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प्रश्न
Why two or more mercury drops form a single drop when brought in contact with each other?
उत्तर
A spherical shape has the smallest surface area to volume ratio of all geometric forms. When a number of droplets coalesce and form a drop, there is reduction in the total surface area. In this case, energy is released to the surrounding.
Let n droplets each of radius r 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
∴ `4/3 pi "R"^3 = "n" xx 4/3 pi"r"^3`
∴ `"R"^3 = "nr"^3`
∴ R = `root(3)("n")"r"`
Surface area of n droplets = n × 4πr2
Surface area of the drop = 4πR2 = 4π(`root(3)("n")"r"`)2 = n2/3 × 4πr2
∴ The change in the surface area = surface area of drop - surface area of n droplets
= (n2/3 × 4πr2) - (n × 4πr2) = 4πr2 × (n2/3 - n)
Since (n2/3 - n) will always be negative there is a decrease in surface area therefore there is a decrease in surface energy.
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