# Taking the temperature of a wire

#### guythreepwood

I'm new here, and I hope I'm posting this in the right place. My colleagues and I are trying to take the temperature of a steel wire as it's heated. We're heating it by putting a current through it. The problem we're encountering is that the thermocouple we're using to take the temperature of the wire only has surface contact at the tip, and we need a more comprehensive idea of the temperature along the wire. The end goal is to determine the coefficient of thermal expansion. Any thoughts?

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#### lewando

Homework Helper
Gold Member
Can you put your sample and fixture into an oven?
The problem we're encountering is that the thermocouple we're using to take the temperature of the wire only has surface contact at the tip, and we need a more comprehensive idea of the temperature along the wire.
Why not use more thermocouples then? If you are limited to one, move it to different positions along the wire. If you can't move it, consider using an IR camera to verify temperature uniformity.

#### guythreepwood

We are exploring alternative heating schemes. Multiple simultaneous thermocouple readings are not an option, and would likely just give simultaneously bad data. IR thermometers won't pick up temperature readings on a string this thin.

#### Nidum

Gold Member
One way is to measure the wire's effective resistance at the different temperatures .

There does though seem to be a danger of you doing some tail chasing science in this project . Can you see why that might be ?

#### JoePhysics

I've done some searching, and this seems to be a nontrivial problem. This and https://www.researchgate.net/figure/260232817_fig3_Figure-3-Temperature-distribution-in-a-current-carrying-wire-with-finite-length-L-with [Broken] seem to suggest that the differential equation that governs such a situation has a complicated solution. The first article in particular arrives at a rather complicated integral.

However, for the case of constant thermal conductivity, first-order thermal coefficient of resistance and neglected radiation, a closed-form solution seems to exist involving hyperbolic cosines.

Let me know if this approach interests you, and we can continue discussing it.

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#### Chestermiller

Mentor
Why do you have to use a wire? Why don't you get something more robust with a decent size?

#### guythreepwood

#4, Regarding resistance, we'd really like to take temperature readings via thermometer or thermocouple, but we may not have a choice. I don't know what "tail chasing science" is.

I'm reading through the papers mentioned in #5, and I'll get back to you.

#6, the wire we're using is analogous to a guitar string. We want to be able to measure changes in frequency as it's heated.

#### Andy SV

Depending on the temperature you are looking for you can go by color
If it's not incandescent try an infrared camera
Just being curious
Are you going to maintain constant tension or let it sag with thermal expansion?

#### BvU

Homework Helper
The end goal is to determine the coefficient of thermal expansion
We want to be able to measure changes in frequency as it's heated
Why don't you tell us some more of what it is you want ? Context and such. You don't seem to realize that heat transfer from a vibrating string to the environment is a hideously complicated thing - as JoeP carefully tried to bring across.

The art and science of physics is to try and isolate single factors in complicated multifactor effects and think of a good way to learn about them one by one.

#### guythreepwood

As I said, I'm currently examining the papers that Joe submitted. I'm aware that the problem is more complex than single contact temperature readings can solve.

Specifically, we are stringing a guitar with high carbon steel wire and running a current through it. The guitar is plucked, producing a frequency. Plotting frequency against temperature yields a slope which, given Young's modulus and the cross-sectional area of the wire, should give the coefficient of thermal expansion. We want a more effective way of measuring temperature off of the heated string.

#### Andy SV

Well I have a very effective way doing just that but it will take some time
Heat the air around the wire and wait for the temperature to equalize
If you want to have a gradient you can flow heated air through a pipe around the wire and raise the temp as you go
Also you can measure the resistance of the wire. It will go up with higher heat

"Taking the temperature of a wire"

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