Thermodynamic properties of the perfect gas

Using (12 25) and (12-49) we obtain for the molecular partition function of a perfect gas whose volume is V, 

Now in (12 51) the only quantity which is a function of F is the term V, In particular, does not depend on F, and this was implicit in the separability discussed in 12 3 and 12 4. (It is because the potential energy for the internal motions of the molecule does not depend on the distance between one molecule and another in a perfect gas phase.) 

If there are n moles of gas in the system then N=Ln, where L is the Avogadro number. Thus (12 52) may be vTitten 

The last equation may be expressed as pVccnT, Now the coefficient of proportionality is usually denoted by the symbol R. Hence 

This serves to identify the Boltzmann constant k as equal to the gas constant per molecule, as was foreshadowed in 11 11. 

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