Apply voltage through electrical fiber that causes Joule heating. How to correlate its temperature
The difference between heat and temperature can be a difficult concept to grasp. Essentially, heat is the total amount of kinetic energy the molecules of a substance have, and is measured in units of joules (J). Temperature is related to the average kinetic energy of the individual molecules, and is measured in degrees. Applying the same amount of heat to different materials will result in different levels of temperature increases, depending on the specific heat capacity of the substance. You can calculate the final temperature if you know the quantity of the substance and its specific heat capacity.
http://sciencing.com/convert-joules-kelvin-8545208.html
Thank you for recommendation. I mean Is there any precise way to do that?
Kieu,
If you apply a voltage across a cable's ends, a current will flow.
The amount of power (joules made each second) can be calculated:
W = I^2 x R
(where R is the resistance of the wire)
If that power (W) is not allowed to escape (maybe the wire is in a vacuum!) then one can indeed calculate how hot, as a temperature, the wire will get after a certain amount of time.
Say, that the wire has a total mass of m (kg), and it is made of copper.
If I have 1kg of copper, and I heat it with 385 Joules of heat, I know that I will warm that copper by 1 deg C. There is a property, called the specific heat capacity, c, that tells you how easy something is to warm up.
So, after a period of time T (sec) I can work out the temperature of the wire thus:
The power, W = I^2 x R.
The temperature change, delta_temp = (T x W) / (m x c)
c for copper is 385 J per kg per degree K. Here m (kg) is the mass of the cable.
It becomes more complicated if the wire is in contact with something else, but in general, this can give you a fair first-approximation of the temperature of a wire after it has been heated for a given time with a given current.
I'm guessing that the 'wire' that you are considering is very fine?
If so, then I can recommend some further refinements, as the greatest heat loss process is not by conduction, but by convection to air.
Can you confirm that these are CNT fibres operated in an everyday 'room' environment?
the fondamental relationship between heat and temperature is an important concept of thermodynamics. for exmaple, MAXWELL gives a new definition of temperature using other variables like volume, pressure and enthropy.
Adel,
With respect, I think that Kieu is simply wanting to know how much a fine conductive wire will warm by when she applies a given current. I do not think that further complications are necessary.
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