Two identical containers A and B have frictionaless pistons. They contain the same volume of an ideal gas at the same temperature. The mass of the gs in A is `m_(A)` and that B is `m_(B)` . The gas in each cylinder is now allowed to expand isothermally to double the intial volume. The chages in the pressure in A and B are fopund to be `Delta` and `1.5Deltap` respectively.

Options

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

Answer

C

Explanation

Let pA, pB be the initial pressures in A and B respectively. When the gases double their volumes at constant temperature, their pressures fall to `(p_(A))/2` and `(pB)/2`
`therefore` For A, `p_(A) - (p_(A))/2 = DeltaP` or `p_(A) =2Deltap`
for B, `p_(B) -p_(B)/2 =1.5 Deltap` or `p_(B) = 3DeltaP`
`therefore p_(A)/p_(B) = 2/3`
Also, `p_(A)V = m_(A)/M RT` and `p_(B)V = (mg)/M RT`
`therefore 3m_(A) = 2m_(B)`