The average translational kinetic energy of gas molecules is directly related to the temperature of the gas. This relationship is based on the principles of kinetic molecular theory, which explains the behavior of gas molecules in terms of their motion.
Let's break this down simply:
1. Temperature and Kinetic Energy:
The average translational kinetic energy of gas molecules is given by the equation:
\( KE_{avg} = \frac{3}{2} k_B T \)
where \( KE_{avg} \) is the average translational kinetic energy, \( k_B \) is the Boltzmann constant, and \( T \) is the absolute temperature in Kelvin. This formula shows that the kinetic energy is directly proportional to the temperature.
2. What This Means:
As the temperature of a gas increases, the molecules move faster, which increases their translational kinetic energy. Conversely, as the temperature decreases, the molecules slow down, resulting in lower kinetic energy.
It is important to note that this relation is independent of the pressure and the number of moles of the gas. While pressure and the number of moles do affect the overall behavior of a gas, they do not directly influence the average translational kinetic energy of individual molecules.
Therefore, the correct explanation is that the average translational kinetic energy of gas molecules depends on temperature only.