Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 16.7-3

ENTROPY AND DISORDER; GENERALIZED CANONICAL FORMULATIONS

Physics — Statistical Mechanics · gruneisen-parameter-debye-crystal

Problem

The frequency

\omega(\lambda)

of the vibrational mode of wave length

\lambda

is altered if the crystal is mechanically compressed. To describe this effect Gruneisen introduced the ``Gruneisen parameter''

\gamma \equiv -\frac{V}{\omega(\lambda)}\frac{d\omega(\lambda)}{dV}

Taking

\gamma

as a constant (independent of

\lambda, V, T, \ldots

) calculate the mechanical equation of state

P(T, V, N)

for a Debye--Gruneisen crystal. Show that for a Debye--Gruneisen crystal

v\alpha = \gamma k_T c_v