Rotational entropy ($S_{\mathrm{rot},\mathrm{m}}=R[\ln q_{\mathrm{rot}}+T{\partial }_T\ln q_{\mathrm{rot}}]$)

The entropy contribution from populated molecular rotational states. A nonlinear rigid rotor has $q_{\mathrm{rot}}\propto T^{3/2}$ at high temperature, giving $S_{\mathrm{rot},\mathrm{m}}=R(\ln q_{\mathrm{rot}}+3/2)$. Its rotational symmetry number removes redundant orientations.