• id: JTHERM-02-N04
• title: Average Translational KE and the Meaning of Temperature
• tags: kinetic-energy, temperature, boltzmann

The average translational kinetic energy per molecule is $\overline{KE}_{\text{trans}} = \frac{1}{2}m\overline{v^2} = \frac{3}{2}k_BT$. This result is universal — it does not depend on the type of gas, molar mass, or molecular structure. Temperature is fundamentally a measure of average translational kinetic energy. For $n$ moles, total translational KE = $\frac{3}{2}nRT$. Important distinction: $\frac{3}{2}k_BT$ is translational KE only. The total internal energy includes rotational and vibrational contributions and equals $\frac{f}{2}k_BT$ per molecule, where $f$ is the total degrees of freedom.