Two identical containers A and B with frictionless pistons contain the same ideal gas at the same temperature and the same velocity 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 `DeltaP and 1.5 DeltaP` respectively. Then

Options

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

Answer

B

Explanation

At constant temperature `PV = constant`
`dP = -P ((dV)/(V))` and `(dV)/(V) = constant`
`:. Dp prop P` …..(1)
from `PV = (m)/(M) RT rArr P = (mRT)/(MV)`
`rArr P prop m` …..(2)
`From `(1)` and `(2) dP prop m`