So I've been told that if you graph the heat capacity of a system under constant pressure (Cp) versus temperature, you get a 'stairlike' graph where the heat capacity goes to infinity during phase changes (since all the energy goes into breaking bonds, not raising temperature, etc.).
Now, if you graph the HEAT of reaction of a system under constant pressure (qP) versus temperature, you get a similar graph. My question is how does this make sense, since if you have ΔH = qP = CpΔT (assume there's 1 mol of the substance in question), and if you differentiate with respect to T (temperature), you get dH/dT = Cp.
Thus, the graph of heat capacity versus temperature should be the derivative of the graph of system heat. But it isn't, since the heat of the system doesn't increase until a phase change. Can someone please help me resolve this confusion?