How do conduction-band electrons affect heat transfer in conductors?

[rubertoda]

Hello. I am about to show how heat is transferred through crystals i. e metals



I know that it should be about conduction, and that the single quantum oscillators start vibrating in higher modes, due to the extra energy.


Now is the question: HOW exactly is the energy trasnferred between adjacent atoms,i.e oscillators? Through phonons?

I mean, should we consider the atoms actually TOUCHING each other?

 

[Simon Bridge]

Depends on what level you want this...
The electrons and atoms in a solid exert an electromagnetic force on each other ... so, when one moves, the others get pushed or pulled differently as a result. It is as if the atoms were connected by springs.

 

[rubertoda]

ok, thanks a lot. So that electromagnetism is exerting force - as photons - to excite the other atom into a higher energy lvl of that quantum oscillator?(in the quantum model)?

 

[Simon Bridge]

In the quantum model - heat is about statistics.
But the basic interaction is electromagnetic - so: mediated by photons.
The details depend on the material - for instance, in solid-state conductors, there are a lot of electrons which are not bound to individual atoms. In a gas, the EM interaction will be between whole atoms or molecules and imparts kinetic energy (though may also change some internal energy state such as exciting a bound electron or a molecular rotational or vibrational level.)
Materials get complicated real fast.

 

[rubertoda]

Ok, but for solid crystalic Iron, the major heat distributor is conduction, through vibrating the atoms and excitiing the oscillators into higher energy modes, and transferring the energy to the neighbours. is this a fair statement? What is the other (less contributing factors).uantum mechanically speaking. Ratio?

 

[Simon Bridge]

Oh I see - you are thinking of an Einstein solid?
Now you realize that the oscillators in the model are not independent.
In conductors, you will also need to account for the effect of conduction-band electrons.
Basically the lattice vibrations store most of the thermal energy but are not good at spreading it around - which is why te Einstein model works well for heat capacity.
Free electrons are good for spreading it around.

You realize that whole textbooks are written on this subject right?
http://www.cse.salford.ac.uk/profiles/gsmcdonald/pp/PPLATOResources/h-flap/p11_4t.pdf
... section 4.4 is what you want.

That's for a general solid. (Notice the "can be understood as" in there? It's just a model and should not be taken for "what actually happens".)

In conductors, the conduction-band electrons can often be treated as a (Fermi) gas. What happens when you heat a gas in one place?

The text (linked above) points out that the conduction band electrons play role in thermal conductivity in proportion to the electrical conductivity of the metal. Compare silver with silicon and glass in table 4 - it is a dominant effect.