Question

An ideal monatomic gas of N particles, each of mass m, is in thermal equilibrium at absolute temperature T. The gas is contained in a cubical box of side L, whose top and bottom sides are parallel to the earth's surface. The effect of the earth's uniform gravitational field on the particles should be considered, the acceleration due to gravity being g.

What is the average kinetic energy of a particle?

Answer 1

The average kinetic energy of a particle in an ideal monatomic gas at absolute temperature T is given by the equation KE = (3/2)kT, where k is Boltzmann's constant, independent of the mass or gravitational field.

Step-by-step explanation:

The student asked about the average kinetic energy of a particle in an ideal monatomic gas that is in thermal equilibrium at an absolute temperature T. According to the kinetic theory of gases, the average kinetic energy (KE) of a molecule in such a gas is given by the equation KE = (3/2)kT, where k is the Boltzmann constant and T is the absolute temperature.

This equation arises from the idea that the temperature of a gas is directly proportional to the average translational kinetic energy of its molecules and is independent of the mass of the molecules or the gravitational field, assuming the gravitational potential energy difference between molecules is negligible in comparison to their kinetic energy. Therefore, gravity does not affect the average kinetic energy calculated