Is the average kinetic energy of gas molecules directly proportional to the temperature of the gas in the Kelvin scale?

The average kinetic energy of gas molecules is indeed directly proportional to the temperature of the gas when measured on the Kelvin scale. This relationship is derived from the kinetic theory of gases, which states that the kinetic energy of gas molecules increases as the temperature increases.

In mathematical terms, the average kinetic energy (KE) of a gas molecule can be expressed as:

[ KE = \frac{3}{2} k T ]

where ( k ) is the Boltzmann constant and ( T ) is the absolute temperature in Kelvin. As the temperature increases, the value of ( T ) increases, leading to a proportional increase in the average kinetic energy of the molecules.

This relationship illustrates that gas behavior can be understood more accurately at the absolute temperature scale (Kelvin), as it directly relates molecular motion and energy without reaching the point of absolute zero, where molecular motion would theoretically cease. Consequently, stating that the average kinetic energy of gas molecules is directly proportional to the Kelvin temperature is a fundamental concept in thermodynamics and gas laws.