## 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*=

*L*

^{3}. 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:

*v*is the

_{x}*x*-component of the initial velocity of the particle.

The particle impacts one specific side wall once every

*L*is the distance between opposite walls).

The force due to this particle is:

*N*particles. Since the assumption of molecular chaos imposes , we can rewrite the force as

*L*

^{2}. Therefore the pressure of the gas is

*V*=

*L*

^{3}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

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