= Low-temperature heat capacity of a three-dimensional Fermi gas
{title2=$C_V=(\pi^2/2)Nk_B(T/T_F)$}
For a three-dimensional <ideal gas> with quadratic dispersion and fixed particle number, the total <density of states> at the <Fermi energy> is $g(E_F)=3N/(2E_F)$. The <Sommerfeld coefficient> then gives $C_V=(\pi^2/2)Nk_B(T/T_F)$ to leading order, where $T_F=E_F/k_B$. The fixed-number <energy> correction is $\Delta U=(\pi^2/4)N(k_BT)^2/E_F$. Only states near the <Fermi surface> change occupation, explaining the small active fraction.
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