The figure shows a horizontal tube sealed at both ends and containing pellet of mercury, which occupies negligible volume. The region marked I contains a mass m of a gas and the region marked II contains a mass 2m of the same gas. If both regions have the same temperature, what fraction of the volume of the tube will be occupied by the gas of mass 2m when the pellet is in equilibrium?

1/4

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1/2

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2/3

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3/4

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Solution

The correct option is D 2/3
$T h e m e r c u r y c o l u m n w i l l c o m e t o e q u i l l i b r i u m w h e n p r e s s u r e t o t h e l e f t o f m e r c u r y c o l u m n = p r e s s u r e t o t h e r i g h t R e g i o n I = g a s o f m a s s s m R e g i o n I I = g a s o f m a s s 2 m w e h a v e P V = n R T V_{1} = m R T / P V_{2} = 2 m R T / p V_{1} + V_{2} = V 3 m R T / P = V h e n c e V_{2} / V = 2 m / 3 m = 2 / 3$

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