order of phase transition/constant volume heat capacity

How do define the order of Phase-transition exactly?
Say we use Cv, constant volume heat capacity. We know that Cv is a first order derivative of U,internal energy, but second order derivative with respect to free energy F, so if Cv is not continuous (when you keep V constant and vary T), what order of phase transition will it be?First(according to U) or Second(according to F)?