 From that probability distribution function, the average kinetic energy (per particle) of a monatomic ideal gas is

where the Boltzmann constant is the ideal gas constant divided by the Avogadro number, and formula_5 is the root-mean-square speed.Thus the ideal gas law states that internal energy is directly proportional to temperature.This direct proportionality between temperature and internal energy is a special case of the equipartition theorem, and holds only in the classical limit of an ideal gas.