Physics · Heat and Thermodynamics

The average translational kinetic energy of a molecule in an ideal gas is given by the formula 3/2R/N_AT, where is the Boltzmann constant and is the absolute temperature. This formula is derived from the equipartition theorem, which assigns of energy per degree of freedom. An ideal gas molecule has three translational degrees of freedom, thus the total translational kinetic energy is . The other options either represent incorrect applications of the equipartition theorem or miscalculate the energy distribution across degrees of freedom.

This is the correct expression for the average translational kinetic energy of a molecule in an ideal gas, where \(k\) is the Boltzmann constant and \(T\) is the absolute temperature.

This expression represents the average kinetic energy in one degree of freedom, not the total translational kinetic energy for all three degrees of freedom.

This expression overestimates the average translational kinetic energy as it does not account for the division by 2.

This expression does not account for the three translational degrees of freedom of motion in an ideal gas.