# Joule heating question

Ok so as fare as I understand the equation for Joule heating in a material with a DC current is I^2*R.
I am trying to calculate for the heating of carbon fiber in an argon environment. Carbon fiber has a resistivity similar to graphite (roughly 5.0*10^-7) I am trying to calculate for 3.3VDc. However I am getting a massive value of 14291338.58 watts dissipated. To get the value of I I'm using the equation V/R=I. What am I doing wrong? I feel 14.2 megawatts is a bit off.

## Answers and Replies

AlephZero
Science Advisor
Homework Helper
You seem to be confusing resistivity, which is a property of a material, with resistance, which depends of the size and shape of a particular piece of the material. Resistivity and resistance are measured in different units.

That is rather like confusing the density of steel with the mass of a particular piece of steel.

See http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

Oh I need to edit that I factored in the dimensions of the material to convert resistivity to resistance

billy_joule
Science Advisor
It doesn't sound off to me. The resistivity of CF is a very small number, the resistance value for a macroscopic CF conductor will also be a very small number.

In reality the heating will be limited by the current supply capability of your voltage source.

If you add the dimensions of the CF someone could check your calculation.

It was a guesstimate at around 2" by 3"

billy_joule
Science Advisor
Giving better information will lead to better help.

I guessed it's a square bar with voltage applied across it's length and using :

ρ = 1 x10^-8 (Ωm)

For CF

(From wiki, as you didn't give units)

And

R = ρl/A

P=V^2/R

=> P = AV^2/ρl

I got 36 MW so you are in the right ball park.

Now all you have to do is find 3.3 VDC supply that'll put out 11 MILLION amps ;-)

Thank you for the help. I actually think I'll be building an adjustable current supply, I'd rather not fuse any atoms.

sophiecentaur
Science Advisor
Gold Member
2020 Award
Power circuits with carbon elements often need current regulation in them because of the Negative Temperature Coefficient of the resistivity, which can give you thermal runaway if you aren't careful.

So would a current regulator paired with an adjustable current source allow me to gradually increase how hot it is?

billy_joule
Science Advisor
So would a current regulator paired with an adjustable current source allow me to gradually increase how hot it is?

Yes.

CF is such a good conductor that unless your CF has a very small CSA most of the power will be dissipated in the connecting cables and the CF will not heat up much.
ie your wires will get hot and the CF will stay cool.

sophiecentaur
Science Advisor
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2020 Award
Yes.

CF is such a good conductor that unless your CF has a very small CSA most of the power will be dissipated in the connecting cables and the CF will not heat up much.
ie your wires will get hot and the CF will stay cool.

Carbon filaments were commonly used for lighting before tungsten established itself as a better material. They worked at mains voltage (you can still buy them, in fact). They are pretty fragile, though, because of their necessary small cross sectional area.

Here's a historical link.

Cool thanks. I'm going to be using large blocks of graphite to act as the cathode and anode and to sandwich the carbon fiber at both ends. Do you think with a maximum of 35Amps I could get the carbon fiber to melt? The melting point of carbon is 3500 degrees C. All in an inert environment of course.

sophiecentaur
Science Advisor
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Using carbon / carbon contact could possibly be a good idea as it may avoid hot spots on contact but I would just have chosen copper blocks as they would dissipate any locally generated heat due to uneven contact. But under pressure, the copper would (?) mould around the fibres to give a good contact.

Cool so the 35 Amps should be sufficient

That's a good idea with the carbon carbon

sophiecentaur
Science Advisor
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Cool so the 35 Amps should be sufficient

It depends entirely upon the cross sectional area of your carbon.

6" by 6"

sophiecentaur
Science Advisor
Gold Member
2020 Award
OMG
Your figure of MW in the OP sounds quite a reasonable answer - it's just an unfeasible project if you don't have a lot of money, I think. Source resistance will really prove to be a problem with such a low resistance load.
Would it be possible to take a step backward and to approach your requirement in a different way? Could you provide the electrical heating in a more conventional way, perhaps? But what is the CSA of your carbon Fibre??? Aren't they very thin and not 6" X 6"?
14MW would melt your whole lab!!!

Ya I don't want to get it nearly that hot it would vaporize I want like 3500 degrees Celsius so I won't be using nearly 14mw

It would be a group of fibers in a cloth. I only need to get it to absorb about 9 jules in the form of heat to get it to 3500 degrees Celsius based off its specific heat

billy_joule
Science Advisor
It would be a group of fibers in a cloth. I only need to get it to absorb about 9 jules in the form of heat to get it to 3500 degrees Celsius based off its specific heat

You need to consider heat transfer too...Objects that are 3500 deg C transfer a lot of heat to their surroundings...

You really need to do this:

take a step backward and to approach your requirement in a different way?

Any ideas on how to get it that hot other than resistive heating? As fare as I know nothing except possibly some forms of thermite burns that hot. And anything but carbon would liquefy so I can't insulate it with anything.

billy_joule
Science Advisor
I don't know of any method.

If you can explain why you want to heat CF and what you intend to do to it once it's heated it may help.
Why do you want to heat a large piece of cloth?

sophiecentaur
Science Advisor
Gold Member
2020 Award
I have just been searching around for the specs of available kilns and furnaces. I couldn't find anything higher than 2k Celcius. So aiming at 3k Celcius is clearly not trivial. You are talking in terms of lamp filament temperatures and that is a seriously clever area of technology.
I think you would need to consider a much smaller scale and very short lived experiment, operating inside a muffle furnace, to increase the ambient temperature to something manageable. All your electrical connections would be very likely to melt / vaporise. A bit of a nightmare.
As billy_joule says, it may help if you tell us the actual purpose and context of this idea. You may be able to achieve what you want in another way.

Hmmm we'll I want to replicate this experiment http://www.rsc.org/chemistryworld/News/2010/March/16031001.asp. It sounded interesting so I wanted to make some to incorporate in a radiation/ micro meteoroid shielding idea I had. I couldn't find what specific nickel catalyst they were using (in less of course they literally mean pure nickel in which case I'm over complicating things). My solution therefore was to use resistive heating to bring the material to the 3000 degrees centigrade required to make it react without a catalyst.