Two water drops, each of radius r, coalesce to form a single bigger drop. If T is the surface tension, the surface energy released is:
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Question

Two water drops, each of radius r, coalesce to form a single bigger drop. If T is the surface tension, the surface energy released is:

G1 Physics · Accepted Answer

Volume is conserved during coalescence. Initial total volume: 2(4πr³/3). If R is the radius of the bigger drop, 4πR³/3 = 2(4πr³/3). Thus R³ = 2r³ ⇒ R = 2^(1/3)r. Initial surface area: Aᵢ = 2(4πr²) = 8πr². Final surface area: A f A_f A f ​ = 4πR² = 4π[2^(2/3)r²]. Surface energy released: ΔU = T(Aᵢ - A f ) A_f) A f ​ ) = 8πr²T - 4π2^(2/3)r²T = 4πr²T[2 - 2^(2/3)]. Correct option: D.