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)`

Explanation

For gas in 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`
Putting `V_(1)=V` and `V_(2)=2V`
We get `DeltaP=(RT)/M (m_(A))/(2V)`
Sumilarly for gas in B, `1.5Delta P=((RT)/M)(m_(B))/(2V)`
From eq. Gas in B `1.5 DeltaP((RT)/M)(m_(B))/(2V)`
From eq. (I) and (II) we get `2m_(B)=3m_(A)`
Hnnce c is correct.