# Phonons and the Dulong-Petit Law

1. Apr 14, 2012

### Sekonda

Hey,

My question is displayed below:

Now I know for large T, β approaches zero. I have used the relation of the heat capacity and the partition function and have found the derivative of lnZ with respect to β twice.

I think this derivative is just the derivative of the logarithm:

$$\LARGE \frac{\partial^2 ln(\frac{e^-\frac{\beta E}{2}}{1-e^{-\beta E}})}{\partial \beta ^2}=\frac{E^2e^{\beta E}}{(e^{\beta E}-1)^2}$$

but I'm not sure where to go from here?

Any advice would be much appreciated,
S