Statistical Mechanics - Classical Statistics : Gibbs Paradox
In terms of partition function Z, the entropy of a perfect gas is S=NklogZ+3/2Nk,where Z is the partition function of the perfect gas. Entropy being an extensive property must satisfy the additive property. But this expression of entropy does not satisfy the additive property. When two different gases each containing the same number of molecules N, are mixed together the entropy of the combined system is more than sum of the entropies of the two systems by 2Nklog2. So additive property of entropy is not obeyed. This is Gibbs Paradox. Gibbs resolved this paradox by assuming that molecules of a perfect gas as identical and indistinguishable.
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