Problem 2.

Calculate the amount of energy needed to break a drop of water of diameter 0.001 meter into 1000000 droplets of equal sizes. The surface tension of water is 0.0072 N/m.

Solution:

In this problem we need to take into account only the surface energy of water drops.

The energy of a drop of water of diameter is

Where is the surface tension and is the area of a spherical droplet. Then

We know the initial diameter, then we can find the initial energy

In the final state all droplets have the same diameter, . To find this diameters we need to use the fact that the initial volume of the water is equal to the final volume:

where is the number of droplets. Then

Then the energy in the final state is

Then