Average KE of a Gas Molecule

This formula gives the average translational kinetic energy carried by one molecule of an ideal gas, and it depends only on absolute temperature, not on the gas species. It comes from the equipartition theorem: in thermal equilibrium, each of the three translational degrees of freedom contributes k_B T to the mean energy, so together they sum to /2 k_B T. That is why hotter gases have faster-moving molecules on average, and why the result is universal for ideal gases.

Use this when you need the microscopic energy of gas molecules from temperature, especially in kinetic theory or ideal-gas problems. It is also useful for connecting temperature to molecular speed, internal energy, and thermal motion.

• Using Celsius instead of Kelvin for T
• Confusing average kinetic energy per molecule with total gas internal energy
• Applying the formula to non-ideal situations without checking whether the gas model is valid