7.2 A diatomic molecule may to a good approximation be considered as vibrating in one-dimensional simple harmonic motion with circular frequency w. According to quantum mechanics such a system possesses an infinite set of nondegenerate energy levels with energy ħω(r + ), r= 0,1,2, . . . ∞. Obtain expressions for the vibrational partition function and the vibrational heat capacity.

What are the high and low temperature limits of this heat capacity?

Obtain the molar vibrational heat capacity of N2 at 1000 K given that the vibrational level spacing ħω is 0.3 eV.