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`

Answer

C

Explanation

(c) Container A
`P_AV=(m_A)/M RT`
`P_A(2V)=(m_A)/M RT`
Container B
`P_BV=(m_B)/M RT`
`P`_B(2V)=(m_B)/M RT`
`rArrP_A-P'_A=(m_ART)/(MV)-(m_ART)/(M(2V))`
`rArrDeltaP=(m_ART)/(2MV)…..(i)`
`P_B-P'_B=(m_BRT)/(MV)-(m_BRT)/(M(2V))`
`1.5 DeltaP=(m_BRT)/(2MV).....(ii)`
Dividing (i) and (ii)
`(1.5DeltaP)/(DeltaP)=(m_B)/(M_A) rArr 3/2=(m_B)/(m_A) rArr 3m_A=2m_B`