Hello! I understand what specific heats are and how to derive them. I just feel that I'm missing a little something in the methodology. Consider the 1st law of thermodynamics and the definition of enthalpy: 1) dU = δQ -δW = δQ - PdV 2) H = Q - VP For the derivation of CV, dV = 0 and the relationship becomes (∂U/∂T)V = (∂Q/∂T)V = CV For the derivation of CP, something happens that I don't quite understand. Sources I've found say that the incremental form of the enthalpy relation is given as 3) dH = δQ - VdP since dP = 0, it becomes (∂U/∂T)P = (∂Q/∂T)P = CP but why do we write it like this? Wouldn't the chain rule for differentiation apply to d(VP) s.t. it becomes d(VP) = VdP + PdV in which case, where does the PdV component in EQ (3) go? Thanks ahead of time for the clarification!