Infinite number of flask are connected to one another as shown above. The volumes and pressure in each flask vary as shown. The stopcocks are initially closed. The common pressure, when all the stopcocks are opened, is : (Assume constant temperature)

Options

A. P
B. `(1)/(2)`P
C. `(P)/(4)`
D. `(4)/(3)`P

Answer

D

Explanation

`n_(T) = n_(1) + n_(2) + n_(3) +`….
`(P_(T).V_(T))/(RT) = (P_(1)V_(1))/(RT) + (P_(2) V_(2))/(RT) + ….. = sum P_(i) V_(i)`
`P_(T) V_(T) = sum P_(i) V_(i) = 2PV + (P.V)/(2) + (P)/(2). (V)/(4) + (P)/(4).(V)/(8) + …. = 2PV [1 + (1)/(4) + (1)/(16) + (1)/(64) + .....]`
`P_(T) V_(T) = 2PV (1)/(1 - (1)/(4)) = 2PV (4)/(3)`
`V_(T) = V_(1) + V_(2) + V_(3) .... = V + (V)/(2) + (V)/(4) + (V)/(8) ... = v [1 + (1)/(2) + .....] = V (1)/(1 - (1)/(2)) = 2V`
`:. P_(T) .2V = 2PV (4)/(3) rArr P_(T) = (4)/(3) P`