how much amount of work is done in forming a soap bubble of radius r
The work done in forming a soap bubble of radius rrr (surface tension TTT) is
W=8πTr2W=8\pi Tr^2W=8πTr2
Key idea
A soap bubble has two liquid–air surfaces: an inner surface and an outer surface.
So, when you create a bubble, you are creating surface area on both sides of the film, and work against surface tension must be done for each surface.
Step-by-step derivation
- Surface area of a sphere of radius rrr is A=4πr2A=4\pi r^2A=4πr2.
- A soap bubble has two surfaces, so total area created is
ΔA=2×4πr2=8πr2.\Delta A=2\times 4\pi r^2=8\pi r^2.ΔA=2×4πr2=8πr2.
3. Work done in creating a surface is
W=T×ΔA,W=T\times \Delta A,W=T×ΔA,
where TTT is the surface tension.
4. Substituting ΔA\Delta AΔA:
W=T×8πr2=8πTr2.W=T\times 8\pi r^2=8\pi Tr^2.W=T×8πr2=8πTr2.
So the amount of work done in forming a soap bubble of radius rrr is
W=8πTr2.\boxed{W=8\pi Tr^2}.W=8πTr2.
Would you like a quick numerical example with actual values of rrr and TTT to see how big this work is in joules?