kinetic theory of gases It is based on the assumption that the laws of motion of classical mechanics (that is the Newton laws) remain valid for molecules or atoms constituting the gas. The relationships of macroscopic properties of the gas like pressure, temperature internal energy, etc.with physical parameters of velocity are derived by computing averages. Other important assumptions of the theory are the following. (i) The molecules of a gas are hard, elastic, point particles with negligible volume which are in incessant random motion. (ii) There is no force of attraction between the molecules. (iii) The duration of a collision is negligible compared to time required to traverse the free path.
The expression of pressure of a gas in a container can be obtained from kinetic theory. The pressure of a gas is due to the collisions of the gas molecules with the walls of the container. We define the root mean square velocity, vrms of the molecules as,
vrms = [ (v12 + v22 + …..+ vn2 )/n] 1/2
The relationship between the rms velocity and pressure of the gas is given by,
vrms = [ 3 p/ r ] 1/2
where r is the density of the molecules. While deriving the above expression, we have assumed that
v2 = vx2 + vy2 + vz2 = 3<vx2 >º vrms2
The relationship between the rms velocity and the temperature of the gas is given by,
vrms = [ 3 kT/m ] 1/2
where k is the Boltzmann constant and m the mass of a molecule.
See also principle of equipartition of energy.