What is the relationship between the temperature and kinetic energy of gas molecules as per the kinetic gas theory?

The correct choice emphasizes that when two different gases are at the same temperature, they exhibit the same average kinetic energy. According to the kinetic molecular theory, the temperature of a gas is directly related to the average kinetic energy of its molecules. This means that if two gases are at the same temperature, it can be concluded that their molecules are moving at an equivalent average speed, resulting in equal kinetic energy.

This relationship arises from the formula for kinetic energy, which is given by ( KE = \frac{1}{2}mv^2 ), where ( m ) is the mass of a molecule and ( v ) is its velocity. Temperature can be related to the average kinetic energy of gas molecules through the equation ( KE_{avg} = \frac{3}{2}kT ), where ( k ) is the Boltzmann constant and ( T ) is the temperature in Kelvin. This demonstrates that temperature serves as a measure of the average kinetic energy, establishing that at a constant temperature, different gases will share the same average kinetic energy, regardless of their molecular weights.