Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 5.3-10

THE EXTREMUM PRINCIPLE IN THE LEGENDRE TRANSFORMED REPRESENTATIONS

Physics — Statistical Mechanics · helmholtz-potential-mixture-ideal-gases

Problem

aa) Show that the Helmholtz potential of a mixture of simple ideal gases is the sum of the Helmholtz potentials of each individual gas: F(T,V,N1,…,Nr)=F(T,V,N1)+⋯+F(T,V,Nr)F(T, V, N_1, \ldots, N_r) = F(T, V, N_1) + \cdots + F(T, V, N_r) Recall the fundamental equation of the mixture, as given in equation 3.40. An analogous additivity does not hold for any other potential expressed in terms of its natural variables.

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