How Do Metals Distribute Energy When Heated and Electrified?

[Mr Boom]

I'm not very familiar with the subject matter, so it's possible that this is an easy question. Here goes:

Let's say I have an ideal solid in which the atoms are unable to translate or rotate but have a certain distribution of vibrational energy related to the temperate. If there is a temperature gradient in the metal than this distribution will change along with it, but let's assume we are at equilibrium. Now since even solids can glow when heated, I'm assuming there is also a distribution function for the electronic states (with radiative lifetimes and quenching rates?) that is also, assuming equilibrium, related to the temperature. Correct me if I'm wrong so far.

So it seems to me that since metals share electrons more willingly, the equilibrate much more quickly. Is this why they make good thermal conductors? Now for the real question: If I pass a current through a wire at steady state, is there a way to calculate these distributions? Will the excited states be uniformly distributed, in agreement with any temperature gradient, or mostly along the surface?

 

[Valerie Park]

Yes, it is possible to calculate the distributions of excited states in a metal wire when a current is passed through it. The exact distribution will depend on the nature of the material, the type of current, and the temperature. Generally speaking, the excited states will be more concentrated along the surface of the wire due to the increased electric field at the surface. However, there will also be some non-uniformity in the distribution due to the thermal gradient, as the metal will be hotter near the current source.