Find the increment of the free energy of the surface layer when two identical mercury droplets, each of diameter `d = 1.5 mm`, merge isothermally.

Explanation

When two mercury drops each of diameter `d` merge, the resulting drop has diameter `d_1`
where `(pi)/(6) d_1^3 = (pi)/(6) d^3 xx 2` or, `d_1 = 2^(1//3) d`
The increase in free energy is
`Delta F = pi 2^(2//3) d^2 alpha-2 pi d^2 alpha = 2pid^2 alpha(2^(-1//3) -1) = - 1.43 mu J`.