Question

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

Answer 1

• 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

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

∴ R³=nr³

\(∴ R =\sqrt[3]{n}\,r\) ....(1)

Surface area of n droplets =n × 4πr²

Surface area of the drop = 4πR² = 4π×n^2/3r² ..... from eq. 1

∴ Surface area of the drop = n^2/3 × 4πr²

∴ The change in the surface area

= surface area of drop — surface area of n droplets

= 4πr² (n^2/3 — n)

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