Boyle’s law : At a constant temperature, the pressure exerted by a fixed mass of gas is inversely proportional to its volume. If P and V denote the pressure and volume of a fixed mass of gas, then, PV = constant at a constant temperature, for a fixed mass of gas. According to the kinetic theory of gases, the pressure exerted by the gas is

P = \(\frac13\)\(\frac{Nmv^2_{rms}}V\)

where N is the number of molecules of the gas, m is the mass of a single molecule, v_rms is the rms speed of the molecules and V is the volume occupied by the gas.

∴ PV = (\(\frac12\)mv² _rms) × \(\frac23\)N

= (KE of a gas molecule) \(\frac23\)N … (1)

For a fixed mass of gas, N is constant. Further, intermolecular forces are ignored so that the corresponding potential energy of the gas molecules may be assumed to be zero. Therefore, \(\frac12\)mv² _rms is the total energy of a gas molecule and N(\(\frac12\)mv²_rms) is the total energy of the gas molecules, which is proportional to the absolute temperature of the gas. Then, the right-hand side of EQ. (1) will be constant if its temperature is constant. Hence, it follows that PV = constant for a fixed mass of gas at constant temperature, which is Boyle’s law.