text: In the kinetic theory of gases, the pressure is assumed to be equal to the force (per unit area) exerted by the individual gas atoms or molecules hitting and rebounding from the gas container's surface.
  Consider a gas particle traveling at velocity, , along the -direction in an enclosed volume with characteristic length, , cross-sectional area, , and volume, . The gas particle encounters a boundary after characteristic time
  The momentum of the gas particle can then be described as
  We combine the above with Newton's second law, which states that the force experienced by a particle is related to the time rate of change of its momentum, such that
  Now consider a large number, N, of gas particles with random orientation in a three-dimensional volume. Because the orientation is random, the average particle speed, , in every direction is identical
  Further, assume that the volume is symmetrical about its three dimensions,  , such that
  The total surface area on which the gas particles act is therefore 
  The pressure exerted by the collisions of the N gas particles with the surface can then be found by adding the force contribution of every particle and dividing by the interior surface area of the volume,
  The total translational kinetic energy  of the gas is defined as
  providing the result
  This is an important, non-trivial result of the kinetic theory because it relates pressure, a macroscopic property, to the translational kinetic energy of the molecules, which is a microscopic property.