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

Answer

C

Explanation

For gas A
`P_(1)=(Rt)/(M)(m_(A))/(V_(1))`
`P_(2)=(RT)/(M)(m_(a))/(V_(2))`
`DeltaP=P_(1)-P_(2)=(RT)/(M)(m_(A))[(1)/(V_(1))-(1)/(V_(2))]`
Putting `V_(1)`=V and `V_(2)`=2V, we get
`DeltaP=(RT)/(M)(m_(A))/(2V)`
Form equation (i) and (ii) we get `3m_(A)=2m_(B)`