= Ideal Bose-gas heat capacity below condensation
{title2=$C_V=\frac{15}{4}Nk_B\frac{\zeta(5/2)}{\zeta(3/2)}(T/T_c)^{3/2}$}
For quadratic three-dimensional dispersion below condensation, the excited-state thermal <energy> is proportional to $T^{5/2}$. Differentiating at fixed particle number and volume gives the displayed <heat capacity>, with limiting value approximately $1.926Nk_B$ at $T_c^-$. The macroscopic ground occupation carries no excitation <energy> in the shifted reference. The exponent differs from the linear-phonon result of an interacting gas.
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