A closed gas cylinder is divided into two parts by a piston held tight. The pressure and volume of gas in two parts respectively are (P, 5V) and (10P, V). If now the piston is left free and the system undergoes isothermal process, then the volumes of the gas in two parts respectively are

Options

A. 2V, 4V
B. 3V, 3V
C. 5V, V
D. 4V, 2V

Answer

A

Explanation

As the piston is allowed to move the gases are kept separated but the pressure has to be equal
`(P_1=P_2)` and final volume x and (6V - x)
`rArr(n_1RT)/x=(n_2RT)/(6V-x)rArrn_1/x=n_2/(6V-x)`
as `PV=nRTrArrn_1=(5PV)/(RT),n_2=(10Pv)/(RT)`
`therefore(5PV)/(xRT)=(10PV)/((6V-x)RT)`
`rArr1/x=2/(6V-x)`
`rArr2x=6V-xrArr3x=6VrArrx=2V`
and 6V-x=6V-2V=4V`
Hence `(2V,4V)`