Types of Molar Heat Capacities

                Since heat is not a state function, neither is molar heat capacity (because molar heat capacity depends on heat). It is, therefore necessary to specify the process by which temperature is raised by one degree. The two important types of molar heat capacities are:

(I).          Molar Heat Capacity at Constant Volume.

(II).         Molar Heat Capacity at Constant Pressure.

(I).          MOLAR HEAT CAPACITY AT CONSTANT VOLUME             

                                When heat is supplied to the system to raise its temperature by 1^oC keeping volume constant is called Molar Heat Capacity at Constant Volume. It is denoted by (C_V).

                                Since   C    =    dq/dT       

                                 Molar heat capacity  =   dq/dT

                                            C_V    =    dq_V/dT   

                                According to First Law of Thermodynamics,

                                             dq    =    dE   +   PdV

                                At constant volume, dV = 0.

                                             dq_V =   dE

                                       \   C_V   =   dE/dT

(II).         MOLAR HEAT CAPACITY AT CONSTANT PRESSURE                                             

                When heat is supplied to the system to raise its temperature by 1^oC keeping pressure constant is called Molar Heat Capacity at Constant Pressure. It is denoted by ‘C_P’ and is equal to dq_P/dT .