The surface tension of water = `72xx10^-3J/m^2`. Find the work done in splitting a drop of water of 1mm radius into 64 small drops.

Explanation

`4/3 pi R^3 = 64 xx 4/3 pi r^3`
`therefore r^3 = (R^3)/(64)`
`therefore r = R/4 = 1/4` mm
initial surface energy
`E_1 = 4piT (R^2)`
Final surface energy
`E_2 = 64 xx 4 piT (r^2)`
`E_2 - E_1 = 4piT (64r^2 - R^2)`
work done
= `4piT (64r^2 - R^2) = 4piT(4 xx 10^-6 - 10^-6)`
`12T xx 10^-6 = 2.7 xx 10^-6 J`