The change in surface energy when a big spherical drop fo radius R is split into n spherical droplets of radius r is (T= surface tension)

Step-by-step solution

According to given situation, Volume of big drop = Volume of n small drops 4 3 R^3=n 4 3 r^3 r^3= R^3 n or r= R n^ 1 / 3 n r^2= n R^2 n^ 2 / 3 =n^ 1 / 3 R^2 (i) Surface area of big drop, A=4 R^2 Surface area of n small drops, A^ =n 4 r^2 A=A^ -A=4 n r^2-4 R^2=4 (n r^2-R^2 )=4 (n^ 1 / 3 R^2-R^2 ) [from Eq. (i)] =4 R^2 (n^ 1 / 3 -1 ) The work done for change in area, W=T A=T 4 R^2 (n^ 1 / 3 -1 ) This work is store in the form of energy.