In this entire problem, keep results to first order in the van der
Waals correction terms \(a\) and $b.
Show that the entropy of the van der Waals gas is \begin{align}
S &= Nk\left\{\ln\left(\frac{n_Q(V-Nb)}{N}\right)+\frac52\right\}
\end{align}
Show that the energy is \begin{align}
U &= \frac32 NkT - \frac{N^2a}{V}
\end{align}
Show that the enthalpy \(H\equiv U+pV\) is \begin{align}
H(T,V) &= \frac52NkT + \frac{N^2bkT}{V} - 2\frac{N^2a}{V} \\
H(T,p) &= \frac52NkT + Nbp - \frac{2Nap}{kT}
\end{align}