# Homework Help: Debye's T^3 Law: Specific heat, Latice and Electronic terms

1. May 6, 2015

### 12x4

1. The problem statement, all variables and given/known data

QUESTION ADDED AS ATTACHMENT AS NEED TO SEE GRAPH.

2. Relevant equations
C = (12NkBπ4/5)(T/θD)3 for T<<θD
C = 3NkB for T>>θD

3. The attempt at a solution
a.)
So I assume the expression for the specific heat as a function of temperature that the question must want:
C = (12NkBπ4/5)(T/θD)3
otherwise I thought that the specific heat wasn't dependent on temperature?

The second part of this question really stumped me. I have looked though all of the books in my university library that aren't currently on loan, of which few relevant ones are left for some reason, and cant find anything that helps me extract lattice and electronic terms in the specific heat. Does any one have any Ideas?

EDIT: Just found something that shows the electronic contribution:
Ce = (π2/3)g(EFkb2T = γT

Therefore the electronic contribution = γ = (π2/3)(3NA/2EF)kB2

Still not sure on the lattice part.
\EDIT

b.) I think I can do.

c.) The low temperature heat capacity for KCl plotted as to demonstrate the T3 law at low temperatures. The fact that the graph of C/T vs T2 goes through the origin indicates the absence of a term linear in T. I.e there is no contribution to the energy via conduction electrons.

Am I along the right lines here?

Last edited: May 6, 2015
2. May 11, 2015

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. May 17, 2015

### Nic_1995

how did you do part b?

4. May 17, 2015

### 12x4

γ is taken as the y intercept on the graph. Then rearrange the electronic contribution formula for EF.

5. May 17, 2015

### Nic_1995

also the lattice term is just C for low temperature, so the term you have written for C