Blundell Thermal Physics · Problem 20.1

The partition function

Physics — Statistical Mechanics · partition-function-high-temperature

Problem

Show that at high temperature, such that

k_BT \gg \hbar\omega

, the partition function of the simple harmonic oscillator is approximately

Z \approx (\beta \hbar \omega)^{-1}

. Hence find

U

C

F

, and

S

at high temperature. Repeat the problem for the high temperature limit of the rotational energy levels of the diatomic molecule for which

Z \approx (\beta \hbar^2/2I)^{-1}

(see eqn 20.35).