Properties

Properties

Pressure and Kinetic Energy

Pressure is explained by kinetic theory as arising from the force exerted by molecules or atoms impacting on the walls of a container. Consider a gas of N molecules, each of mass m, enclosed in a cuboidal container of volume V=L³. When a gas molecule collides with the wall of the container perpendicular to the x coordinate axis and bounces off in the opposite direction with the same speed (an elastic collision), then the momentum lost by the particle and gained by the wall is:

where v_x is the x-component of the initial velocity of the particle.
The particle impacts one specific side wall once every

(where L is the distance between opposite walls).
The force due to this particle is:

The total force on the wall is

where the bar denotes an average over the N particles. Since the assumption of molecular chaos imposes , we can rewrite the force as

This force is exerted on an area L². Therefore the pressure of the gas is

where V=L³ is the volume of the box. The fraction n=N/V is the number density of the gas (the mass density ρ=nm is less convenient for theoretical derivations on atomic level). Using n, we can rewrite the pressure as

This is a first non-trivial result of the kinetic theory because it relates pressure, a macroscopic property, to the average (translational) kinetic energy per molecule which is a microscopic property.