Determine the ratio of surface energy of 1 large drop to 1 small drop, if 1000 small drops combined to form 1 large drop.

Step-by-step solution

Let the radius of the small drop be r and the radius of the large drop be R . Since 1000 small drops combine to form 1 large drop, the total volume remains conserved. 4 3 R^3 = 1000 4 3 r^3 R^3 = 1000 r^3 R = 10r The surface energy of a drop is given by E = T A , where T is the surface tension and A is the surface area. Surface energy of 1 large drop, E_ L = T 4 R^2 Surface energy of 1 small drop, E_ S = T 4 r^2 The ratio of their surface energies is: E_ L E_ S = T 4 R^2 T 4 r^2 = ( R r )^2 Substituting R = 10r : E