Question

A water drop of diameter 1 cm breaks into 1000 similar droplets of same diameter. What will be the gain or loss in the surface energy? (Take surface tension as 0.075 N/m)

(a) gain of 0.424 mJ

(b) gain of 0.212 mJ

(c) loss of 0.212 mJ

(d) loss of 0.424 mJ

This question was posed to me in quiz.

The origin of the question is Surface Tension topic in portion Properties of Fluids of Fluid Mechanics

Answer 1

Correct answer is (b) gain of 0.212 mJ

To elaborate: According to the Principle of Conservation of mass, M = 1000 * m, where M = mass of the big drop, m = mass of each droplet. Assuming density to be constant, D^3 = 1000 * d^3, i.e. D = 10d, where D = diameter of big drop, d = diameter of a droplet.

Change in surface energy = Surface tension * Change in surface area = 0:075*(1000 * πd^2 – πD^2) = 0:075 * (10 * πD^2 – πD^2) = 0:075 * 9π * (10-2)^2 = 0:212 mJ Since, the change is positive, there will be a gain in the surface energy.