A cylindrical container is shown in figure in which a gas is enclosed. Its initial volume is V and temperature is T. As no external pressure is applied on the light piston shown, gas pressure must be equal to the atmospheric pressure. If gas temperature is doubled, find its final volume. In its final state if piston is clamped and temperature is again doubled, the ratio of final pressure and initial pressure of the gas is ____________.

In the initial state the pressure, volume and temperature of gas P0V and T respectively if P0 is the atmospheric pressure. It is given that temperature of gas is increased to double its value i.e. up to 2T.As in initial and final state pressure of gas remains constant as initially as well as finally the piston is exposed to atmospheric pressure. Thus we have from Charles and Gay Loussac lawV1T1=V2T2 Here, V2=V1T2T1=2V As V1=V,T1=T and T2=2TThus after increasing the gas temperature to 2T , its volume becomes 2V. Now the piston is clamped that means, now the volume of gas remains constant. Again its temperature  is doubled from 2T to 4T, let the pressure changes from P0 to P'. Thus we haveP1T1=P2T2 or  P2=P′=P1T2T1=2P0 As P1=P0,T1=2T and T2=4T ] Thus in final state gas pressure becomes 2P0.