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Two identical containers A and B with fr...

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

A

`4m_(A)=9m_(B)`

B

`2m_(A)=3m_(B)`

C

`3m_(A)=2m_(B)`

D

`9m_(A)=4m_(B)`

Text Solution

Verified by Experts

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`, we get `DeltaP=(RT)/(M)(m_(A))/(2V)`………`(1)`
Similarly, for Gas in `B`, `1.5DeltaP=((RT)/(M))(m_(B))/(2V)`......`(2)`
From Eqs. `(1)` and `(2)`, we get `2m_(B)=3m_(A)`
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