Equipartition Theorem

The equipartition theorem is a result in classical statistical mechanics that relates the temperature of a system to the average energy stored in each of its independent forms of motion, called degrees of freedom. It states that in thermal equilibrium, energy is shared equally among all of these degrees of freedom, so that, for example, the average kinetic energy per degree of freedom in a molecule rotational motion equals the average kinetic energy per degree of freedom in its translational motion. As one consequence, the theorem predicts that every atom in a monatomic ideal gas has an average kinetic energy of three halves times the Boltzmann constant times the temperature. The theorem can be used to derive the ideal gas law and to predict the specific heat capacities of solids, and it applies to any classical system in thermal equilibrium no matter how complicated, though it becomes inaccurate at low temperatures where quantum effects dominate.