The radius R of the soap bubble is doubled under isothermal condition. If T be the surface tension of soap bubble. The work done in doing so it given by

Options

A. `32piR^(2)T`
B. `24piR^(2)T`
C. `8piR^(2)T`
D. `4piR^(2)T`

Answer

A

Explanation

Surface energy of a bubble
E = Tension `xx` surface area
`E=TxxA`
For soap bubble
`E=2TxxA`
`E=2Txx4piR^(2)`
Here, R= radius of bubble
If radius is double then we have
`E'=2Txx4piR^(2)`
`E'=2Txx4pi(2R)^(2)`
`E'=32piR""^(2)T`