Question

A container contains certain gas of mass 'm' at high pressure. Some amount of gas has been allowed to escape from the container and after some time the pressure of the gas becomes half and its absolute temperature becomes ${\left(\frac{2}{3}\right)}^{rd}$. The amount of gas escaped is :

• A. $\frac{2}{3}m$
• B. $\frac{1}{2}m$
• C. $\frac{1}{4}m$
• D. $\frac{1}{6}m$

Answer 1

The correct option is C $\frac{1}{4}m$

Gas equation is $PV=\frac{m}{M}RT$......... (i)

Again,

$\frac{P}{2}V=\frac{m_1}{M}R\frac{2}{3}T$......... (ii)

Dividing (i) by (ii),

$2=\frac{m}{m_1}\times \frac{3}{2}$

$m_1=\frac{3}{4}m$

$\therefore$ Gas escaped $=m-\frac{3}{4}m=\frac{1}{4}m$

Hence, option $C$ is correct.