Cp-Cv For a gas following Van Der Waal equation of state
You could start with $C_V=(\partial U/\partial T)_V=T(\partial S/\partial T)_V$  and H and p instead of U and V for $C_p$ as appropriate. Then generate an expansion for S as $dS=(\partial S/\partial V)_T dV+(\partial S/\partial T)_VdT$ and differentiate wrt T. You should then get an expression in $C_V$ and $C_p$ plus other terms that you can find using the vdw equation.