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

The relationship between temperature and the kinetic energy of gas molecules is found in the kinetic molecular theory of gases. According to this theory, the temperature of a gas is a measure of the average kinetic energy of its molecules. When the temperature of a gas increases, the average kinetic energy of the molecules also increases. This means that the molecules move faster and collide more frequently and with greater force, which is directly related to the temperature measured in Kelvin.

As temperature increases, the kinetic energy, calculated using the formula (\text{KE} = \frac{3}{2}kT) (where (k) is Boltzmann's constant and (T) is the absolute temperature), shows a clear direct proportional relationship. Thus, as the temperature rises, so does the kinetic energy of the gas molecules without any inversely proportional or independent associations.

This direct relationship is foundational in understanding how gases behave under different temperature conditions, forming a key principle in the study of thermodynamics and gas laws.