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

Answer

c

Explanation

For containers A and B , the initial and final volumes are V and 2V , under isothermal conditions. T remains constant.
According to gas equation ,
`PV = m/M RT`
` :. P Delta V + V Delta P = 0 `
or ` Delta P = - P ((Delta V)/V) " or " Delta P = (-P(V - 2 V))/ V = P `
or ` Delta P = (mRT)/(MV) = m ((RT)/(MV)) = " constant " xx m `
` :. ((Delta P)_(A))/((Delta P)_(B)) = m_(A)/m_(B) " or " (Delta P)/(1.5 Delta P) = m_(A)/m_(B)`
or ` 3m_(A) = 2m_(B)`