A Show That The Entropy Of The Vander Waals Gas

(a) Show that the entropy of the Vander Waals gas is

σ = N{log[nQ(V – nb)/N] + 5/2}.

(b) Show that the energy is

U = 3/2 Nτ – N2α/V

(c) Show that the enthalpy H ≡ U +PV is

H(τ, V) = 5/2Nτ + N2bτ/V – 2N2α/V;
H(τ, P) = 5/2Nτ + NbP – 2NαP/τ.

All results are given to first order in the Vander Waals correction terms α, b.

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