Inside a cylinder having insulating walls and closed at ends is a… - Vidyadip

MCQ

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
$0.5$
✓
$0.67$

✓

Answer

Correct option: 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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