[QUE/SM-04004]

The canonical partition function of a system is given by \hfill \HighLight{\fbox{\tiny KPN}} \begin{eqnarray*} Q(T,V,N) &=& \frac{V^N}{N!}\frac{1}{\Lambda^{3N}}\ ;\ \Lambda = \frac{h}{\sqrt{2\pi mk_BT}}. \end{eqnarray*}

1. Derive an expression for entropy : $S(T,V,N)$.
2. Consider a quasi-static reversible process in which entropy does not change and $N$ does not change; volume and temperature, however, can change. Show that $TV^{2/3}$ is a constant during such a process.