# Law of Equi-Partition of Energy

The law of equipartition of energy sates that for any dynamical system in a thermal equilibrium, the total energy is equally divided among the degrees of freedom. The energy associated with a molecule for one degree of freedom is where k is the BoltzmannÃ¢â‚¬â„¢s constant and T is the temperature.

According to kinetic theory of gases, the average kinetic energy per molecule is given by = where k = R/N, is the BoltzmannÃ¢â‚¬â„¢s constant. A monoatomic gas has three degrees of freedom. So average K.E. per degree of freedom is In one mole of a gas there are N atoms. So total energy per mole of the gas = 3 x .

In the case of a diatomic gas there are 5 degrees of freedom. The average K.E. per molecule = 5 x . The total energy per mole of the gas = .

In the case of a non-linear triatomic molecule there are 6 degrees of freedom. So average K.E. per molecule = 6 x . The total energy per molecule = 3kT Ã—x N = 3NkT = 3RT.