# Heat capacity in general $d$ dimensions given the density of states $D(\omega)$

I hope someone knows a reference or knows how to solve the following question. (I am pretty sure I won't be getting any answers, but why not try?! :-)).

Find an integral expression for the heat capacity: $$C_V=\partial_T \sum_{\vec{k},s}\frac{\omega_s(\vec{k})}{e^{\beta \hbar \omega_s(\vec{k})}-1}$$

in a general $n$ dimensions given density of states $D(\omega)$, for an isotropic crystal with an infinite volume $V\to \infty$.

Thanks.