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

Answer

C

Explanation

Initial conditions `P_(1)V = n_(1)RT, P_(2)V= n_(2)RT`
Final condition `(P_(1) - DeltaP)2V = n_(1)RT`
`(P_(2) - 1.5DeltaP)2V = n_(2)RT implies (n-_(1)RT)/(2V) = DeltaP`
`(n_(2)RT)/(2V) = 1.5DeltaP implies (n_(1))/(n_(2)) = (1)/(1.5) = (2)/(3) implies (m_(A))/(m_(B)) = (2)/(3)`