Quantum theorem of heat capacity at constant volume

Quantum theorem of heat capacity at constant volume 

We are going to use relation [7.127] but by introducing the mean values of the different energies obtained at lower temperatures. 

The temperature is always high enough so that the mean translational energy keeps the value given by relation  

With regard to the rotational term, if the temperature is lower than the characteristic temperature of rotation, this mode is not excited and its contribution is zero. For higher temperatures, we must use expression [6.51]  

With regard to the vibrational term, the mean energy can be expressed by expression [6.76]  

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