A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions . If T is the surface tension of soap solution , the energy spent in blowing

Options

A. `3piTr^2`
B. `6piTr^2`
C. `12piTr^2`
D. `24piTr^2`

Answer

D

Explanation

Initially, area of the soap bubble is
`A=4pir^(2)`
`therefore` Change in area,
`Delta A=2(A_(1)-A_(2)) =2(16pir^(2) - 4pir^(2))=24pir^(2)`
Energy spent or work done,
`W=TxxDeltaA=T.24pir^(2)`
`therefore W=24piTr^(2)J`.