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 voluem of the gas in two parts respectively are

Options

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

Explanation

When the piston is allowed to move, the gases are kept separated but the pressure has to be equal.
The pressure on each side will be
`((p+10p)/(2))=(11)/(2)p`
The volume on both side will be adjusted such that the original pressure `xx` volume is kept constant (isothermal change).
On the left hand side,
`pxx5V=(11)/(2)pxx4V`
`therefore m=(10)/(11)`
On the right hand side,
`10PxxV=(11)/(2)pxxnV`
`therefore n=(20)/(11)`
Hence `((10)/(11)V,(20)/(11)V)` most of the option.