= Translational partition function
{title2=$q_{\rm trans}=V(2\pi mkT/h^2)^{3/2}$}
For a free molecule of mass $m$ in a large three-dimensional volume $V$, replacing the translational state sum by an integral gives the displayed <partition function>. For identical classical molecules the many-molecule <canonical partition function> is $q_{\rm trans}^N/N!$, not simply $q_{\rm trans}^N$. Differentiating its <Helmholtz free energy> at fixed volume gives the ideal-gas translational <entropy>.
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