Equipartition Theorem
A classical statistical mechanics theorem stating that every independent quadratic degree of freedom contributes ½ kB T to a system's average energy in thermal equilibrium.
Governing formula
E_avg = (f / 2) kB T
SI unit
J
In depth
A monoatomic ideal gas has 3 translational degrees of freedom ($f=3$), yielding $E_{avg} = 1.5 k_B T$. Diatomic molecules at room temp add 2 rotational degrees ($f=5$), yielding $2.5 k_B T$.
Examples in the real world
Predicting molar heat capacity $C_v = 1.5 R$ for noble gases like helium and argon.