**Why two or more mercury drops form a single drop when brought in contact with each other?**

- A spherical shape has the minimum surface area-to-volume ratio of all geometric forms.
- When two drops of a liquid are brought in contact, the cohesive forces between their molecules coalesces the drops into a single larger drop.
- This is because, the volume of the liquid remaining the Same, the surface area of the resulting single drop is less than the combined surface area of the smaller drops.
- The resulting decrease in surface energy is released into the environment as heat.

**Proof :** Let n droplets each of radius coalesce to form a single drop of radius R. As the Volume of the liquid remains constant,

volume of the drop = volume of **n** droplets

\(\frac{4}{3}πR^3\) = \(n × \frac{4}{3}πr^3\)

∴ R^{3}=nr^{3}

\(∴ R =\sqrt[3]{n}\,r\) ....(1)

Surface area of n droplets =n × 4πr^{2}

Surface area of the drop = 4πR^{2} = 4π×n^{2/3}r^{2} ..... from eq. 1

∴ Surface area of the drop = n^{2/3} × 4πr^{2}

∴ The change in the surface area

= surface area of drop — surface area of n droplets

= 4πr^{2} (n^{2/3} — n)

Since the bracketed term is negative, there is a decrease in surface area and a decrease in surface energy. .