Application of Equipartition of Energy- Specific Heat of a Gas

Following the equipartition principle, the mean total energy of a molecule having f degrees of freedom is:

(4.173)

and the total energy of N molecules is

(4.174)

or, the molal internal energy , and molal specific heat at constant volume

(4.175)

For an ideal gas

(4.176)

(4.177)

and  

(4.178)

It  is to be noted that c_v.c_p and γ are all the constant and independent temperature. For a monatomic gas which has only transnational kinetic energy, f = 3. Thus,  

A diatomic molecule is commonly pictured as having the dumbbell structure (Fig. 4.23). Its moment of inertia about y and z axes is very much greater than that about x axis, and the latter is neglected.