My textbook states the following:
"The total heat capacity, $C$ (Heat required to raise the temperature of the system by 1°C) is an intensive path function. On the other hand, $C_V$(Molar heat capacity at constant volume) and $C_P$ (Molar heat capacity at constant pressure) are intensive but state functions."
Firstly, I don't understand why $C$ is an intensive property, especially because it does depend on the mass of the system. It does, however, make sense to say that $C_V$ and $C_P$ are intensive properties, since the heat considered in the calculations involving these two, is the heat per mole of the substance and this quantity will remain constant for any amount of the same substance.
Secondly, I am very confused as to why $C$ is a path function where as $C_V$ and $C_P$ are not. I am not able to understand whether they ought to be path/state functions, because on the one hand, temperature is a state function, where as heat is only defined for a process.
Please share your insights. MUCH thanks in advance :) Regards.