= Rotational temperature
{title2=$\theta_r=\hbar^2/(2Ik_B)$}
{wiki}
For a <linear rigid rotor>, <rotational temperature> expresses the rotational <energy> constant in kelvins: $E_J=k_B\theta_rJ(J+1)$, where $I$ is the perpendicular <moment of inertia>. With all integer $J\geq0$ allowed and degeneracies $2J+1$, its rotational <canonical partition function> is $Z=\sum_J(2J+1)e^{-\theta_rJ(J+1)/T}$. It approaches $1+3e^{-2\theta_r/T}$ at low <temperature> and $T/\theta_r$ at high <temperature>. The latter limit gives mean rotational <energy> $k_BT$ and <heat capacity> $k_B$ per rotor.
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