[QUE/TH-13003] TH-PROBLEM

Derive the fundamental relation

\[ S=\frac{S_0N}{N_0} + NR \ln[\Big(\frac{U}{U_0}\Big)^{3/2}\Big(\frac{V}{V_0}\Big)\Big(\frac{N}{N_0}\Big)^{-5/2} ] \]
for a perfect gas.