Question

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

• 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 change in $A$,
$P_{OA}V=P_A(2V)\Rightarrow P_A=\frac{P_{OA}}{2}$
or $\Delta P=\left(\frac{-P_{OA}}{2}\right)$
For isothermal change in $B$
$P_{OB}V=P_B(2V)\Rightarrow P_B=\frac{P_{OB}}{2}$
or $1.5\Delta P=\left(\frac{-P_{OB}}{2}\right)$
$\Rightarrow \frac{1.5\Delta P}{\Delta P}=\frac{P_{OB}}{P_{OA}}$
But $P_{OA}=\left(\frac{m_A}{M}\right)\frac{RT}{V}$
and $P_{OB}=\left(\frac{m_B}{M}\right)\frac{RT}{V}$
$\Rightarrow 1.5\frac{\Delta P}{\Delta P}=\frac{m_B}{m_A}$
or $\frac{3}{2}=\frac{m_B}{m_A}$
or $3m_A=2m_B$