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 the isothermal process, then the volume of the gas in two parts, respectively are

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 the 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

Tardigrade Admin · Accepted Answer

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

6 V - x .

∵ p_{1} = p_{2}

P (5 V) = n_{1} RT

\Rightarrow n_{1} = \frac{5 P V}{RT}

∴ \frac{n _{1} RT}{x} = \frac{n _{2} RT}{6 V - x}

\Rightarrow \frac{n _{1}}{x} = \frac{n _{2}}{6 V - x}

∵ 10 p V = n_{2} RT

\Rightarrow n_{2} = \frac{10 P V}{RT}

\Rightarrow \frac{5 P V}{x RT} = \frac{10 P V}{RT ( 6 V - x )}

\Rightarrow \frac{1}{x} = \frac{2}{6 V - x}

∴ x = 2 V

and

6 V - x = 4 V

$4 V, 2 V$

$5 V, V$

$2 V, 4 V$

$3 V, 3 V$

Q. 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 the isothermal process, then the volume of the gas in two parts, respectively are

4V,2V

5V,V

2V,4V

3V,3V

$4 V, 2 V$

$5 V, V$

$2 V, 4 V$

$3 V, 3 V$