# Specific Heat Capacity and Resistance Coursework

goku999
Hi,
I have decided for my advanced level coursework to investigate whether the specific heat capacity of a few metals affects their resistivity in any way. (prob in a circuit)
I am at the stage of planning and i have less than a week to complete this stage.
I have a few ideas about measuring the specific heat capacity of a few metals which include :
Aluminium, Nickel, Brass and Iron.
And i am going to set up a circuit of some sort to test their resistivity varying the lengths (and thicknesses if my school has the equip).
Draw graphs and find the gradients and try to relate them.
See if there are any patterns in my results and use science to try and explain why these patterns (if any) occur.

Apart from this I can't think of any other related ideas which links the specific heat capacity of metals and their resistance.

I am not asking ppl on this forum to provide me with the answers but If you can, provide me with some ideas which is related to the coursework title .

Then i can research these new ideas and put them into practice, making my coursework more interesting.

Thanks

inha
Advanced level coursework in HS or uni?

Resistivity and specific heat capacacity have do have a thing in common: phonons contribute to both. The only thing you're going to get out of manipulating the wire geometry is how it affects the resistivity. To study the phonons you'd have to use inelastic neutron or x-ray scattering which I doubt you have access to.

goku999
hi inha,

this coursework is in High school (sixth form)
I have done the rutherfords alpha particle scattering experiment and the different ways in probing different sized atoms.

I think you are going way to advanced for me atm, thanks for the info though.

The geometry of the wire i was planning to test the resistivity of the wire from the metals i am investigating. E.g. some made from iron, nickel etc.

inha
You might be able to detect a correlation but to explain it you'd have to get into solid state physics way beyond HS level. Maybe just studying how the wires' geometry affects the resistivity would suffice for the labwork? Or study the resistance of the wires as a function of temperature?

goku999
The thing is my teacher tells me for my A2 level piece of physics coursework, the coursework itself must include things from at least two modules which i have done.

So i thought of a title which would include word from Electrons and Photons And Thermal Physics.

My friends chose to do something about simple harmonic motion and damping, specific heat capacity of water and antifreeze.

But i do hope that my coursework title would include enough 'bits' to get the high marks in the specification.

Also my teacher told me about a thermal couple system. I have no idea what is it

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Staff Emeritus
Gold Member
1. You want to see if there is any correlation between resitivity (electrical) and specific heat capacity - is this right ? Are you going to restrict yourself to metals ? I think you might find something valuable out of including a few non-metals in the list.

2. You've described how you plan to determine the resitivity of different metals...but you haven't said how you will find the specific heats.

3. With one or two of the metals - and ONLY do this under supervision - see if you can measure the resitivity and specific heats at (two) different temperatures. You can use dry ice or liquid nitrogen (whichever you school lab has) to get a low temperature. Seeing what happens to the two quantities when you lower the temperature will bring out a key correlation (that we could help you understand theoretically).

Homework Helper
Brass (not being an element) would be less consistent samples than copper.
Lead is easy to work with, as are tin and indium. pure iron is not.
pure Al is fairly difficult to find.

If you can measure specific heat capacities at low and high Temperatures,
3 or 4 elements ought to be enough ... if only at room T, you should probably look at Be or Na, as well, or Cl ... or NaCl ...

goku999
Gokul43201 said:
1. You want to see if there is any correlation between resitivity (electrical) and specific heat capacity - is this right ? Are you going to restrict yourself to metals ? I think you might find something valuable out of including a few non-metals in the list.

2. You've described how you plan to determine the resitivity of different metals...but you haven't said how you will find the specific heats.

3. With one or two of the metals - and ONLY do this under supervision - see if you can measure the resitivity and specific heats at (two) different temperatures. You can use dry ice or liquid nitrogen (whichever you school lab has) to get a low temperature. Seeing what happens to the two quantities when you lower the temperature will bring out a key correlation (that we could help you understand theoretically).

1. Yes it is, I can try and see what other non-metals my school has which i can use to find the specific heat capacity of.

2. I have done a little experiment on finding the specific heat capacity of an aluminium block.
The mass of the block is weighed with a pair of scales.
Its temperature is measured in a room temperature environment.
Then its like setting up a circuit with a voltmeter and an ammeter.
This would provide power needed for the heater to heat up the aluminium block.
Measurements will be taken on its change in temperature every 30 or 60 seconds along with the ammeter and voltmeter reading.

Then i assume all energy supplied to the block is received.
VIt = mc∆θ then c = VIt/ m∆θ

The average voltage and current are taken in the calculation to find its specific heat capacity.

My teacher said there are some things i would have to think about.
The insulation on the block and the efficiency of the heater.

3. I don't really understand what you are saying Gokul43201.
Are you trying to say get a metal at room temperature (warm) and get the same metal but very cold and measure the specific heat capacities of both and compare. if so (i have to do the experiment at room temperature) then the colder one would be affected by the temperature of its surroundings more so than the other one. ALso i will get a bigger percentage error in my results and while its being heated my the heater, the atmospheric temperature plays a roll in its heating process.
But i assume that this error would be reduced significantly is i can insulate it 'properly'.

I see if my school has dry ice or liquid nitrogen but i can do antifreeze.

Thanks for the ideas, keep them coming

Staff Emeritus
Gold Member
goku999 said:
1. Yes it is, I can try and see what other non-metals my school has which i can use to find the specific heat capacity of.
...and the resistivity I hope, though this part will be tough.

2. I have done a little experiment on finding the specific heat capacity of an aluminium block.
The mass of the block is weighed with a pair of scales.
Its temperature is measured in a room temperature environment.
How do you plan to measure the temperature of the block. This is an important detail.
Then its like setting up a circuit with a voltmeter and an ammeter.
I'm not sure I follow. Are you trying to build a heater circuit and then use this heater to heat up the block ? Or are you going to pass a current directly through the block and allow it to heat up ? I wouldn't recommend either method. It would be far more accurate an experiment if you use some kind of typical calorimetry method.

In any case, would you give us a little more detail on how you plan to implement the heating ?

This would provide power needed for the heater to heat up the aluminium block.
Measurements will be taken on its change in temperature every 30 or 60 seconds along with the ammeter and voltmeter reading.

Then i assume all energy supplied to the block is received.
VIt = mc∆θ then c = VIt/ m∆θ
The above assumption will completely destroy the accuracy of this experiment. In fact, a few minutes into the experiment, you might find that "none of the energy supplied to the block is received" unless you take careful precautions to insulate the block and ensure that it does not lose heat by radiation or convection. But if you do that, and you are not directly heating the block (by passing current through it), you won't get the heat into it either.

The average voltage and current are taken in the calculation to find its specific heat capacity.

My teacher said there are some things i would have to think about.
The insulation on the block and the efficiency of the heater.
The first of these two points, I've addressed above. The second is important as well. How much of the power produced by the heater actually goes into the block ?

And, in addition to these, these other considerations that are important : like the shape of the block. Something like a plate or rod will be preferable to a block. This allows the metal to become isothermal (have roughly the same temperature at its center and surface) faster. If the metal is not isothermal, then by measuring the temperature at some point, you are not really measuring the temperature of the entire block.

3. I don't really understand what you are saying Gokul43201.
Are you trying to say get a metal at room temperature (warm) and get the same metal but very cold and measure the specific heat capacities of both and compare.
Yes, that's what I'm saying. Measure the specific heat of the metal (say copper) at room temperature and measure it again at some low temperature. The two numbers will not be the same if you get low enough. And similarly, measure the resitivity at room tmperature and at the low temperature. Compare how the specific heat changes with how the resistivity changes (when you cool the metal).

if so (i have to do the experiment at room temperature) then the colder one would be affected by the temperature of its surroundings more so than the other one. ALso i will get a bigger percentage error in my results and while its being heated my the heater, the atmospheric temperature plays a roll in its heating process.
But i assume that this error would be reduced significantly is i can insulate it 'properly'.
Your concerns are certainly valid, and again I'd suggest that you use a calorimetric method (like for instance : You cool the block/plate down to Liq Nitrogen temperature, and then allow it to warm back up by say, 10 degrees. Then you find out how much liq nitrogen you boil off when you try to cool it back down through these same 10 degrees.)

I see if my school has dry ice or liquid nitrogen but i can do antifreeze.
Antifreeze may not be enough. Find out what your lab can give you.

goku999
Though I am only studying my second year of A-Level Physics, i tried to keep the investigation solely on metals as most metals conduct electricity and I can measure their resistivity. But the suggestion made by Gokul43201 about different temperatures is a very good idea and i am willing to give this a try. Though at this moment in time i have no idea on how to measure the resistivity of non-metals. I'd expect some of the non-metals don't conduct electricity therefore putting it in a circuit and passing current through it may produce null readings.

Well what i explained in my previous post was about a preliminary experiment i had done last year and the class was warned that there are massive errors.
In that experiment there was a heater (immersion) which stuck inside the middle of the cylindrical block of aluminium connected to a power supply. energy was transferred to the immersion heater which i turn heats up the block from its centre. There was a little hole where the thermometer would sit to measure its temperature. but since the thermometer reading was hotter than the actual block temperature as it was close to the immersion heater. It did not measure the average temperature of the block itself.

This was the way the teacher told us to do.

The block has a layer of thick cardboard wrapped round the outside, not sure what was on the bottom but there wasnt much we could do with the top as the immersion heater and the thermometer stuck out. This method was the heater circuit you mentioned.

Though i would research about the calorimetry method you suggested.
Are these used in chemistry?? I remember from AS chemistry about calorimeters and a great long accurate thermemoter like device capable of measuring the temperature in a great amount of accuracy.

Its a bit of a bad time now to find out what my school has as its our one week holiday.
It was set yesterday and the planning stage must be finished in a week and its one month for the practical, analysis and evaluation.

If i am able to plan the experiments for both metals and non-metals(especially the resistivity part) then i will include it in and see what the teacher thinks about this.

Staff Emeritus
Gold Member
Your concern that a non-metal will have an impossibly high resistance is understandable, but ...

Recall the formula for resistance : $R = \rho l/A$. Even if the resistivity $\rho$ is extremely large, the resistance can be brought down to a manageable value simply by making $l/A$ be tiny. This is not hard to do : you just have to use a shape that is a thin sheet and pass the current through its thickness. That way $l$ becomes the thickness of the sheet which is tiny and A, the area, is large, so $l/A$ is really small. However, this will involve one little difficulty - you can't just connect wires to the sides of the sheet. This way, the cirrent will not make use of the full area. What you'll have to do is use copper plates on either side of the sheet and attach the wires to the plates.

Another thing to keep in mind for the resistivity measurement is that you want the resistance of the metal block/plate/wire to be large compared to other resistances in your circuit.

For another suggestion on a metal to use : I recommend stainless steel. It has a considerably poor thermal conductivity and will make for an interesting data point.

My suggestions for materials (will update as I get better ideas) :

Elemental metals :
1. copper,
2. aluminum (a little care needed in attaching to circuit)
3. tin
4. lead (use disposable gloves when handling; see safety data before use)

Alloys :
2. bronze (copper + tin)
3. stainless steel

Non-metals - still thinking about it...

goku999
I understand what you are saying Gokul43201.
The length and thickness of the non-metal should be small in order for its resistivity to be measured.

I know that by using leads as connectors to conencted the various devices together to form a circuit, the actual physical conenctions made do have little resistance and i think i will include that in the coursework and there isn't much i could do.

And there is one part about fair testing.
If i make the non-metals significantly small, do i have to make the other materials the same length and thickness. (in my mind i think i will have to)
But it shouldn't be a problem.

Staff Emeritus
Gold Member
goku999 said:
And there is one part about fair testing.
If i make the non-metals significantly small, do i have to make the other materials the same length and thickness. (in my mind i think i will have to)
But it shouldn't be a problem.
You do not have to, for the following reasons :

(i) you understand that there is an inherent difference between a conductor and an insulator and are hence justified in using different approaches,

(ii) the resistivity is a material property and does not depend on geometry - you will establish this if you use different geometries for the same material.

goku999
Gokul43201 said:
(ii) the resistivity is a material property and does not depend on geometry - you will establish this if you use different geometries for the same material.

This makes things a little easier then thanks.
I need to have a word to my teacher next week about what equipment is available and ask him about the temperature change, alloys and non-metal suggestions.
BEcause i don't want to overload myself with work as i have coursework for other subjects as well at the same time.

ANd also if i measured the specific heat capacity of a aluminium block let's say, i will have to measure the resistance of the same block then calculate its resistivity.
Could i measure the resistance of a wire made of the same material and do repeats in this area to find its resistivity?

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goku999
From looking at the equipment my school can provide, it seems i would have to measure the specific heat capacity of the blocks using the heater circuit method.
At the moment i would have to use the same block to measure the resistivity as well.

I am thinking of a solder method for this and whether it is appropriate?
I will use a thin metal sheet of copper or another metal and solder it to the bottom of the block.
I will have to measure its resisticity in some way by passing a current though it which at the moment i have no idea on how to do.

I will have to obtain a lot of results and hopefully plot a scatter graph with specific heat capacity and resisivity as the axis.

Is this a valid method?

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Staff Emeritus
Gold Member
goku999 said:
At the moment i would have to use the same block to measure the resistivity as well.

I am thinking of a solder method for this and whether it is appropriate?
I will use a thin metal sheet of copper or another metal and solder it to the bottom of the block.
I'm not sure why you are soldering a copper sheet to the bottom. I would solder on two thickish sheets/plates to opposite sides of the block and solder on the leads to these plates.

I will have to measure its resisticity in some way by passing a current though it which at the moment i have no idea on how to do.
I think you are referring to the block (right ?). To drive a current, all you need is a DC power supply that gives say, 0 to 5V.

From what measured quantities would you calculate the resistivity ? And what is the equation for this ?

goku999
After having a discussion about how i was going to do things, it ended up with me measuring the specific heat capacity of the blocks using the heater circuit method.

The resistivity will not be done using the solder method as there will be lots of errors and i will do this using wires made of the same material as the block.

But i mentioned the resistivity formula where i measure the resistance of the wire of length say 100cm and measuring the average voltage and average current readings and using the calculated value to get the resisitance of the wire. i will get the resistivity of the wire by doing a substitution into the resistivity formula, buy, she said that this was one method and there was another method i could do to find this out.

So far i will measure the specific heat capacity of an aluminium block and an iron block, resistivity of the aluminium and iron wires, repeat at least 3 times. (My school were unable to find any different blocks)
And i am allowed to look in the data book for other metals and their resistivities and hopefully see if there is any correlation between the specific heat capacity (y axis) and the resistivity (x-axis).

goku999
The school has gave me a roll of iron wire but its a littl bit rusty, will this have a major effect on the resistance of the wire?

ANd also i have a question.
Can the cooling correction be applied to an aluminium block as well as liquids?

This is where you leave the block to get to its max temperature without passing current through it and record the time it takes for the temperature to be 10 degrees below its maximum.

thanks

Staff Emeritus
Gold Member
goku999 said:
The school has gave me a roll of iron wire but its a littl bit rusty, will this have a major effect on the resistance of the wire?
No, it will not. It may, however, affect your measurement of its diameter.

ANd also i have a question.
Can the cooling correction be applied to an aluminium block as well as liquids?

This is where you leave the block to get to its max temperature without passing current through it and record the time it takes for the temperature to be 10 degrees below its maximum.

thanks
What do you do with the time you've measured ?

goku999
With the time measured, i think i would have to draw a graph with temperature against time and find the area underneath the part with a negative gradient (cooling stage).

And one thing, the cooling correction on the aluminium took very long to cool down by 10 degrees average about an hour whilst the iron took about 35 mins. I pass current through the block for 20mins.

Will there be much error if i decided to measure the time taken for the metal block to cool by 5 degrees?

Staff Emeritus
Gold Member
I can't say anything about this, because I don't know what you do with the area under the graph. How does this area serve as a correction, and what does it correct ?

goku999
hmmm...

I have to find the constant of proportianality k ?

the rate of change of temperature with respect to time dQ/dt = k(its max temp - room temp)

The total loss in heat during heating is equal to the total loss in heat during cooling?

let T1 = time taken to get to max temp
let T2 = time taken to cool by 5 degrees

so the constant k multiplied by the integral between 0 and T1 is heat lost during heating? (Q)

The constant k multiplied by the integral between T1 and T2 is heat lost during cooling? (Q')

The change in temperature is what I am trying to find here.

Loss in heat (Q) / Loss in heat (Q') = Area A (0 to T1) / Area B (T1 to T2)

Q = C theta
Q' = C' theta'

Theta (The correction) = (Area A/ Area B) x theta'

Is this what the cooling correction is?

And also i tried to measure the resistance of the aluminium wire using a circuit and was no good. Its resistance was to high and i got null results so i used the wheatstone bridge method which relied on the ratio/proportion and by using a bridge to calculate the resistivity.

I used the meter bridge which consisted of a wire of uniform resistance, galconometer, a known resistance (soldered three resistors), unknown resistance.
There were like to gaps in the whole circuit, one was for the resistor and one was for the unknown resistance.
When putting the unknown resistance (aluminium) on the left gap and the knwon resistance on the right gap, i moved the jockey which was like a pen along the wire of uniform resistance. Once the galvonometer reading was 0 this was the balance point so i took the readings from the left. The ratio between L1 and L2. It came out to be very close to the actual resistivity about 15% error.

But the thing is if a repeated the experiment by switching the unknown resistance and the known resistance (soldered resistors) and find the balance point, it shifts about 6 cm!. I did not change the circuit at all. (Length of unknown resistance is 3 m btw and known resistance was 1.67)
The percentage error this time was vey large compared with it the other way round.

My teacher said this could happen, i did it with a different element (Iron) and had the same effects.

Does anyone know the likely causes of this?

goku999
i don't know how to edit the above post but i redid the experiment using another meter bridge and the differences were smaller.

Now i think I am ready for the analysis. THe big question is about the degree of accuracy.

I have used a joulemeter instead of a voltmeter and ammeter so it reduces the sources of error from two to one. Also the counteron the joulemeter is giving whole numbers only but I don't know how much i trust it.

Also the same for the parallax error from the thermometer taking the temperature of the block. I decided to read it to the nearest half a degree because it is more easier to read/make judgement from like the neasest 1/10 of a degree. (Thermometer only shows whole degrees)

Obviously each piece of apparatus is not 'perfect' 100% accurate.

I don't really understand the 'why do/ how much do you trust it' thing and coming up with an answer...

goku999
I have less than a week to complete this coursework and am having a prob with the jouelmeter.
Im at the analysis stage and have good results.

Problem is the joulemeter took a few seconds for the counter to start. I have a feeling that during this length of time the power is needed to do something inside the joulemter but i cannot find any websites which tell me what's inside. Can anyone help or give me a clue?

I don't have much time...