In a sample of oxygen gas at room temperature, the average kinetic energy of all the balls stays constant. Which postulate of kinetic molecular theory best explains how this is possible?

The kinetic energy of gas particles depends on temperature. Greater the temperature higher will be the average kinetic energy

Kinetic energy is related to the temperature as:

KE = 3/2 kT

where k = Boltzmann constant

T = temperature

In the given example, since the temperature of O2 gas is maintained at room temperature, the average KE will also remain constant.

The fifth postulate of the kinetic molecular theory which states that the temperature of the gas depends on the average KE of the particles of the gas explains the above observation.