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

Answer 1

The correct option is C $3m_A=2m_B$

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