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A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be:
- (1) 2T/J (1/r − 1/R)
- (2) 2T/(rJ)
- (3) 3T/(rJ)
- (4) 3T/J (1/r − 1/R)
Correct answer: (4) 3T/J (1/r − 1/R)
Solution
The correct option is derived from the relationship between surface tension and the change in energy when smaller droplets merge into a larger one. The formula accounts for the difference in surface area before and after the merging process, leading to a rise in heat energy proportional to the surface tension and inversely related to the radii of the drops.
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