Question

Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The mass of the gas in $A$ is $m_A$ and that in $B$ is $m_B$. The gas in each container is now allowed to expand isothermally to the same final volume $2V$. The changes in the pressure in $A$ and $B$ are to be found $\Delta p$ and $1.5\Delta p$ respectively, then relation for masses will be

• A. $4m_A=9m_B$
• B. $2m_A=3m_B$
• C. $3m_A=2m_B$
• D. $9m_a=4m_B$

Answer 1

Answer: (C)

For isothermal expansion of an ideal gas
$pV=$ constant
$\Rightarrow p\Delta V+V\Delta p=0$
For container $A$,
$p_{iA}(V)+V(\Delta p)=0$
$\Rightarrow p_{iA}=-\frac{V\Delta P}{V}=-\Delta p$ ...(i)
where, $p$ is initial pressure.
For container $B$,
$p_{iB}(V)+V(15\Delta p)=V$
$\Rightarrow p_{iB}=-15\Delta p$ ...(ii)
From Eqs. (i) and (ii), we have
$p_{iA}=\frac{p_{iB}}{15}=\frac{2}{3}{p}_{iB}$
$\Rightarrow m_A=\frac{2}{3}mB$
$\Rightarrow 3m_A=2mB[\because p\propto m]$