Question

In a container $mg$ of a gas is placed. After some time some gas is allowed to escape from container. The pressure of gas becomes half and absolute temperature becomes $2/3^{rd}$. The amount of gas escaped is:

• A. $2m/3$
• B. $m/2$
• C. $m/4$
• D. $m/5$

Answer 1

Answer: (C)

$m/4$

Let $x$ gas is allowed to escape from container

We know that $PV=w\frac{RT}{M}$

$P_1{P}_2=\frac{w_1}{w_2}\frac{T_1}{T_2}$

$P_1=P,P_2=P/2,T_1=T,T_2=\frac{2}{3}T$

$w_1=m,w_2=m-x$

$\frac{P}{P/2}=\frac{m}{mx}\times \frac{T}{2T/3}$

$2=\frac{m}{m-x}\times \frac{3}{2}$

$4(m-x)=3m$

$4m-4x=3m$

$m=4x$

or $x=m/4$

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