In a container `m` g of a gas is placed. After some time some gas is allowed to escape from container. The pressure of the gas becomes half and its absolute temperature `2//3 rd`. The amount of gas escaped is

Options

A. `2//3`
B. `1//2`
C. `1//4`
D. `1//6`

Answer

C

Explanation

We know that `PV = w (RT)/(M)`
`:. (P_(1))/(P_(2)) = (w_(1))/(w_(2)) (T_(1))/(T_(2))`
`P_(1) = P, P_(2) = (P)/(2), T_(1) = T, T_(2) = (2)/(3) T`
`w_(1) = m, w_(2) = m - x`
`(P)/(P//2) = (m)/(m x) xx (T)/(2T//3)`
`2 = (m)/(m - x) xx (3)/(2)`
`4 (m - x) = 3m`
`4 m - 4 x = 3m`
`m = 4x`
or `x = m//4`