# Equipartition

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in classical statistical mechanics each degree of freedom that appears
quadratically in the energy (Hamiltonian) has an average value of $\frac{1}{2}k_B T$,
where $k_B T$ is the  thermal energy.

Thus, the thermal energy is shared equally ("equipartitioned") by all these degrees of freedom. This is a consequence of the equipartition theorem, which is very simple mathematically. As an immediate corollary, the translational energy of a molecule must equal $\frac{3}{2}k_B T$, since translations are described by three degrees of freedom.