Solution
= Solution
The one-particle translational partition function is
$$
q_1=\frac{V}{h^3}\int_{\mathbb R^3}
e^{-\beta p^2/(2m)}\,d^3p
=\frac{V}{\lambda_T^3},
\qquad
\lambda_T=\frac{h}{\sqrt{2\pi mk_BT}}.
$$
For a classical <ideal gas>,
$$
\boxed{\mathcal Z=\sum_{N=0}^\infty
\frac{(e^{\beta\mu}q_1)^N}{N!}
=\exp\!\left(\frac{Ve^{\beta\mu}}{\lambda_T^3}\right)},
$$
and hence
$$
\boxed{\Phi=-\frac{k_BTVe^{\beta\mu}}{\lambda_T^3}}.
$$