How is the average kinetic energy of gas molecules related to temperature?

In the kinetic theory of gases, the temperature of a gas is directly related to the average kinetic energy of its molecules. As the temperature of a gas increases, the random thermal motion of its particles increases, resulting in a higher average kinetic energy.12

This relationship is described by the equipartition of energy, a principle of statistical mechanics. For a system in thermal equilibrium at an absolute temperature $T$, the average energy associated with each translational degree of freedom is $\frac{1}{2}kT$, where $k$ is the Boltzmann constant.34

Since a monatomic gas atom has three translational degrees of freedom (moving in the x-, y-, and z-directions), its average total kinetic energy is $\frac{3}{2}kT$. Consequently, the macroscopic temperature of a gas serves as a measure of the average energy corresponding to these random molecular motions.341