The kinetic theory relates the macroscopic temperature ($T$) to the microscopic average translational kinetic energy ($\bar{K}$) of molecules: $\bar{K}=\frac{1}{2}m{\bar{v}}^2=\frac{3}{2}{k}_{B}T$ where:

• $k_B$ is the Boltzmann constant ($\approx 1.38\times 10^{-23}\text{ J/K}$).
• This result comes from the pressure equation $P=\frac{1}{3}\frac{N}{V}m{\bar{v}}^2$ and the ideal gas law $PV=N{k}_{B}T$.
• This energy depends only on temperature, not on the pressure, volume, or type of the ideal gas.