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

Q: 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 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

c (c) Process is isothermal. There fore, $T =$ constant, $\left( {P \propto \frac{1}{V}} \right)$ volume is increasing, therefore pressure will decreases. In chamber $A$ : $\Delta P = {P_i} - {P_f} = \frac{{{\mu _A}RT}}{V} - \frac{{{\mu _A}RT}}{{2V}} = \frac{{{\mu _A}RT}}{{2V}}$…..$(i)$ In chamber $B$ : $1.5\Delta P = {P_i} - {P_f} = \frac{{{\mu _B}RT}}{V} - \frac{{{\mu _B}RT}}{{2V}} = \frac{{{\mu _B}RT}}{{2V}}$…..$(ii)$ from equations $(i)$ and $(ii)$ $\frac{{{\mu _A}}}{{{\mu _B}}} = \frac{1}{{1.5}} = \frac{2}{3}$ ==> $\frac{{{m_A}/M}}{{{m_B}/M}} = \frac{2}{3}$==> $3{m_A} = 2{m_B}.$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

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 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$4{m_A} = 9{m_B}$
B$2{m_A} = 3{m_B}$
C$3{m_A} = 2{m_B}$
D$9{m_A} = 3{m_B}$

IIT 1998,AIIMS 2010, Diffcult

STD 11 Science
NEET
STD 11 - 11. thermodynamics
Physics

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