The work done in expanding the radius of a soap bubble from R to 3R is W . The surface tension of the soap solution is given by:

Step-by-step solution

The work done in expanding a soap bubble is equal to the change in its surface energy. A soap bubble has two free surfaces (inner and outer), so the effective surface area is twice the geometric surface area. Initial surface area, A_i = 2 4 R^2 = 8 R^2 Final surface area, A_f = 2 4 (3R)^2 = 2 4 (9R^2) = 72 R^2 Change in surface area, A = A_f - A_i = 72 R^2 - 8 R^2 = 64 R^2 Work done, W = T A W = T 64 R^2 Therefore, the surface tension is: T = W 64 R^2 Answer: W 64 R^2