Q$2.(8$ Points$)$ Derive a relation for the internal energy change for a gas that obeys

the EOS: $P=(R\frac{T}{V}-b)-(\frac{a}{T}{V}^2).$ Assume that in the range of interest, $C_r$ varies

according to the relation $C_4=c_1+c_{2}T,$ where $c_1$ and $c_2$ are constants