A liquid drop having surface energy E is sprayed into 512 droplets of same size. The final surface energy is

Step-by-step solution

The surface energy of a sphere is directly proportional to its surface area. Initially, with a drop of radius R and surface tension T , the energy is E = 4 R^2 T . After spraying into N = 512 droplets, volume conservation requires R^3 = N r^3 , where r is the radius of each small droplet. Solving yields r = R / 8 . The final surface energy is the sum over all droplets: E' = N 4 r^2 T . Substituting r = R / 8 gives E' = N 4 (R^2 / 64) T = (N / 64) 4 R^2 T . Since E = 4 R^2 T , it follows that E' = (512 / 64) E = 8E