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.
Best Answer
For a given process, the heat added divided by the temperature change of the system (I am assuming they are calling this C) varies with the amount of work that is done. Like you, I can't see why they would possibly call this an intensive property, although it is certainly a path function. Maybe intensive is a typo, and they meant extensive.
The specific heat capacities Cv and Cp are intensive state functions, because they are defined as the partial derivatives of the specific internal energy and the specific enthalpy, respectively, with respect to temperature (the former at constant volume and the latter at constant pressure), and the specific internal energy and specific enthalpy are state functions.