The difference between Cp and CV is larger in case of gases as compared to solid and liquid. In solids and liquids, the change in their volume,i.e. ΔV is negligible. From the equation, u=q+pΔV. For constant volume, dV=0, thus u=q For constant pressure also, u=q (as change in volume is nearly zero for solids and liquids). Since, for both the cases internal energy is same, hence heat capacity won't change for liquids and solids.