The amount of work done in forming a soap bubble of radius rrr with surface tension SSS is given by:

W=8πr2SW=8\pi r^2SW=8πr2S

Explanation:

• A soap bubble has two surfaces (inner and outer), so the total surface area is twice the surface area of a sphere.
• The surface area of a sphere of radius rrr is 4πr24\pi r^24πr2.
• Therefore, the total surface area of the soap bubble is 2×4πr2=8πr22\times 4\pi r^2=8\pi r^22×4πr2=8πr2.
• Work done WWW is the energy required to create this surface area against surface tension, so:

W=Surface tension×Total surface area=S×8πr2W=\text{Surface tension}\times \text{Total surface area}=S\times 8\pi r^2W=Surface tension×Total surface area=S×8πr2

This formula accounts for the energy needed to form both surfaces of the bubble

. In summary, the work done in forming a soap bubble of radius rrr is 8πr2S8\pi r^2S8πr2S.