# 7.6: More Realistic Models

- Page ID
- 6376

*7.4 Debye frequency *

In the Debye model, a solid with average sound speed *c _{s}* 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 *ω _{D}*(

*N, V, c*), and write

_{s}*G*(

*ω*) in terms of

*ω*.

_{D}*7.5 Debye model energy and heat capacity *

Find *E*(*T, V, N*) and *C _{V}*(

*T, V, N*) for a harmonic solid in the Debye model, in terms of

*ω*and the function

_{D}