One large soap bubble of diameter 'D' breaks into 64 bubbles having surface tension 'T'. The change in surface energy is

Step-by-step solution

Let R be the radius of the large bubble and r be the radius of each small bubble. Equating the initial and final volumes: 4 3 R^3 = 64 4 3 r^3 R^3 = 64 r^3 r = R 4 A soap bubble has two free surfaces. The initial surface energy is: U_i = T 2 4 R^2 = 8 R^2 T The final surface energy of 64 small bubbles is: U_f = 64 T 2 4 r^2 = 512 r^2 T Substituting r = R 4 : U_f = 512 ( R 4 )^2 T = 512 R^2 16 T = 32 R^2 T The change in surface energy is: U = U_f - U_i = 32 R^2 T - 8 R^2 T = 24 R^2 T Given the diameter D = 2R , we s