Inifinite number of flasks are connected to one another as shown above. The volume 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

4

Explanation

`n_(T)=n_(1)+n_(2)+n_(3)+................`
`(P_(T).V_(T))/(RT)=(P_(1)V_(1))/(RT)+(P_(2)V_(2))/(RT)+..............=SigmaP_(1)V_(1)`
`P_(T)V_(T)=SigmaP_(1)V_(1)`
`=2PV+(P.V.)/(2)+(P)/(2).(P)/(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)`
`P_(T)=(4)/(3)P`