WHen talking about phase transitions, in a graph of Temperature vs. Heat Capacity, does the PT occur at when the graph has a gradient of 0 or somewhere else?

The phase transition occurs where there is a discontinuity in the specific heat. At the transition temperature, it becomes what is known mathematically as a multiple of the delta function, with an infinite height but a finite integral ve. T. The Cp dT integral there is equal to the latent heat of the phase change. In calculating enthalpy, do it by segment for each phase, and add the heat of the phase change.