- 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. .