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 )`

Answer

C