How do you derive the relation
$$C_p-C_v= R\left(1 + \frac{2a}{RTV}\right)$$
for a gas obeying van der Waals equation of state? Any leads?
How do you derive the relation
$$C_p-C_v= R\left(1 + \frac{2a}{RTV}\right)$$
for a gas obeying van der Waals equation of state? Any leads?
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.