiment. e.g. The Simple Pendulum of length L with

the period T =

g

L2 . Here, we vary L and investigate how T changes with L. Sometimes, we have

three variables. e.g. The attractive force F between the earth, with mass m1 , and an object of mass

m2 at a distance r from the centre of the earth is given by 221

r

mmGF = . Here, out of the three

variables F, m2 and r2, we keep one variable constant and investigate the relation between the

other two.

The results of such experimental investigations can be displayed attractively through graphs. Since

it is easier to pull out a lot of useful information from straight line graphs, most of the time, we

represent the data in straight line graphs.

Any straight line graph can be represented by the equation, y = m x + c. Here, x represents the

variable plotted along the X-axis & y the variable plotted along the Y-axis. The constant m = slope or

gradient of the straight line, while the constant c = the y-intercept.

The constants m & c may be +ve, -ve or zero. Note that when m is +ve, y increases with x i.e. the

line moves upward. However, when m is -ve, y decreases with x i.e. the line moves downward.

When m is zero, y does not change with x and hence the line is horizontal. When c is +ve, the line

hits the Y- axis on the +ve side i.e. above the X-axis. But, when c is -ve, the line hits the Y-axis on the

-ve side i.e. below the X-axis. Of course, when c is zero, the line goes through the origin.

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LESSON 1: If you want to get a straight line graph for your data, before plotting them, rearrangethe formula relating your two variables so that it looks like y = m x + c.

e.g. 1) T =g

L2 )(

4)(

42

22

2L

gT

g

LT

==

. This is in the

form y = m x + c, if y = T2 & x = L. Note that the slope m = 42/g & the y-intercept c = 0

i.e. the line would go through the origin.

e.g. 2)2

21

r

mmGF = , where, the variation of F with r is studied, keeping m2 constant.

=

221

1)()(

rmmGF . This is in the form y = m x + c, if y = F & x =

2

1

r. Note that

the slope m = G m1 m2 & the y-intercept c = 0.

LESSON 2: If there is a straight line graph, you can get its equation, by measuring the slope m ofthat line & the y-intercept c, and substituting them in the formula y = m x + c.

EXERCISES

1.For the simple pendulum, T =g

L2 . If T is plotted along the Y-axis (instead of T

2), what

should you plot along the X-axis, in order to get a straight line? In this case, what is the slope of

the straight line?

2.The magnetic field at a distance y from the centre of a bar magnet, along its axis, is given by

32 y

MB

= , where M is a constant for the given bar magnet. In an experiment, for 8

values of y, a student measures the corresponding 8 values of B. How would you plot these

measurements in order to get a straight line? How would you get M of the given bar magnet

from your graph?

3.The current I through a resistor R in an electrical circuit is given by2+

=R

EI o , where Eo is an

unknown constant. If you are given 8 values of R and the corresponding I, how will you plot

these data so as to get a straight line? How would you obtain the value of the unknown

constant Eo from your graph?

4.Obtain the equations for the following straight line graphs. Note that the variables that areplotted are not x and y all the time.

A B C

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EXP. 1 Introductory Experiment

Aim: To investigate the variation of volume with temperature at constant pressure, Charles Law.

Theory:

A manometer is a pressure measuring instrument consisting of a vertical column of liquid with both

ends of the liquid exposed to different temperatures. The height of the column will rise or fall to

denote the difference in pressures between to the ends. When the amount of mercury in the

manometer has been adjusted so that the two columns are the same height, the pressure of the

gas is equal to atmospheric pressure.

Procedure:

1. Open the webpage http://www.chm.davidson.edu/vce/gaslaws/charleslaw.html and scroll tothe simulation at the bottom of the page.

2. A small volume of air has been trapped inside the manometer shown on the left of the screen.The air has been coloured green to make it visible.

3. Construct your table to include the following measurements: the height of air in themanometer, the volume of air in the manometer and the corresponding temperature. Note

well that all readings taken should be recorded.

4. Carefully measure the height of the air in the manometer and find its volume. The insidediameter of the tube is 4.286cm. Please note that the manometer scale is in mm.

5. Measure the temperature and record this value.6. Adjust the temperature value by dragging the temperature scale up or down as desired. Record

the new temperature value.

7. Adjust the height of the mercury in the manometer by clicking on the orbuttons to decrease or increase the volume of mercury in the manometer until the air inside

the manometer is at atmospheric pressure.

8. Record the new height of air in the manometer and find the volume.9. Repeat steps six to eight until you have eight sets of readings.10.Plot a graph of volume vs temperature. Use a suitable axis so that the graph may be extended to

V=0, which should intercept the negative x-axis.11.Find the gradient of your graph and the value for the x-intercept (V=0).12.Compare this value to the theoretical value for absolute zero.13.Discuss your results including errors, a description of your graph and what that implies about

the relationship between volume and temperature of a gas. Thus, state Charles Law.

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EXP. 2 Simple Harmonic Motion

Aim: To investigate simple harmonic motion in the oscillation of a simple pendulum using

simulation and hands on.

Theory:

Simple harmonic motion (SHM) results when a body is acted on by a restoring force Fthat is

always proportional and in the opposite direction to its displacement from the mean position i.e.

F = - k x (1)

wherex = displacement and kis a constant of proportionality.

Newtons 2nd Law F = ma a = F/m

Substituting from equation (1) a = - k x/m a = - 2x (2)

where a is the acceleration. Such an equation can be satisfied by the motion

x = A cos t (3)

whereA is the amplitude and the angular frequency. may also be written in terms of the period

of the oscillation T as

T = 2 / (4)

A common example of simple harmonic motion is the simple pendulum, shown in Figure 1

below. The motion of the bob in the horizontal plane can be shown to be simple harmonic for

small displacements i.e. for 8o

(see Fig. 1). Thus, using eq. 1, the simple pendulum can give a

measurement ofg, the acceleration due to gravity.

For a simple pendulum of length L, g

LT 2=

(5)

Figure 1

8o

L (30 cm to 150 cm)

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Procedure:

Part 1. Simple Pendulum

1. Suspend the heavier bob by a fairly long piece of string from the retort stand and measure thestring length L to the centre of gravity of the bob. Air draughts will cause errors so try to have a

draught-free position for your stand.

2. Time 10 oscillations (remembering that in one complete oscillation the bob passes the centralposition twice).

3. Repeat for a second set of 10 oscillations and hence find the average period Tfor the length ofstring. Make sure that the oscillations are of small amplitude, as this theory is only valid for

small oscillations.

4. Repeat for 7 different lengths of string, making sure you choose lengths whose values arereasonably spaced.

5. Tabulate your results neatly, using SI units, keeping in mind eq. 1. Be sure to include the error inyour measured readings.

6. Plot your data suitably so as to get a straight line using equation (5).7. Find the gradient of your graph and hence calculate g, the acceleration due to gravity.8. Comparing your result with the published value, obtain the percentage error and comment on

your results.

9. How do you expect the period of the pendulum to vary with the mass of the bob?(Check your answer by repeating one set of swings with the same length of string but with a

different pendulum bob)

10.Sketch eq. 3, with t along the X-axis. Show A and T in this sketch.Part 2. Simple Harmonic Motion on the Moon

11.How do you expect the period and amplitude to change if this experiment was carried out onthe moon?

a. Open the Phet simulation on the computer.b. From the menu options on the right select moon and photogate timer. Adjust the length

and mass to values used in your experiment and press the start button.

c. Record the values of length and period.d. Describe your observations and explain why you think you got these results.e. Vary the length for five additional sets of readings and plot a suitable graph. Obtain a

value for g on the moon.

12.Change the selection from moon to Jupiter. Press play. What can you tell about gravity onJupiter from your observations?

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EXP. 3 The Spiral Spring

Aim To investigate the way spring constants add up, when 2 springs are connected in series & in

parallel.

Apparatus Simple pendulum, two identical spiral springs and masses

Theory

Simple harmonic motion (SHM) results when a body is acted on by a restoring force Fthat is always

proportional and in the opposite direction to its displacement from the mean position i.e.

F = - k x (1)

wherex = displacement and kis a constant of proportionality.

Another common example of SHM is that of a mass m suspended from a spiral spring, with the

spring constant k. For the oscillations of a mass m in a spring, of spring constant k,

k

mT 2=

(2)

Procedure

Part 1

1. Suspend one of the springs from the retort stand and hang an appropriate mass m (neither toobig, nor too small) from it. Give it a small vertical displacement and time 20 oscillations.

2. Repeat for 7 other masses.3. Tabulate your data neatly in SI units, keeping in mind eq. 24. Plot your data suitably and hence find the value of the spring constant k.

Qn. 1 Would you expect the same value of k if you were to repeat the experiment on the Moon?

Explain.

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Part 2

1. The above formula for the period of a spring is derived assuming that the extension of thespring is proportional to the applied force, i.e. F = - k x, where Fis the applied force andxthe

extension of the spring from equilibrium. For the spring used, friction between the coils tends

to prevent the initial extension of the spring when a very small force is applied. To eliminate

this effect, hang an initial mass of about 0.100 kg from the spring such that the coils are

separated.

2. Now measure the additional extensionsxdue to additional forces Fcreated by hanging variousweights from the spring.

3. Tabulate neatly in SI units your data on additional masses and the additional extensions.4. Plot your data suitably so as to get a straight line. Refer eq. 15. Obtain k from your graph. Compare this with the value determined above.

Qn. 2 Two springs are made of two different materials, from wires of the same thickness. Both the

springs have the same length and the same number of turns. Explain whether their spring

constants will be the same, or not.

Qn. 3 When two springs (with spring constants k1 and k2) are connected in series, or in parallel,

the effective spring constant keffis given by one of the following:

21kkkeff += OR

21

111

kkkeff

+=

a) Suppose two springs (with spring constants k1 and k2) are connected in parallel. Predict whether

keffwill be greater than, or less than, k1 and k2. Check by an experiment if your prediction is correct

or not. Hence, determine which of the above two equations is valid for parallel combination of

springs.

b) Suppose the two springs are connected in series. Predict whether keffwill be greater than, or less

than, k1 and k2. Check by an experiment if your prediction is correct or not. Hence, determine which

of the above two equations is valid for series combination of springs.

Reading: Physics 7th edition by Cutnell & JohnsonChapter 10 Simple Harmonic Motion

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EXP.4 Calorimetry

Aim To determine the latent heat of fusion of ice& the specific heat capacity of a solid and a liquid

Apparatus Copper calorimeter, thermometer, ice, brass masses in a can of boiling water,

electrical aluminium calorimeter, power supply, rheostat, switch, voltmeter and fluorescein

solution

Theory

The latent heat of fusion of ice L is the amount of heat required to melt one kg of ice at Co to water

at Co

.

The specific heat capacity S of a substance is defined as the heat energy required to raise the

temperature of one kg of the substance by one Co .

Temperature reading in K i.e. Kelvin = Temperature reading in Co + 273.15

T in K = T in Co (e.g. change of 5.0 K = change of 5.0 Co ) (1)

In Part 1 and 2, we use the method of mixtures i.e. we take a hot body (or bodies), mix it with a

cold body (or bodies), and determine the final equilibrium temperature of the mixture. Since

thermal energy is conserved we have:

Heat lost by hot bodies = Heat gained by cold bodies (2)

Procedure

Part 1 Latent Heat of Fusion of Ice L

1. Measure the mass mc of the empty copper calorimeter & stirrer (without outer can andlagging).

2. Now add tap water to the calorimeter until it is about full.

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3. Measure the new mass mn. Calculate (mn mc), the mass of water in the calorimeter, mw.4. In order to minimize the effects of heat exchanges with the surroundings, heat the calorimeter

containing water to about 6 Co above room temperature, by adding a little bit of boiling water.

During the heating, use the stirrer to keep the water well mixed, but do not splash or lose

water.

5. When ready, note the temperature Th of the hot bodies.6. Now, add quickly small pieces of ice (at the cold body temperature Tc = 0 Co ), dried on a paper

towel, until the temperature falls to about 6 Co below room temperature with all the ice

melted and the mixture properly stirred.

7. Note the final temperature of the mixture Tf. (You will need to leave the lid off the calorimeterto do this experiment).

8. Measure the final mass mf i.e. of the calorimeter & stirrer + initial water added + ice added,which has melted to water. Calculate (mf mn), the mass of ice added, m i.

The hot bodies consist of the calorimeter & stirrer + water + thermometer. The cold body is the ice.

The heat required to melt the ice is equal to the latent heat of fusion of ice times the mass of ice

added. Further heat is required to raise the temperature of the melted ice from 0 Co to the final

temperature of the mixture. Thus equation (2) takes the form below:

(mc Sc + mw Sw + k) (Th Tf) = mi L + mi Sw (Tf Tc) (3)

where, Sc = specific heat capacity of the calorimeter & stirrer = 390 J kg-1

K-1

Sw = specific heat of water = 4200 J kg-1

K-1

k = correction for heat capacity of thermometer which is quite small

and will be neglected

9. Using your data in (3), calculate L.

Part 2 Specific Heat Capacity Sb of Brass

In Part 1, you have already measured the mass mc of the empty copper calorimeter & stirrer

(without outer can and lagging).

1. Now add tap water to the calorimeter until it is about half full. In order to minimize the effectsof heat exchanges with the surroundings, cool the calorimeter containing water to about 6 C

o

below the room temperature. For this, add a little bit of ice and keep stirring until all the ice has

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melted. Note the temperature, and repeat this process until the temperature of the water is

around 4 to 6 Co below the room temperature.

2. Measure the new mass mn.3. Calculate (mn mc), the mass of water in the calorimeter, mw.4. Some brass masses will be found in a can of boiling water. Just before adding the brass mass,

note the temperature Tc of the cold water in the calorimeter.

5. Take one brass mass, at the temperature Th = 100 Co , from the boiling water, quickly removeany water adhering, lower it in the calorimeter containing water cooled below room

temperature and, stirring continuously.

6. Note the final temperature Tfto which the mixture rises. This is not particularly accurate andyou will need to be very quick in transferring the mass, but dont splash! Take care also not to

touch the hot mass with the thermometer.

7. In the brass mass, you may be able to read directly its mass mb. If that is not possible, measurethe final mass mf i.e. of the calorimeter & stirrer + cold water + brass mass. (mf - mn) give themass mb of brass added.

Now, the cold bodies consist of the calorimeter & stirrer + water + thermometer. The hot body is

the brass block. Heat lost by the hot body is gained by the cold bodies. Thus, eq. (2) becomes

mbSb (Th Tf) = (mcSc + mwSw + k) (Tf Tc) (4)

Using your data in eq. (4), calculate the specific heat capacity Sb of brass.

Qn. 1 What are the main sources of error in 1 and 2?

Part 3 Specific Heat Capacity of a Solution Using an Electrical Calorimeter

1. Measure the mass mc of the empty aluminium calorimeter & stirrer & heater (without outercan and lagging).

2. Now add flourescein solution (with the specific heat capacity Ss) to the calorimeter until it isabout three quarters full. (When the top is in place, the resistance wire of the heating coilmust

be completely immersed in the solution).

3. Measure the new mass mn.4. Calculate (mn mc), the mass of flourescein solution in the calorimeter, ms.5. Now set up the circuit as in Figure 1.

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6. Switch on the power supply and quickly adjust the rheostat for a voltmeter reading of 2.0 V.(The voltmeter reading must be maintained constant at 2.0 V throughout the experiment, by

adjusting the rheostat again, if needed).

7. Keep mixing the solution gently with the stirrer. With the thermometer vertical, read thetemperature and start the clock.

8. Approximately every 2 minutes, read the temperature as well as the exact elapsed time.Continue this until the temperature exceeds the initial value by a little more than 10 Co .

Remember all along to keep mixing the solution gently with the stirrer.

9. Plot a graph of the temperature T against the time t (in seconds), with T along the Y-axis. Theslope of this graph gives

t

T

.

10.Consider a small time interval t. During this time interval,the amount of heat supplied by the heating coil = t

R

V

2(5)

where V is the voltage across the heating coil i.e. the voltmeter reading,

R the resistance of the heating coil.

This amount of heat has caused an increase in temperature of the system (calorimeter & stirrer &

heating coil + thermometer + solution) by T.

Power SupplyRheostat

V

Voltmeter

Calorimeter

Switch

Figure 1

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The amount of heat received by the system = (C + msSs + k) T (6)

where C is the heat capacity of the calorimeter & stirrer & heating coil, given by the manufacturer

as 40 J/K. (Note that the calorimeter and the heating coil are made of different materials

and hence we cannot replace C with mcSc, as we did earlier when we used the copper

calorimeter without the heating coil).

k is the same as given before in eq. (4) and will be neglected. Equating (6) & (7),

(C + msSs) T = tR

V

2

( )

!

2

graphyourofslopet

T

SmCR

V

ss

=

=

+(7)

= C

slopeR

V

mS

s

s

21

(8)

Using the manufacturers values of R = 0.65 and C = 40 J/K along with your experimental data,

calculate the specific heat capacity Ss of fluorescein solution.

Qn. 2 What effect would heat losses have on the shape of the graph?

Reading: Physics 7th edition by Cutnell & Johnson

In Chapter 12 Specific heat capacity & latent heat

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EXP. 5 Methods of Heat Transfer

Aim To investigate heat transfer via convection and radiation

Apparatus Glass bottles, 3x5 index cards, thermometers, power supply, bulbs, metal cans,

Styrofoam covers, food colouring, and fluorescein solution

Theory

Heat transfer refers to the exchange of thermal energy from one physical system to another.

Examples of heat transfer are conduction, which usually occurs in solids, convection, which usually

occurs in fluids and thermal radiation through electromagnetic waves.

Convection:

The mass movement of fluids from one place to another facilitates the transfer of heat from

warmer parts of the fluid to colder parts of the fluid. This occurs as a result of the difference in

density of the two fluids. In this experiment, warm water is less dense and hence lighter in weight,

than cold water. Thus the warm water will seek to rise to the top and the more dense cold water

stays in the bottom. The movement of water will be clearly seen as the yellow and blue food

coloring mix, creating a green liquid.

Figure 1 Placement of bottles for convection demonstration

Radiation:

Radiation is the transfer of energy via electromagnetic waves. When these waves hit an object, they

can either be reflected from the object as is the case with metallic or white objects, or they can be

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absorbed into the object as with objects of darker colours. Therefore, different objects absorb

thermal radiation at different rates. Lighter or metallic colours will absorb less and darker colours

will absorb more.

Figure 2 Placement of cans for radiation experiment

This absorption of energy may be quantified by measuring the relative temperature increases for

different objects which are exposed to the same electromagnetic radiation and then comparing the

temperatures. The object which has a higher temperature gain has absorbed more radiation energy

than the object with lesser increase in temperature.

Procedure

Part 1 - Convection

1. Fill one bottle with warm water and the other bottle with cold water. Use food coloring to colorthe warm water yellow and the cold water blue. Each bottle must be filled to the brim with

water.

2. Hot over cold: Place the index card over the mouth of the warm water bottle. Hold the card inplace as you turn the bottle upside down and rest it on top of the cold water bottle. The bottles

should be positioned so that they are mouth to mouth with the card separating the two liquids.

(You may want to do this over a sink).

3. Carefully slip the card out from in between the two bottles. Make sure that you are holdingonto the top bottle when you remove the card. Observe what happens to the colored liquids in

the two bottles.

4. Record your observations.5. Cold over hot: Repeat steps 2 and 3. This time place the bottle of cold water on top of the warm

water. Observe what happens.

6. Record your observations.7. Discuss your results.

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Part 2 Radiation

1. Pour the same amount of water in each of the two cans (about 200 ml), put the lid on, put thethermometer in, and place the cans in front of the lamps as shown.

2. Measure and record the original temperature. The initial temperatures of the liquids should bethe same.

3. Turn on the lamps and start the stopwatch. Read and record the temperature of thethermometers each minute. After 20 minutes stop the experiment.

4. On the same graph sheet, plot the temperatures versus time for both cans. (Make sure toremember what container each data point came from!)

5. Find the gradient of both lines and compare them. What does this say about the energyabsorbed by both cans?

6. Discuss your results.

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EXP. 6 Gay-Lussacs Law and Boyles Law

Aim: To investigate Boyles Law and Gay-Lussacs Law

Theory:

The relationship between the pressure, temperature, mass, and volume for gases at relatively low

pressures and high temperatures is referred to as the ideal gas equation of state:

pV = nRT

where, p = pressure

V = volume

T = temperature

n = number of moles =molarmass

mass

R = universal gas constant = 8.315J/(mol.K)

Procedure:

Part 1 Boyles Law (Pressure - Volume Relationship)

1. Calibrate the sensor.Connect the pressure sensor to one of the Analog Channels of the interface. Open DataStudio

and create a new experiment. Click on the Add Sensor or Instrument tab and add the pressure

sensor (absolute). Make sure the syringe is not attached and that the tube and sensor are open

to the atmosphere. Select a sample rate of 20Hz. Select the Calibrate Sensors tab and select the

option 1 Point (Adjust offset only) then click on the button Read from Sensor. This should give

the reading for atmospheric pressure.

2. Adjust the syringe to 2ml.3. Connect the pressure sensor to the spout on the syringe.4. Press the start collection button to begin taking readings from the pressure sensor.5. Record the corresponding reading on the pressure sensor.6. Adjust the syringe to gain seven additional volume readings and record the corresponding

pressure for each reading.

7. Rearrange the ideal gas equation to obtain an expression for pressure with respect to volume.8. Plot a suitable graph and find its gradient.9. From the gradient of the graph, find a value for mass of air in the flask, given that the molar

mass of air is 29.0g/mol and the temperature is 300K.

10.Boyless Law defines the relationship between pressure and volume at constant temperature.State Boyles Law from your results.

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Part 2 Gay-Lussacs Law (Temperature - Pressure Relationship)

1. Calibrate the sensor as in Part 1 above.2. Connect the pressure sensor to the side arm of the round bottom flask via the rubber tube.3. Insert the rubber bung with the thermometer at the mouth of the flask to seal the flask. Ensure

that the thermometer is not touching the sides of the flask.

4. Pour the boiling water into calorimeter to about half full.5. Place the flask into the water and cover the calorimeter. Ensure that the flask is completely

immersed.

6. Open the Data window by dragging the graph icon and dropping it in the window. This shows apressure vs. time graph.

7. Allow the air in the flask to heat up and record the maximum temperature reached.8. Press the start collection button to begin taking readings from the pressure sensor.9. Record the corresponding temperature reading by clicking on the note button (A) and entering

the temperature value for the relevant pressure on the graph.

10.Allow the water to cool and record the temperature every minute.11.Once the cooling has slowed add a few chips of ice and record the temperature and pressure

after a minute.

12.Repeat for at least 8 additional temperature and pressure readings. Include in these readings areading as close to 0

oC as possible.

13.Rearrange the ideal gas equation to obtain an expression for temperature with respect topressure.

14.Plot a suitable graph and find its gradient.15.From the gradient of the graph, find a value for mass of air in the flask, given that the molar

mass of air is 29.0g/mol and the volume is 0.1l.

16.Gay-Lussacs Law defines the relationship between pressure and temperature at constantvolume. State Gay-Lussacs Law from your results.

17.Given the high speeds that a race car travels, do you expect the temperature in the tire to behigher or lower than a normal car? Thus would you suggest that a race car driver use a higher or

lower pressure than a normal car driver in his tires? Explain your answer.