1
$\begingroup$

This is about contribution of electronic specific heat to metals. Most of the books ( I have checked Mermin) have done electronic specific heat calculations at low temperatures using sommerfield expansions and all, and they show that electronic specific heat goes as proportional to $T$. But what is the proportionality at high temps.?

Also,Looking at the general graph of Total specific heat ( phononic + electronic) v/s $T$, I see it saturates at $3K_B$. I have also seen books writing that electronic $C_v$ is visible at very low temps only, and at high temps. the phononic contribution dominates. If this is the case, since insulators and conductors differ only in number of free electons and phonon contribution is same, the heat capacity of both insulators and conductors should become nearly same at high temperatures? Why is it not so?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
4
+25
$\begingroup$

The Dulong-Petit law says that at high temperatures, the molar heat capacity of a solid substance approaches $3R$, regardless of whether it is an electrical conductor or insulator. It is a simplification - realistic systems depart from this law to varying degrees - but it is quite a good approximation.

I have also seen books writing that electronic $C_v$ is visible at very low temps only, and at high temps. the phononic contribution dominates.

Yes, that's right. The electronic contribution to the heat capacity is proportional to $T/T_F$, where $T_F$ is the Fermi temperature of the material which is generally far larger than the temperature at which the material would be a solid in the first place.

If this is the case, since insulators and conductors differ only in number of free electons and phonon contribution is same, the heat capacity of both insulators and conductors should become nearly same at high temperatures? Why is it not so?

It is so.

Improve this answer
$\endgroup$