assignment Homework
Van der Waals gas Enthalpy Entropy
Thermal and Statistical Physics 2020
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}