Past exam of the thermal and statistical physics course of the University of Cambridge / 2014 / Paper 1 / 1 / c

For $N$ identical classical noninteracting particles, use $Z_N=Z_1^N/N!$. At fixed $N$,so the canonical partition-function identities giveThus, for one mole,The supplied $T^{3/2}$ dependence includes only three translational degrees of freedom; additional thermally active internal modes would change the heat capacity.