Heat Capacity
The previous amount assume the energy added goes into INTERNAL energy, and not into doing any work. This is true if there is no force through a distance (or no change in volume).
If the pressure remains constant, there must then be a change in volume, and so work is done in extending the volume of the gas. The amount of work done is P*DV = nR?T, so we need to add an amount nR in this case:
Cmolar-constant P = Cmolar-constant V + R .