• id: JTHERM-02-N05
• title: Law of Equipartition of Energy
• tags: equipartition, degrees-of-freedom, energy-distribution

The equipartition theorem states that in thermal equilibrium, each quadratic term in the energy expression contributes $\frac{1}{2}k_BT$ per molecule. Translational motion has 3 quadratic terms ($\frac{1}{2}mv_x^2, \frac{1}{2}mv_y^2, \frac{1}{2}mv_z^2$), giving $f = 3$ for monatomic gases. Linear diatomic molecules add 2 rotational degrees ($f = 5$). Non-linear polyatomic molecules have 3 rotational degrees ($f = 6$). Vibrational modes contribute 2 degrees each (kinetic + potential), but are "frozen out" at room temperature for most diatomic gases and activate only above ~1000 K.