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

Answer

D

Explanation

For isothermal changes PV = nRT
For A, `DeltaP=P_(i)-P_(f)=(n_(A)RT)/V=-(n_(A)RT)/(2V)`
`thereforeDeltaP=(n_(A)RT)/(2V)=((m_(A))/(M))(RT)/(2V)" "thereforen_(A)=m_(A)/M.......(1)`
Similarly for B, `3/2DeltaP=(m_(B)/M)(RT)/(2V)" "....(2)`
Dividing (1) by (2)
`2/3=m_(A)/m_(B)or3m_(A)=2m_(B)`