Vessel A contains an ideal gas at a pressure `5xx10^(5)` Pa and is connected with a heat source which maintains its temperature at `300 K`. Another vessel B which has four time greater inner volume contains the same gas at a pressure `10^(5)` Pa and is connected to a heat source which maintains its temperature at `400 K`. What will be the pressure of entire system if two vessels are connected by a narrow tube tap:-

Options

A. `10^(5)Pa `
B. `2xx10^(5)Pa`
C. `4xx10^(5)Pa`
D. `5xx10^(5)Pa`

Answer

B

Explanation

`(P_(A)V_(A))/(RT_(A))+(4P_(B)V_(A))/(RT_(B)) = (pV_(A))/(RT_(A))+(4pV_(A))/(RT_(B))`
`(p_(A))/(T_(A))+(4p_(B))/(T_(B))=(p)/(T_(A))+(4p)/(T_(B))`
`(5xx10^(5))/(300)+(4xx10^(5))/(400) = (p)/(300)+(4p)/(400)`
`((20+12)xx10^(5))/(1200) = (4p+12p)/(1200)`
`32xx10^(5) = 16p`
`p = 2xx10^(5) N//m^(2)`