We know, heat capacity ratio,  … (i)

Where, C_p = Specific heat at constant pressure, C_v= Specific heat at constant volume

And, n = Degree of freedom is the total number of co-ordinate or independent quantities required to describe completely the position and configuration of the system.

Suppose, a polyatomic gas molecule has ‘n’ degree of freedom.

Total energy associated with a gram molecule of the gas i.e.

Where, N = Total number of molecules, R =  Universal gas constant or (R = NK), K = Boltzmann constant.

As, specific heat at constant volume,

Now, specific heat at constant pressure,