# 7.6: More Realistic Models


7.4 Debye frequency

In the Debye model, a solid with average sound speed cs has density of normal-mode frequencies

$G(\omega)=\left\{\begin{array}{cl}{\frac{3 V}{2 \pi^{2} c_{s}^{3}} \omega^{2}} & {\text { for } \omega<\omega_{D}} \\ {0} & {\text { for } \omega>\omega_{D}}\end{array}\right..$

Find a formula for ωD(N, V, cs), and write G(ω) in terms of ωD.

7.5 Debye model energy and heat capacity

Find E(T, V, N) and CV(T, V, N) for a harmonic solid in the Debye model, in terms of ωD and the function

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