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P = RT/(v+c/T^2)
1) use maxwell relations to prove that the entropy of the system using this substance between states p1 and p2 is given as
s2-s1 = R Ln(p2/p1) - 2v/T (p2-p1)
2) use maxwell relations and prove that the ratio of compressive coefficient at constant temperature to the one at costant entropy is
Cp/Cv = Xt/Xs = γ
Cp -Cv =vT (β^2 /Xt)
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