Two identical constaners A and B having same volume of an ideal gas at same temperature hace mass of the gas as `m_(1)` and `m_(2)` respectively and `2m_(1) = 3m_(2)`. The gas in each cylinder expands isomthermally to double of its voume. If change in pressure in A is `300 Pa`, then the change in pressure in B is

Options

A. `200 Pa`
B. `300 Pa`
C. `400 Pa`
D. `500 Pa`

Answer

A

Explanation

`2m_(1) = 3m_(2)`
`P_(1)V = (m_(1))/(M) RT` and `P_(2)V = (m_(2))/(M)RT = (2)/(3)(m_(1))/(M)RT`
`(P_(1))/(P_(2)) = (3)/(2)`
The process is isothermal `(P_(1)V_(1) = P_(2)v_(2))`
Hence, `DeltaP_(1) = P_(1) - (P_(1))/(2) rArr P_(1) = 2DeltaP_(1)`
`DeltaP_(2) = P_(2) - (P_(2))/(2) = (P_(2))/(2) = (1)/(2)(2)/(30P_(1) = (P_(1))/(3)`
`DeltaP_(2) = (2)/(3) DeltaP_(1) = (2)/(3).300`
`DeltaP_(2) = 200 pa`