Which one of the following physical quantities is the same for molecules of all gases at a given temperature?

According to the kinetic theory of gases, the average translational kinetic energy of a gas molecule is directly proportional to the absolute temperature of the gas. Specifically, the relationship is defined as KE = (3/2)kT, where k is the Boltzmann constant and T is the temperature. This implies that at a given temperature, all gas molecules, regardless of their mass or chemical identity, possess the same average kinetic energy. Other physical quantities like speed and momentum depend on the mass of the molecule; for instance, lighter molecules move faster than heavier ones at the same temperature to maintain the same kinetic energy. Mass is a fixed property of the specific gas molecule [2], and momentum is the product of mass and velocity. Therefore, only kinetic energy remains uniform across different gases at a constant temperature.

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 20: Earths Atmosphere > Permanent Gases of The Atmosphere > p. 271
2. [2] Science , class X (NCERT 2025 ed.) > Chapter 4: Carbon and its Compounds > 4.2.4 Homologous Series > p. 67