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This formula is more commonly known as the 'spectroscopic entropy'. It is basically the derivative of the free energy in terms of T with V held constant. É© is h/(2 pi m k T)^1/2. The formula differs from yours only by the inclusion of a factor representing the weight of the lowest electronic state, w.
S/N V/N É¡
----- = ln w----- + -----
k É©^3 É¡-1
Wilson: Thermodynamics and Statistical Mechanics, Cambridge, 1960