Phonons and the Dulong-Petit Law

  • Thread starter Sekonda
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Hey,

My question is displayed below:

Quantum.png


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:

[tex]\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}[/tex]

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

Any advice would be much appreciated,
S
 

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