Surface Tension

We are given the surface tension , the radius of the drop , and the change in surface energy , and we need to find the number of identical drops .
Step 1: Use the formula for change in surface energy. The change in surface energy when a drop of radius divides into identical drops can be expressed as: where is the change in the surface area.
Step 2: Surface area of a drop. The surface area of a spherical drop is given by: where is the radius of the drop.
Step 3: Initial and final surface areas. - Initial surface area of the liquid drop: - Final surface area after division into drops:
Step 4: Change in surface area. The change in surface area is:
Step 5: Calculate the change in surface energy. Now, using the relation for the change in surface energy, we have: Substitute the given values for , , and : Simplifying: Thus: Thus, the value of is 27.