Two identical containers `A` and `B` having volume of ideal gas at the same temperature have mass of the gas as `m_(A)` and `m_(B)` respectively. `2 m_(A) = 3 m_(B)`. The gas in each cylinder expand isothermally to double its volume. If the change in pressure in `A` is `Delta p`, find the change in pressure in `B`:

Options

A. `2 Delta p`
B. `3 Delta p`
C. `(2)/(3) Delta P`
D. `(4)/(3) Delta P`

Answer

C

Explanation

d. `2m_(A) = 3m_(g)`
`p_(A) V = (m_(A))/(M) RT`
`p_(B) V = (m_(B))/(m) RT = (2)/(3) (m_(A))/(M) RT` So, `(p_(A))/(p_(B)) = (3)/(2)`
The expanion is isothermal, so pressure will reduce to half when volume is doubled.
`p_(A) - (p_(A))/(2) = Delta P` or `p_(A) = 2 Delta p`
`p_(B) - (p_(B))/(2) = (p_(B))/(2) = (1)/(2) . (1)/(3) p_(A) = (2)/(3) Delta p`
So, `p_(B) = (4)/(3) Delta p`