Assuming the expression for the pressure exerted by the gas on the walls of the container, it can be shown that pressure is

Explanation

Boyle's law : At a constant temperature , the pressure exerted by a fixed mass of gas is inversely proportional to its volume.
According to the kinetic theory of an indeal gas , the pressure exerted by the gas is given by `p = 1/3 (Nm_(0)c^(2)rms)/V`,
where N is the number of molecules of the gas , , `m_(0)` is the mass of a single molecule, `c_(rms)` is the rms speed of the molecules and V is the volume occupied by the gas.
`:. pV = (1/2 m_(0)c_(rms)^(2) )xx 2/3 N = ("KE of a gas molecule ")xx 2/3 N`
For a fixed mass of gas , N is constant . Further , intermolecular forces are ignored in the ideal - gas model , so that the potential energy of the gas molecules may be assumed to be zero. Therefore , `1/2 m_(0) c_(rms)^(2)` is also the total energy of a gas molecule and `N(1/2 m_(0) c_(rms)^(2))` is the total energy of the gas molecules, which is proportional to the absolute temperature of the gas . Then , pV will be constant if the temperature of the gas is constant.
Hence, it follows that `p propto 1/V` for a fixed mass of gas at a constant temperature.
This is Boyle's law.