[QUE/TH-09002] TH-PROBLEM

The equation of state of system is given by ( in standard notation).
The internal energy of the system is

$$ P\,=\,\frac{aT^3}{V} $$

$$ U\,=\,BT^n{\ln}(\frac{V}{V_0})\,+\,f(T), $$

where $B\,,n$ and $V_0$ are all constants. $f(T)$ is a function of only $T$.
Find $n$ and a relation between $a$ and $B$. ( Use the fact that entropy is a perfect differential.)