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 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 $△P$ and 1.5 $△P$ respectively. Then

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Process is isothermal. There fore, T = constant, $(P\propto \frac{1}{V})$ volume is increasing, therefore pressure will decreases

In Chamber A :

$△P=P_i-P_f=\frac{{\mu }_{A}RT}{V}-\frac{{\mu }_{A}RT}{2V}=\frac{{\mu }_{A}RT}{2V}$ ------------(i)

In Chamber B :

$1.5△P=P_i-P_f=\frac{{\mu }_{B}RT}{V}-\frac{{\mu }_{B}RT}{2V}=\frac{{\mu }_{B}RT}{2V}$ ------------(ii)

from equations (i) and (ii) $\frac{{\mu }_A}{{\mu }_B}=\frac{1}{1.5}=\frac{2}{3}$

$\Rightarrow \frac{\frac{m_A}{M}}{\frac{m_B}{M}}=\frac{2}{3}\Rightarrow 3m_A=2m_B$.