Solution
= Solution
Using $C_V=T(\partial S/\partial T)_V$ and the stated <Maxwell relation>, interchange derivatives within a smooth single <phase>:
$$
\left(\frac{\partial C_V}{\partial V}\right)_T
=T\frac{\partial}{\partial T}\left(\frac{\partial S}{\partial V}\right)_T
=T\left(\frac{\partial^2p}{\partial T^2}\right)_V=0.
$$
Therefore \b[$C_V$ depends only on <temperature>] for the given temperature-linear <equation of state>. It need not be constant in <temperature>.