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)=3m_(B)`

Answer

C

Explanation

Process is isothermal , therefore `T`= constant
`(P prop 1/V)` volume is increasing , therefore pressure will decreases.
In chamber A:
`Delta P = P_(i)-P_(f)=(mu_(A)RT)/(V)-(mu_(A)RT)/(2V)=(mu_(A)RT)/(2V)`...(i)
In chamber B:
`1.5DeltaP=P_(i)-P_(f)=(mu_(B)RT)/(V)-(mu_(B)RT)/(2V)=(mu_(B)RT)/(2V)`....(ii)
From equation (i) and (ii) `(mu_A)/(mu_B) = 1/1.5 = 2/3`
`implies (m_(A)//M)/(m_(B)//M) = 2/3implies 3m_(A) = 2m_(B)`.