Question

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 volume of the gas in two parts respectively are

• A. 2V, 4V
• B. 3V, 3V
• C. 5V, V
• D. 4V, 2V
• E. 2.5V, 3.5V

Answer 1

Answer: (E)

Not of the given options is correct. 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
$ \left( \frac{P+10P}{2} \right)=\frac{11}{2}P $
The volume on both sides will be adjusted such that the original pressure $ \times $ volume is kept constant (isothermal change). On the left hand side,
$ P\times 5V=\frac{11}{2}P\times 4V $
$ \therefore $ $ m=\frac{10}{11} $
On the right hand side,
$ 10P\times V=\frac{11}{2}P\times nV $
$ \therefore $ $ n=\frac{20}{11} $
Hence, $ \left( \frac{10}{11}V,\frac{20}{11}V \right) $ must be the option.