Air is pumped into a soap bubble of radius r , doubling its radius. Given that the surface tension of the soap solution is S , the work done during this process is

Step-by-step solution

A soap bubble has two free surfaces, an inner surface and an outer surface. Initial surface area of the soap bubble, A₁ = 2 4 r^2 = 8 r^2 Final radius of the soap bubble is 2r . Final surface area of the soap bubble, A₂ = 2 4 (2r)^2 = 32 r^2 Change in surface area, A = A₂ - A₁ = 32 r^2 - 8 r^2 = 24 r^2 Work done in increasing the radius is equal to the change in surface energy. W = S A = S 24 r^2 = 24 r^2 S