513.001 Molecular and Solid State Physics

Einstein model

The Einstein approximation for the phonon density of states is,

D(ω) = 3nδ(ω - ω₀) .

Here n is the density of atoms, and δ is a Dirac delta-function.

(a) Give an expression for the internal energy u in J/m³.

(b) Give an expression for the phonon specific heat in this approximation.