Q.A certain number of spherical drops of a liquid of radius r coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then

Surface Energy: The Cost of Making a Surface

Imagine you are blowing a soap bubble. You have to keep blowing — pushing air in — even after the bubble is fully formed. Why? Because every time the bubble gets bigger, you are creating new surface. That surface is not free. The liquid film resists being stretched, and you have to do work against that resistance.

That resistance is surface tension. But the work you do — the energy you spend — to create that new surface is surface energy.

The Intuition: Molecules at the Edge

Inside a liquid, a molecule is surrounded by neighbours on all sides. It feels a net pull of zero — it is happy. But a molecule on the surface has neighbours only below and to the sides, not above. It is pulled inward. That means every molecule on the surface is in a higher-energy state than one in the bulk. To bring a molecule from the inside to the surface, you must do work against this inward pull. …