Task id10287

Task id10287

Using the well-known relation of quantum statistical mechanics W = - 2/3 E, we can calculate the heat capacity Cv of a Fermi gas at constant volume as follows. Let us find the entropy of the system S for which the equality S = - dW/dT = 2/3 dE/dT is valid. Using approximation (3.20) for the energy E, found in the previous problem, we obtain for S the expression S = 2/3 n2/3 k2 p(κ0) T. Now for the heat capacity Cv we find Cv = T dS/dT = 2/3 n2 /3 k2 p(κ0) T. How to reconcile this result with formula (3.21) of the previous problem?

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