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 volumes of the gas in two parts respectively are

• A. $2V,4V$
• B. $3V,3V$
• C. $5V,V$
• D. $\frac{10}{11}V,\frac{20}{11}V$

Answer 1

The correct option is A $2V,4V$

The volume on both sides will be so adjusted that the original pressure x volume is kept constant as the piston moves slowly (isothermal change)
$P.5V=P^{{}^{\prime }}{V}^{{}^{\prime }}$......(1)
$10PV=P^{{}^{\prime }}{V}^{{}^{\prime \prime }}$......(2)

From (1) and (2), $V^{{}^{\prime \prime }}=2V^{{}^{\prime }}$
and from $V^{{}^{\prime }}+V^{{}^{\prime \prime }}=6V$
$V^{{}^{\prime }}=2V,V^{{}^{\prime \prime }}=4V$