Characteristic temperature of vibration

In this model, the crystalline solid is a system of 3N oscillators, in which all have the same fundamental frequency Vfe. The corresponding characteristic temperature of vibration, defined on the basis of the relation ... 

Analogous to the above characteristic temperature of vibration it is now sensible to define a characteristic temperature of rotation via... 

The characteristic temperature of vibrations for oxygen is = 2273 K at T = 298 K. What is the vibrational contribution to the heat capacity How does it compare to the translational contribution ... 

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