A cylinder with a movable piston contains air under a pressure `p_(1)` and a soap bubble of radius 'r' . The pressure `p_(2)` to which the air should be compressed by slowly pushing the poston into the cylinder for the soap bubble to reduce its size by hald will be (The surface tension is `sigma` and the temperature T is maintained constant).

Options

A. `[8p_(1)+(24 sigma)/(r )]`
B. `[4p_(1)+(24 sigma)/(r )]`
C. `[2p_(1)+(24 sigma)/(r )]`
D. `[p_(1)+(24 sigma)/(r )]`

Answer

A

Explanation

`p_(i)V_(i)=p_(f)V_(f)`
`:.(p_(1)+(4 sigma)/(R ))(4/3 pir^(3))=(p_(2)+(4 sigma)/(r//2))(4/3 pi)(r/2)^(3)`
Solving this equation we get
`p_(2)=8p_(1)+(24 sigma)/(r )`.