When comparing the kinetic energy of gases at constant temperature, what is true?

At a constant temperature, the average kinetic energy of gas molecules is directly related to the temperature they are at, according to the kinetic molecular theory of gases. The equation for the average kinetic energy of a gas is given by:

[ KE_{avg} = \frac{3}{2} k T

]

where (KE_{avg}) is the average kinetic energy, (k) is the Boltzmann constant, and (T) is the temperature in Kelvin. This equation demonstrates that the average kinetic energy is dependent only on temperature, not on the type or molecular weight of the gas.

Therefore, all gases, regardless of their molecular weights or types (monatomic, diatomic, etc.), will have the same average kinetic energy when they are at the same temperature. This principle holds true for ideal gases and is a fundamental concept in understanding gas behavior.

The other options suggest varying kinetic energies due to differences in molecular weight or imply limited applicability to specific types of gases, which contradicts the established principles of thermodynamics and kinetic theory for ideal gases. In essence, at a constant temperature, all gases will demonstrate the same average kinetic energy, and this is a vital concept in thermodynamics and physical chemistry.