b$)$ Given that the entropy $S$ is function of $T$ and $P$:$,S=S(T,p),$ show that $dS=\frac{Cp}{T}dT-(\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{T}}{)}_{p}dp,$ and deduce expressions of $S$ for an ideal gas behavior $pv=RT$ and for non$-$ideal gas behavior $pv=ZRT$

And what about if the gas behavior obeys Van Der Vaals equation.