= Grand-canonical chemical potential of a classical ideal gas
{title2=$\mu=k_BT\ln(n\lambda^3)$}
For one internal species, the <grand canonical partition function> of a classical <ideal gas> satisfies $\ln\Xi=zV/\lambda^3$, with <quantum gas fugacity> $z=e^{\beta\mu}$ and <thermal de Broglie wavelength> $\lambda=\sqrt{2\pi\hbar^2/(mk_BT)}$. Differentiating the <grand potential> gives $N=zV/\lambda^3$, hence $\mu=k_BT\ln(n\lambda^3)$. An internal partition factor must be included consistently if internal states are available.
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