Equipartition theorem

The mean kinetic energy of a particle is directly proportional to the thermodynamic temperature:

$$ u = \frac {3}{2} kT $$

For the total energy of 1 mol of gas:

$$ U_p = \frac {3}{2} RT $$

Characteristics
Monatomic molecules of gases perform only a translational movement described in space by the axes x, y, z, i.e. they have three degrees of freedom (i = 3).

Biatomic molecules also perform vibrational and rotational movements (i = 5).

Equipartition theorem: the number of degrees of freedom of a gas depends on the number of atoms in its molecules.

The general equation for the total energy of the gas is therefore:

$$ U = \frac {i}{2} RT $$