A soap bubble of radius r si blown up to form of bubble of radius 3r under isothermal conditions . What is the energy spent in doing so if the surface tension of soap solution is S.

Options

A. `32 pi R^(2)T`
B. `24 pi R^(2)T`
C. `8pi R^(2)T`
D. `64 pi R^(2)T`

Answer

D

Explanation

initial suface energy
`U_(1)=2xx4pi R^(2)T=8pi R^(2)T`
Final surface energy
`U_(2)=2xx4pi (3R)^(2)T=72pi R^(2)T`
Hence, required energy
`=72 pi R^(2)T-8pi R^(2)T=64pi R^(2)T`