Ans.

Let the pressure p, volume = v and absolute temperature be T of a gas of definite volume, then

 (i) According to Boyle’s law Va 1/p, when T is constant.  P

 (ii) According to Charle’s law VaT when p is constant.

 Therefore, when pressure and temperature change simultaneously, Va T/P

 or V = K. T/p where K is a constant.

 or pv KT or pv/T = k

 Here the value of K depends on the amount of gas.  The volume of a gas is proportional to the volume of the gas.  Hence the value of K is proportional to the volume of the gas.  That is, proportional to the mole of the gas.  Therefore, K = nRT where n is the number of moles and R is the gas constant per mole.

 ..pv=nRT