Possible error sources in thermal conductivity experiment?

• Stephen Lanford
In summary, Stephen Lanford is working on a Physics II lab. He is using data from thermal conductivity experiments to solve for the thermal conductivity of four materials. His errors were found to be in either the convection or radiation heat transfer systems. He needs help understanding how these systems work and determining the sources of his errors.
Stephen Lanford
Hello, my name is Stephen Lanford and I am currently working on a Physics II lab.

I am solving for the thermal conductivity of four materials (glass, plexiglass, pine, and sheetrock) using data from thermal conductivity experiments. The experiments consist of a steam chamber at 100 C, a block of ice inside an ice mold (with one side exposed to allow water to run off when it melts), and one of the four materials clamped between the hot and cold surfaces, through which energy is transferred. Using the thermal conductivity formula K = (m)Lf(h) / A(TH-TC)t---where m is the mass of the melted water, Lf is the latent heat of fusion, h is the thickness of the material, A is its area TH and TC the temperatures of the hot and cold sides of the experiment, and t the time elapsed---I made a calculation of the thermal conductivity for each of the four materials.

Unfortunately, some of the thermal conductivity values I calculated were nowhere close to the stated literature values of thermal conductivity for these same materials.

I am asked to describe the potential sources of my errors. I suspect that some energy is being lost to either conduction or radiation (thus marring the accuracy of the conduction measurements), but I am not exactly sure how. Moreover, my assignment asks me two questions:

(1) What would likely be a significant source of error in performing this experiment on a material that has a very low thermal conductivity that you would not see as much for materials that have higher thermal conductivities?

(2) What would likely be a significant source of error in performing this experiment on a material that has a very high thermal conductivity that you would not see as much for materials that have lower thermal conductivities?

All I could think of for question 1 is that an experiment performed with lower conductivity materials would result in more energy being lost to the environment (since less heat would escape through a low conductivity barrier than through a high conductivity barrier), but this would make no sense: energy loss to the surrounding air would not increase just because energy loss through the material barrier has decreased!

All I could think of for question 2 is that higher conductivities would result in faster heat transfer and more chance that water could overflow or leak out (resulting in an inaccurate final measurement of the water from melted ice), but the experiment was set up with precautions so that there would be no water loss during the time measured.

Clearly, I am not thinking correctly about either of these scenarios. Can someone please help me to understand the situation better and determine the sources of error?

Also, both the pine and the sheetrock were wrapped in aluminum foil for waterproofing. Is it likely the aluminum foil also prevented much of the convection that would have otherwise occurred between the material and the surrounding air? Would this make for a more accurate final measurement of thermal conductivity? Would wrapping the glass and plexiglass in aluminum foil also be a good idea for improving accuracy---even though waterproofing is unnecessary for these materials?

Thanks so much for your help with these questions!

- Stephen Lanford

Look closely at all film coefficients plus radiation heat transfer. They are part of your system, and must be calculated.

jrmichler said:
Look closely at all film coefficients plus radiation heat transfer. They are part of your system, and must be calculated.

Would you mind specifying what you mean by "film coefficients." Also, would you mind explaining how exactly the radiation transfer would operate with this specific experimental set-up. I'm a little unsure. Would radiation be a bigger cause of error when using a low thermal conductivity barrier or a high conductivity one? Thanks a lot for your help!

Lord Jestocost said:

The document you shared does a great job in explaining how this whole experiment works, but I did not see anything about potential sources of error (except for a step at the end of the assignment that said to state and explain the sources of error---which I cannot do if I am not sure what they are in this experiment).

Is there something I am missing? Thanks so much for your help!

Can you supply a photo or at least a sketch of your setup? I can imagine a few things that could happen depending on the configuration.

Cheers,
Tom

The material under test covered one side of the block of ice? What about the other five sides?
How did you maintain a good contact between ice and material under test?
Stephen Lanford said:
energy loss to the surrounding air would not increase just because energy loss through the material barrier has decreased!
Maybe not, but what is the relative uncertainty for your measurement in the different cases?

Tom.G said:
Can you supply a photo or at least a sketch of your setup? I can imagine a few things that could happen depending on the configuration.

Cheers,
Tom
I certainly can provide a diagram of the experiment setup. You will find one on the first page of this physics experiment instructional sheet. Thanks so much for your help!

Attachments

• Exp 1 - Written procedure.pdf
162.5 KB · Views: 518
Uhmm... that attachment is something about a cannon and a mountain... although I suppose there is some connection between an avalanche and an ice cube.

Tom

Tom.G said:
Uhmm... that attachment is something about a cannon and a mountain... although I suppose there is some connection between an avalanche and an ice cube.

Tom
Ha, I sure did send you the wrong one! Here is the correct experiment. Thanks again!

Attachments

• Exp 2 - Written Procedure(1).pdf
342.1 KB · Views: 572
In general:
- Everything you measure has an uncertainty. Try to estimate how well you can measure it. What could lead to a deviation and how large?
- Everything you assume about the experiment can be wrong, or you might even know it is just an approximation. What are the assumptions you made to calculate the conductivity?

That's a list you can start with. Then you can see which of these effects are a problem for good/poor conductors and how large they could be.
Stephen Lanford said:
Is it likely the aluminum foil also prevented much of the convection that would have otherwise occurred between the material and the surrounding air?
As long as the wrapped material is solid anyway the aluminium shouldn't have had an influence on convection. Where do you expect convection anyway?

mfb said:
In general:
- Everything you measure has an uncertainty. Try to estimate how well you can measure it. What could lead to a deviation and how large?
- Everything you assume about the experiment can be wrong, or you might even know it is just an approximation. What are the assumptions you made to calculate the conductivity?

That's a list you can start with. Then you can see which of these effects are a problem for good/poor conductors and how large they could be.As long as the wrapped material is solid anyway the aluminium shouldn't have had an influence on convection. Where do you expect convection anyway?
I am not sure which of the values I plugged into the thermal conductivity formula are "assumptions"; the area, thickness, latent heat of fusion, time, and cold/hot temperature differential should all be fairly solid quantities.

We're your results higher or lower than the accepted values?

Stephen Lanford said:
I am not sure which of the values I plugged into the thermal conductivity formula are "assumptions"; the area, thickness, latent heat of fusion, time, and cold/hot temperature differential should all be fairly solid quantities.
These are two different things.

Measurements: Your measurement of the ice diameter won't be exact. Your measurement of the thickness won't be exact. The latent heat of fusion is a value you looked up, it will have a negligible uncertainty. And so on. I don't expect any of these to be dominant uncertainties, but you should still estimate them or at least determine that they are negligible.

Assumptions: Your ice won't be a perfect cylinder - the conversion between diameter and area won't be perfect. You assumed that the measured amount of water is exactly the amount of water that melted during the given time - that won't be the case in general. And so on (there are many more!).

These are things you should figure out. Ideally before starting the experiment so you know where you have to pay attention to get it right.

I expect the largest issue to come from here:
mfb said:
The material under test covered one side of the block of ice? What about the other five sides?

mfb said:
These are two different things.

Measurements: Your measurement of the ice diameter won't be exact. Your measurement of the thickness won't be exact. The latent heat of fusion is a value you looked up, it will have a negligible uncertainty. And so on. I don't expect any of these to be dominant uncertainties, but you should still estimate them or at least determine that they are negligible.

Assumptions: Your ice won't be a perfect cylinder - the conversion between diameter and area won't be perfect. You assumed that the measured amount of water is exactly the amount of water that melted during the given time - that won't be the case in general. And so on (there are many more!).

These are things you should figure out. Ideally before starting the experiment so you know where you have to pay attention to get it right.

I expect the largest issue to come from here:
All a lot to think about and analyze here. Thanks for greatly expanding my miserably limited horizons!

Tom.G
mfb said:
I expect the largest issue to come from here:
I was wondering about the "steam chamber". As stated in the experiment outline, the steam chamber is to maintain a "definite" 100 degrees C. Depending upon the sophistication of design, is that possible for a classroom technology? If open to the atmosphere, which it seems to be, since there is a collector of condensed steam runoff, I would consider the barometric pressure to be of some importance. At an altitude of one mile, steam generation would be at a temperature of about 95 degrees C. Unless, of course, the steam generator is of a type that contends with water vapour in a supersaturated state, then why the steam runoff collector?
Certainly full percentage error not mentioned in the experiment.
This lends itself to the comment by, @CWatters.

The attachment said 99.1 degrees C - that looks like someone thought about the pressure.

1. What is thermal conductivity and why is it important to measure it?

Thermal conductivity is the property of a material that describes its ability to conduct heat. It is important to measure because it helps us understand how efficiently a material can transfer heat, which is crucial in various fields such as engineering, materials science, and thermodynamics.

2. What are the potential sources of error in a thermal conductivity experiment?

There are several possible sources of error in a thermal conductivity experiment, including measurement errors, variations in experimental conditions, and inaccuracies in the equipment used. Other factors such as sample preparation, environmental factors, and human error can also contribute to errors in the results.

3. How can we minimize errors in a thermal conductivity experiment?

To minimize errors in a thermal conductivity experiment, it is important to carefully control and monitor all experimental conditions, such as temperature, pressure, and sample size. Using high-quality and calibrated equipment, following proper experimental procedures, and repeating the experiment multiple times can also help reduce errors.

4. What are some common techniques for measuring thermal conductivity?

Some common techniques for measuring thermal conductivity include the guarded hot plate method, the transient hot wire method, and the heat flow meter method. Each method has its own advantages and limitations, and the choice of technique depends on the type of material being tested and the required accuracy of the measurement.

5. How can we ensure the accuracy and reliability of thermal conductivity measurements?

To ensure the accuracy and reliability of thermal conductivity measurements, it is important to use standardized and well-validated experimental procedures, calibrate equipment regularly, and conduct multiple measurements to reduce errors. It is also important to compare the results with those obtained from other techniques or published data to verify the accuracy of the measurements.

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