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

In a container m g of a gas is placed. After some time some gas is all

1.	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
Answer» `2//3` `1//2` `1//4` `1//6` Solution :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`