Inside a cylinder having insulating walls and closed at ends is a movable piston, which divides the cylinder into two compartments. On one side of the piston is a mass $m$ of a gas and on the other side a mass $2 m$ of the same gas. What fraction of volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium $?$ Consider that the movable piston is conducting so that the temperature is the same throughout
A$0.25$
B$0.33$
C$0.5$
D$0.67$
Medium
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D$0.67$
d From, $PV = \mu RT$
$P(V - {V_1}) = \frac{m}{M}RT$ $... (i)$
and $P{V_1} = \frac{{2m}}{M}RT$ $... (ii)$
$\Rightarrow$ $\frac{{{V_1}}}{V} = \frac{2}{3}$
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