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

Process is isothermal. Therefore, `T=`constant. Volume is increasing, therefore, pressure will decrease `(p prop(1)/(V))` . In chamber `Ararr`
`Deltap=(p_(A))_(i)-(p_(A))_(f)=(n_(A)RT)/(V)-(n_(A)RT)/(2V)`
`=(n_(A)RT)/(2V)`
In chamber `Brarr`
`1.5Deltap=(p_(B))_(i)-(p_(B))_(f)=(n_(B)RT)/(V)-(n_(B)RT)/(2V)`
`=(n_(B)RT)/(2V)`
From Eqs. (i) and (ii) ,
`(n_(A))/(n_(B))=(1)/(1.5)=(2)/(3)`
`(m_(A)//M)/(m_(B)//M)=(2)/(3)`
`(m_(A))/(m_(B))=(2)/(3)`
`3m_(A)=2m_(B)`