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Consider a system of free fermions in d dimensions, with the energy spectrum
where c > 0 and a > 1.
(a) Calculate the prefactor A of the relation pV = AU.
(b) Calculate the Fermi energy as a function of volume V and number of particles N.
(c) Calculate an asymptotic expression, in the limit T << TF , for the specific heat at constant volume.
Physics
In the thermodynamic limit, we have
Also, we have
Thus,
In order to derive the Fermi energy, we write
and note that
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