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 piston into the cylinder for the soap bubble to reduce its size by half will be : (The surface tension is `sigma`, and the temperature `T` is maintained constant)

Options

A. `P_(1)+(4T)/r`
B. `4P_(1)+(12T)/r`
C. `8P_(1)+(24T)/r`
D. `P_(1)+(2T)/r`

Explanation

Isothermal process.
`(P_(1)+(4T)/r)(4/3pir^(3))=(P_(2)+(4T)/(r//2))(4/3 pi(r//2)^(3))`
`P_(2)=8P_(1)+(24T)/r`