EE Thermodynamics

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EXTENDED ESSAY - PHYSICS BHUPENDRA SINGH NAGPURE

EXTENDED ESSAY – PHYSICS

BHUPENDRA SINGH NAGPURE

WORD COUNT- 3,380

TOPIC:

“DOES THERE EXIST A RELATIONSHIP BETWEEN THE ‘SPECIFIC HEAT CAPACITY’

AND THE ‘THERMAL CONDUCTIVITY’ OF A LIQUID?”

SUPERVISOR: DR. DAVID JOHN WILKINSON

CANDIDATE NUMBER: D0969- 069

INTERNATIONAL BACCALAUREATEMAY 2002

THE MAHINDRA UNITED WORLD COLLEGE OF INDIA




TABLE OF CONTENTS

CONTENTS: PAGE:

INTRODUCTION ...................................................................... 1

THEORY...................................................................................... 2

THE EXPERIMENTS ................................................................ 5

SUMMARY OF THE RESULTS ............................................... 9

DISCUSSION OF THE RESULTS ............................................ 10

CONCLUSION ........................................................................... 14

APPENDIX-1 .............................................................................. 15

APPENDIX-2 .............................................................................. 16

BIBLIOGRAPHY........................................................................ 17




ABSTRACT

The closeness of the terms specific heat capacity and thermal conductivity as both

phenomenon involve heat transfer, made me think about the relationship between them.

Since, there were not any direct interpretations of these terms that can join them, Ithought about finding them out.

The simple reason responsible for having a high or low specific capacity is the molecular composition of that matter. Heat transfer through conduction also is dependent on also

the molecular composition. So both phenomenon are dependent on the vibrations of

molecules. Now what makes molecules vibrate slower or faster if the amount of heatgiven is constant is the intermolecular forces working on them. Thus, I came up with the

question:

“Does there exist any relationship between the ‘specific heat capacity’ and the

‘thermal conductivity’ of a liquid?”

I calculated the specific heat capacity of five liquids and arranged them in the increasing

order of their values. Then I determined the relative conductivity of each of them and didthe same. On comparing both the orders, I observed that the liquid, which has the lowest

heat capacity (paraffin oil) also, has the lowest thermal conductivity! And the liquid,

which has the highest specific heat capacity (salty water with low concentration) also, hasthe highest thermal conductivity! Rest of the liquids had same pattern.

Thus I discovered that they have a direct relationship. However, I could not investigatethe exact mathematical relationship. I also observed that a viscosity test, which gives the

idea about the massiveness of molecules of liquids, should have been carried out. It

would have helped to explain the relationship more deeply because vibrations of molecules is also dependent on the mass and not only on the intermolecular forces.




INTRODUCTION

While studying heat and thermodynamics in physics, I came to know about the terms

‘specific heat capacity’ of a liquid and ‘conduction’ through a liquid. I observed that

these terms seem quite relative to each other as both involve heat transfer. I tried to look for a relationship between them, if any exists, but all the sources available for physics

disappointed me, as I could not find out anything that shows any mathematical

relationship between them. With this Extended Essay, therefore, I found an excellentopportunity to try some experiments on my thoughts to “discover” if there exists a

relationship between the specific heat capacity of a liquid and the rate at which heat is

transferred through the liquid by conduction.

Hence, this Extended Essay is a product of my curiosity. The topic chosen might be

interesting, important and worthy of study if there exists any relationship between the

terms I have mentioned. This relationship might be useful to give an idea about the bestliquid to use to be warmed by a solar panel in less time and also the system can be used

during the night. If not, then at least it will satisfy my curiosity and thoughts. Thus the

question I came up with is as follows:

“Does there exist a relationship between the ‘specific heat capacity’ and the

‘thermal conductivity’ of a liquid?”

For my investigation, I am going to find the specific heat capacity and the relative

thermal conductivity of five liquids; distilled water, salty water with two differentconcentration, paraffin oil and refined oil. Comparing the order of liquids in both the

terms I will conclude the relationship, if any, and if possible, a specific trend will be

found.

If a liquid that has a lower specific heat capacity is a better conductor of heat, then it can

be concluded that the liquid that has a higher specific heat capacity will conduct heat

more slowly. Also, If a liquid which has a higher specific heat capacity conducts heatmore slowly, then it can be concluded that a liquid that has a lower specific heat capacity

will conduct heat more quickly. This hypothesis of mine is based on the fact that higher

thermal conductivity molecules of a liquid are vibrate faster and hence will have a lowspecific heat capacity because the molecules pass gain heat more quickly.




THEORY

1. SPECIFIC HEAT CAPACITY OF A LIQUID

The term Specific Heat Capacity of a liquid means “The amount of heat absorbed or

released by a unit mass of a liquid to change its temperature by 1°C.”

Why are there differences in the Specific Heat Capacities of different liquids? The

answer is that different liquids have different molecular structures and bonding

compositions of their molecules. But what does the energy, which is needed to raise thetemperature of objects, do? In the case of a liquid, it increases the net kinetic and

potential energies of the molecules. As the liquid gets hotter, its molecules move around

much faster and usually move slightly away from one another.

So what makes the specific heat capacities of diverse liquids different from one another?

As mentioned above, it must be the molecular structure, including the mass of the

molecules themselves. If the liquid has more mass molecules, then we would expect moreenergy needed to make the temperature of a fixed amount rise by the same amount as a

liquid whose molecules are less massive.

The specific heat capacity ‘C’ is related to heat transfer to a body by the equation:

Q = M * C * Δθ

Where, Q is heat transfer measured in joule (J)

M is the mass of the object measure in (g)

C is the specific heat capacity in (Jg-1 °c-1)

Δθ is the temperature difference in (°c)

2.THERMAL CONDUCTIVITY OF A LIQUID

Conduction is the process whereby heat is transferred directly through a material,

any bulk motion of the material playing no role in transfer.

The most important way in which heat is transferred through a liquid is by convection.

This occurs through the bulk movement of its molecules in the form of a convection

current. In this experiment, however, I am investigating how heat can be conductedthrough a liquid by setting up the apparatus to minimize the possibility of a convection

current being set up.

In this case, I will expect the conduction process to occur because heated molecules will

move faster, collide with other molecules and so transfer their energy. If it requires more

energy to make a molecule of greater mass increase in velocity by the same amount as aless massive, one then I expect conduction to occur at a lesser rate in this case. By




comparing this simplified aspect of thermal conductivity with specific heat capacity, Imight find that there is a relationship.

The thermal conductivity of a substance is defined in the following way:

Figure 1: Flow of Heat by Conduction

Q /t = { kA (θ1 - θ2)} / x

When a steady state is reached, the heat transferred through the material every second

depends on its area of cross section (A) and upon temperature difference (θ1 - θ2) across a

distance ‘x’. ‘k’ is the thermal conductivity of the material.

In my experiment, I will set up a glass tube to minimize the possibility of a convectioncurrent forming. I will measure the temperature at two points, equidistant from the outlets

of the hollow tube, until these are constant. ( Refer figure 2 )

Figure 2: Glass Tube




In every case I will assume that the rate of heat supplied is constant. So that we have:

k l ∝ 1 / (θ1 - θ2)

The values of 1/ (θ

1 -θ

2) which I record will be in inverse proportional to the thermalconductivity of the liquids I am investigating. The SI unit of thermal conductivity is(J s

-1m

-1°c

-1).




THE EXPERIMENTS

Five liquids were chosen and for each liquid the specific heat capacity and the relative

thermal conductivity were measured. The liquids chosen were:

(1) Distilled water.

(2) Salty water 1 (300ml tap water + 60g of salt)(3) Salty water 2 (300ml tap water + 40g of salt)

(4) Refined oil.

(5) Paraffin oil.

EXPERIMENT (1)

1. MEASURING THE SPECIFIC HEAT CAPACITY OF THE FIVE LIQUIDS

APPARATUS:A copper calorimeter, an ammeter, a voltmeter, a thermometer, distilled water, paraffin

oil, salt, refined oil, conducting wires, a battery power source, measuring cylinders,

beakers, stop watch, a weighing scale and a rheostat.

VARIABLES:

Controlled: current provided

Dependent: voltage and temperature.Independent: time, specific heat capacity of the liquid and the calorimeter.

First, the mass of the copper calorimeter was measured with a weighing scale. Then 100ml distilled water was poured in it. The initial temperature of the water was recorded and

the apparatus was set out as shown in the diagram below:

Figure 3: Electric Circuit Set-up for Measuring Specific Heat Capacity




The experiment was started by putting the plug key on the circuit. At the same time, thetime on the stopwatch was recorded. The rheostat was used to control the current passing.

Thus the current was kept constant through out the experiment. The water inside was

being stirred continuously so that heat was gained by whole amount of the water rather

than partially.

After 10minutes the circuit was disconnected and the final temperature of the water was

recorded. The voltage and current value were also noted down. The whole experimentwas repeated with each of the five liquids.

HOW TO WORK OUT THE SPECIFIC HEAT CAPACITY OF A LIQUID

To work out how much energy is needed to heat up a liquid, I will need the following

information:

Energy in =Voltage * Current * Time

Energy in = Energy absorbed by the liquid + Energy absorbed by the calorimeter

Energy absorbed by the liquid = Mass of the liquid * Specific heat capacity of the liquid

* Temperature rise.

Energy absorbed by the calorimeter = Mass of the calorimeter * Specific heat capacity of

the calorimeter * Temperature rise

To make things easier in my working, I am going to use the following variables:Current (measured in Amperes) I

Voltage (measured in Volts) V

Time (measured in seconds) tTemperature difference (°c) Δθ

Specific Heat Capacity (Jg-1

°c-1

) C

Specific Heat Capacity of liquid Cl

Specific Heat Capacity of calorimeter CC

Mass (g) M

Mass of liquid Ml

Mass of the calorimeter MC

So the energy = Energy absorbed by the liquid + Energy absorbed by the calorimeter.

I * V * T = Ml* CC * Δθ + MC* CC* Δθ

⇒ Cl = {(I * V * t) – M l * CC *Δθ} / (Ml* Δθ) ------------eqn (1)

ΔCl = C [ΔV/V± ΔI/I ± Δt/t ± 2ΔMl / Ml ± Δ( Δθ)/Δθ ± ΔMC / MC]---eqn (2)




EXPERIMENT (2)

COMPARING THE CONDUCTIVITY OF THE FIVE LIQUIDS:

APPARATUS:

A hollow glass tube (25cm long and 2cm in diameter), two steel cylindrical boxes (20cmhigh and 11cm in diameter), a burner, two stands, two thermometers, ice, water and the

five liquids.

VARIABLES:

Controlled: time.

Dependent: temperatureIndependent: time.

Two glass-corks were used to close the outlet of the hollow glass tube and were fixed

with a strong adhesive. Then a hole was made in each cylindrical box so that the glass

tube could be inserted horizontally. After inserting the glass tube, each hole was sealedwith the same strong adhesive to avoid water leakage, which was poured in the boxes

afterwards. The whole set up was done as the figure below:

Figure 4: Set-up for Measuring Relative Thermal Conductivity




The water and the ice water were poured into the respective boxes and the experimentwas started by lightening the burner. The flame was kept constant so that the rate of

transfer of heat was constant. The heat was supplied continuously until the temperatures

in both the thermometers were constant. The final temperature was noted down. The

temperature noted down from the hole near the boiling water is θ1 and the temperature

noted down from the ice water hole is θ2. The whole experiment was repeated for theremaining four liquids.

HOW TO WORK OUT THE RELATIVE THERMAL CONDUCTIVITY OF LIQUIDS

The thermal conductivity of a liquid is inversely proportional to the value of (θ1 - θ2 )

Measuring the value 1/ (θ1 - θ2 ) gives us the relative thermal conductivity.

⇒ Relative k l = 1 / (θ1 - θ2) -----------------------------eqn. (3)

Δ k l = 2/ (θ1 - θ2)2 ----------------------------eqn. (4)




SUMMARY OF THE RESULTS

Using equations (1) and (2) and the raw data, the following values for specific heat

capacity were calculated and, using the equations (3) and (4), the order of relative

conductivity for the five liquids was also determined. The object was not to measure the

actual thermal conductivity as this is not possible with these apparatus. What are provided are the relative values of thermal conductivity

Raw data can be found in appendices 1 and 2.

Serial

no.

Liquid Specific Heat Capacity

(Jg-1 °c

–1 )Relative Conductivity

(°c–1 )

01. Paraffin oil 2.240 ± 0.451 0.044 ± 0.004

02. Refined oil 2.410 ± 0.460 0.056 ± 0.006

03. Distilled water 3.945 ± 1.062 0.125 ± 0.0311

04. Salty water 2(Less conc.)

4.020 ± 1.281 0.167 ± 0.056

05. Salty water 1(More conc.)

4.153 ± 1.438 0.250 ± 0.125

Figure 5: The Order of Specific Heat Capacity and Conductivity of the Liquids




DISCUSSION OF THE RESULTS

Comparing the specific heat capacities and the relative conductivity of the five liquids

used, I found that there is a definite trend in relationship. The liquid which has the higher

specific heat capacity, has a higher conductivity and, the liquid which has a lower specific heat capacity, has a lower conductivity. The relationship can be seen clearly on

the graph of specific heat capacity against relative conductivity which is shown below:

Figure 6: Graph: Specific Heat Capacity against RelativeThermal Conductivity of Five Liquids

Specific heat capacity against relative conductivity

2

2.5

3

3.5

4

4.5

5

0 0.05 0.1 0.15 0.2 0.25 0.3

Relative conductivity ( °c ̂ -1

S p e c i f i c h e a t c a p a c i t y ( J g ^ -

1

° c

)




On the molecular stage, the molecules of the liquid which have a higher specific heat

capacity are vibrating very slowly. The molecules of such liquids take a greater amount

of heat to heat up because their molecules vibrate appreciably and collide withneighbours to pass energy to them. It means they can not conduct heat faster then the

liquid, which has a lower specific heat capacity, i.e. whose molecules are vibrating faster.

But in my result I found totally the opposite pattern. The results are opposite to my

hypothesis, which show that there are some more factors (beside the molecular vibration)which also contribute in the thermal conductivity and specific heat capacity of a liquid.

Since now I know that there are other factors responsible for the specific heat capacityand the thermal conductivity, I am sure that one of the factors might be the mass of the

molecules of a liquid. The reason is simple that mass of the molecules is also the part of a

molecular composition and hence is also responsible for vibration of them. However, Ihave mentioned this before in the theory of specific heat capacity that ‘if the liquid has

more mass molecules then we would expect more energy needed to make the temperature

of a fixed amount rise by the same amount as a liquid whose molecules are less massive’.

This discrepancy leads me to recommend a viscosity test for the further understanding of

the concept of relationship between the specific heat capacity and the thermal

conductivity of a liquid. A viscosity test is used to determine the density of liquid.Simply, it gives us the idea of whether the molecules or massive or not. Hence, if I were

to have used this test then the trend I would have found in the specific heat capacity and

the thermal conductivity of the liquids would have been explained in terms of the mass of the molecules, too.

The error ranges in the values of the specific heat capacity and the relative conductivityare respectively: 20-35% and 9-50%, which show that the values of the relative

conductivity is not reliable compare to values of specific heat capacity. However, thelarge error range in the values of relative thermal conductivity is due to the fact that when

a subtraction is carried between two comparable values the final value becomes very lesswhereas the error is added. So I can say that though I have 50% error range for one value

of relative thermal conductivity, it is reliable, too.

DISCUSSION OF ERRORS AND SUGGESTIONS

ERRORS IN THE VALUES OF SPECIFIC HEAT CAPACITY

The following are the few things I could have done to improve my experiment, and makemy findings more accurate.

One of the biggest problems in working out the specific heat capacities was HEATLOSS. If heat loss were to be reduced, than the specific heat capacities, which could be

worked out, would be a lot more accurate. Heat loss could have been reduced in many

ways:




(1) Foil could have been added around the calorimeter, which would have reduced heatloss by radiation.

(2) Insulation could have been put across the top of the calorimeter. This would have

reduced the amount of heat that would have been lost due to convection in the air.

(3) The top of the heater that was not in the liquid would have lost heat. All of the heater

can not be put into the liquid that is being heated up, so this means there will always be aheat loss here.

• Since all the liquids were exposed to the surrounding in the same conditions for thesame amount of time, I had assumed that heat lost in all liquids would be the same.

However, I know that it can not be the same for all different liquids. Heat lost is

totally dependent of the molecular composition of the liquid. The liquid which has agood capacity to gain heat, would lose more heat than the liquid that has a lower

capacity, because the liquids that can gain heat very quickly also can lose heat very

much more quickly as the vibrations of molecules are faster and thus the rate of heatloss will obviously be faster.

This heat lost during experiments can not be avoided fully and also can not accounted

totally because it makes a much broader subject, which can not be included in my mainextended essay.

• More materials should have been tested to try and see if all the liquids follow thesame pattern related to the specific heat capacity and conductivity. I could have tested

some more oils which would have been better to compare rather than testing the water

and salty water.

• I should have taken more readings more frequently, in between the start (0s) and the

end (10mins) of the experiment. I could have then worked out the specific heat

capacity for each of the time differences, eg.0-5mins, and 0-10 minutes. Once I hadthe specific heat capacity for each of these, if they were not the same, then I could

have worked out the mean and this would have given me a more accurate specific

heat capacity.

ERRORS IN THE VALUE OF CONDUCTIVITY:

• Heat loss contributes errors in thermal conductivity, too. However, it can not be

avoided fully though I should have reduced it by some of the following methods: a

non-conductive foil could have been wrapped around the glass tube and the still boxes to avoid heat loss by radiation.

• A thermometer with a least count of 0.1°c should have been used. This would have

given an accurate temperature reading to one decimal place, whereas the thermometer

which I used could only measure as a whole number, or added half if the reading was




between two of the readings on the thermometer. This would have given better readings for working out the relative thermal conductivity.

• While the water was boiling in one of the boxes, the horizontal tube was shaking

slowly due to the boiling motion of the water. It might have caused a slight heattransfer by convection. Some heavy weight should have been kept on the boxes to

reduce the shaking of the horizontal glass tube.




CONCLUSION

From what I have done so far, I have come to the conclusion that there exists arelationship between the specific heat capacity of a liquid and its thermal conductivity.

I have able to find out the existence of a direct relationship: that is, liquid having a higher specific heat capacity shows the higher thermal conductivity and a liquid, having lower

specific heat capacity shows the lower thermal conductivity. However, I could not

conclude the exact mathematical relationship.

One question which is still unresolved in this aspect of the relationship is, “How the mass

of the molecules of a liquid contributes in its specific heat capacity and the thermal

conductivity? A viscosity test might be useful to determine the massiveness of themolecules of a liquid and then to determine whether it is related to either of specific heat

capacity or thermal conductivity. Thus knowing the contribution of the mass of the

molecules of a liquid in its specific heat capacity and thermal conductivity will be useful

to understand the relationship more deeply.




APPENDIX (1)

Mass of the liquid: 100g ± 1g

Mass of the copper calorimeter: 46.5g ± 0.1g

Time (initial): 0 sTime (final): 600 s

1. SPECIFIC HEAT CAPACITY OF THE LIQUIDS:

Ser

i-alno.

Liquid

Temperature (t)

(Initial)(ºc) ± 1ºc

Temperature (t)

(Final)(ºc) ± 1ºc

Current (I)

(A) ± 0.05A

Voltage (v)

(V) ± 0.25V

01. Distilled water 27 39 1.65 5.00

02. Refined oil 27 49 2.00 4.75

03. Salty water 1(More conc.)

27 36 2.00 3.25

04. Salty water 2(Less conc.)

27 37 2.00 3.50

05. Paraffin oil 27 48 2.00 4.25




APPENDIX (2)

2. THE RELATIVE THERMAL CONDUCTIVITY OF THE LIQUIDS:

Liquid Temperature at steady state (°c)

θ1 θ2

K ∝ (1/ (θ1 - θ2 ) in °c-1

Distilled water 59 51 0.125

Refined oil 62 44 0.056

Salty water 1(More conc.)

60 56 0.250

Salty water 2(More conc.)

60 54 0.167

Paraffin oil 68 45 0.044




BIBLIOGRAPHYBook:

1. Cutnell, J. D. & Johnson, K. W., Cutnell & Johnson Physics, 5th

ed.; Wiley: New

York, 2001.

2. Sears, F.W., Zemansky, M.W. & Young, H.D., University Physics, 6th

ed.; Narosa:

New Delhi, 1997.

Website:

1. http://www.webelements.com/webelements/properties/text/definitions/thermal-conductivity.html , 02/11/2001

2. http://www.sasked.gov.sk.ca/docs/physics/u4a2phy.html, 02/11/2001

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