Kinetic Energy And Temperature

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Two containers hold helium and oxygen respectively at the same absolute temperature, so how do the average translational kinetic energies of a single helium atom and a single oxygen molecule compare?

RankGuru · Accepted Answer

A cornerstone result from NCERT Class 11, Chapter 13 (Kinetic Theory) is that the average translational kinetic energy of a gas molecule depends only on the absolute temperature, expressed as $\overline{KE} = \frac{3}{2}k_BT$, where $k_B$ is Boltzmann's constant. This relation contains no reference to molecular mass or the type of gas, so at a given temperature every molecule, whether light helium or heavier oxygen, carries the same average translational kinetic energy. Since both containers are at the same temperature, the two averages are identical. The option that oxygen has more energy because it is heavier confuses kinetic energy with mass; heavier molecules simply move more slowly to keep the same energy. The option that helium has more energy because it is lighter makes the opposite error. The option of an eightfold difference wrongly invokes a mass ratio that does not enter the energy expression. A sanity check reinforces this: temperature is precisely a measure of average molecular kinetic energy, so equal temperature must mean equal average translational kinetic energy regardless of the gas.

Kinetic Energy And Temperature

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