Question

A closed gas cylinder is divided into two parts by a piston held tight. The pressure and the 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. 4V, 2V
• B. 5V, V
• C. 2V, 4V
• D. 3V, 3V

Answer 1

Answer: (C)

2V, 4V

When the piston is allowed to move the gases are kept separated but the pressure has to be equal $(p_1=p_2)$ and the final volumes are x and 6V - x.
$\because p_1=p_2$
$P\left(5V\right)=n_{1}RT$
$\Rightarrow n_1=\frac{5PV}{RT}$
$\therefore \frac{n_{1}RT}{x}=\frac{n_{2}RT}{6V-x}$
$\Rightarrow \frac{n_1}{x}=\frac{n_2}{6V-x}$
$\because 10pV=n_{2}RT$
$\Rightarrow n_2=\frac{10PV}{RT}$
$\Rightarrow \frac{5PV}{xRT}=\frac{10PV}{RT(6V-x)}$
$\Rightarrow \frac{1}{2}=\frac{2}{6V-x}$
$\therefore x=2V$ and $6V-x=4V$