Two identical vessels A and B with frictionless pistons contain the same ideal gas at the same temperature and the same volume V. The masses of gaş in A and B are `m_(A)` and `m_(B)` respectively. The gases are allowed to expand isothermally to the same final volume 2 V. The change in pressures of the gas in A and B are found to be `Deltap` and 1.5 `Deltap` respectively. Then

Options

A. `9m_A=4m_B`
B. `3m_A=2m_B`
C. `2m_A=3m_B`
D. `4m_A=9m_B`

Answer

B

Explanation

If `P_(1)` ande `P_(2)` are initial and final pressures respectively, then
`Delta P =P_(1) - P_(2) = - (mu_(A)RT)/(2V)`
`= -[m_(A)/m] (RT)/(2V)…..(1)`From (1) and (2) equations, `1.5 = m_(B)/m_(a) = 3/2`
`therefore 2m_(B) = 3m_(A)`