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

Last updated date: 14th Jul 2024
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Hint:Mercury is a silvery-white liquid metal with a heavy consistency. It is a bad heat conductor compared to other metals, but a good conductor of electricity. Mercury is a highly toxic or radioactive material that can be ingested in a variety of forms. If you ingest it, such as from a broken thermometer, the majority of it moves through the body with very little being consumed.

The term "cohesive forces" refers to the mutual intermolecular forces (such as hydrogen bonding and van der Waals forces) that are responsible for liquids' bulk resistance to separation. These attractive forces occur specifically between molecules of the same material.

Of all geometric shapes, a spherical shape has the smallest surface area to volume ratio. When two liquid drops collide, the cohesive forces between their molecules coalesce the drops into a single larger drop. This is because, with the same amount of liquid, the surface area of the resulting single drop is less than the sum of the smaller drops' surface areas. Heat is released into the air as a result of the decrease in surface energy.

Proof: Allow n droplets, each with a radius of r, to coalesce into a single drop with a radius of $R$. As long as the liquid's volume stays unchanged.
The volume of one drop = The volume of n droplets
$\Rightarrow \dfrac{4}{5}\pi {R^3} = n \times \dfrac{4}{3}\pi {r^3} \\ \Rightarrow {R^3} = n{r^3} \\ \therefore \;R = {(n{r^3})^{\dfrac{1}{3}}} \\$
If there are n droplets, then its surface area is given by = $n \times 4\pi {r^2}$
Surface area of one drop = $4\pi {R^2} = {n^{\dfrac{2}{3}}} \times 4\pi {r^2}$
The change in surface area is given by = surface area of a drop – surface area of $n$ droplets
The change in surface area is given by$= 4\pi {R^2} = ({n^{\dfrac{2}{3}}} - n)$
There is a decrease in surface area and a decrease in surface energy since the bracketed word is negative.

Note:Mercury is mainly used in the production of industrial chemicals as well as in electrical and electronic applications. It's found in some thermometers, especially those that measure high temperatures.