Two identical cylinders A and B with frictionless pistons contain the same ideal gas at the same temperature and the same voluem V. The mass of gas `Ais m_(A) and that of B is m_(B)` .The gs in eah cylinder is notw allowed to expand isothermally to the same final volume 2V . The change in the pressure in A and B are found ot be `DeltaP and 1.5 DeltaP` respecitvely Then

Options

A. `4 m_(A) = 9 m_(B)`
B. `2 m_(A) = 3 m_(B)`
C. `3 m_(A) = 2 m_(B)`
D. `9 m_(A) = 4 m_(B)`

Answer

C

Explanation

c. For the gas in container `A`
`Delta P = (P_(A))_(fi n a l) - (P_(A))_(fi n a l) = (n_(A) RT)/(2V) - (n_(A) RT)/(V)`
`Delta P = - (n_(A) RT)/(2V)`
For gas in container `B`
`1.5 Delta P = (P_(B))_(fi n a l) - (P_(B))_(I n it ial) = (n_(B) RT)/(2V) - (n_(B) RT)/(V)`
`1.5 Delta P = - (n_(B) RT)/(2V)`
From Eqs. (i) and (ii), we get
`n_(B) = 1.5 n_(A)`
`implies 2 n_(B) = 3 n_(A)`
`implies 2 m_(B) = 3 m_(A)`