= Solution
In the classical limit the fugacity is small and $\operatorname{Li}_s(z)=z+O(z^2)$. The <Bose-Einstein distribution> approaches the <Maxwell-Boltzmann distribution>, giving
$$
N\simeq Bz\Gamma(\tfrac92)(k_BT)^{9/2},\qquad E\simeq Bz\Gamma(\tfrac{11}2)(k_BT)^{11/2}.
$$
Taking the ratio eliminates both $z$ and $B$, yielding $\boxed{E\simeq\tfrac92Nk_BT}$. The coefficient $9/2$ follows from this density of states, rather than the $3/2$ of a free three-dimensional gas.
Back to article page
