Thermodynamics, Statistical Physics, and Quantum Mechanics

The energyEand heat capacityCare then

So, at low temperatures the heatcapacitycorresponding to the rotational
degrees of freedom is exponentiallysmall.This impliesthat therewould be
no difference, in this limit,between theheat capacity formonatomic and
diatomicmolecules. In theoppositecase, at hightemperatures,
the sum may be replaced by anintegral:

where Proceedingfrom(S.4.44.18), we have

Replacing the sum byan integral, weobtain

Therefore, in theclassicallimit (hightemperatures),

The energyEand heat capacityCare given by

THERMODYNAMICS AND STATISTICAL PHYSICS 145