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
Text Solution
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Process is isothermal. Therefore, T = constant,
$\left(\mathrm{P} \propto \frac{1}{\mathrm{V}}\right)$ volume is increasing, therefore pressure will decrease.
In chamber A:
$\Delta P = P_i - P_f = \frac{\mu_A RT}{V} - \frac{\mu_A RT}{2V} = \frac{\mu_A RT}{2V} \ldots \ldots (i)$ In chamber B: $1.5 \Delta P = P_i - P_f = \frac{\mu_B RT}{V} - \frac{\mu_B RT}{2V} = \frac{\mu_B RT}{2V} \ldots \ldots (ii)$ from equations (i) and (ii) $\frac{\mu_A}{\mu_B} = \frac{1}{1.5} = \frac{2}{3}$ $\Rightarrow \frac{m_A / M}{m_B / M} = \frac{2}{3} \Rightarrow 3 m_A = 2 m_B.$
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