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Suppose several small water droplets are formed from a big blob of water at room temperature. Will the temperature of resultant water droplets or the surrounding air decrease? Consider it as an isolated system. (I understand that when water droplets are formed from the big blob the surface area increases and so the molecules have to work against cohesive forces since more molecules come to the surface due to increase in area. But I can't get what happens after that.)

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You're nearly at the answer. Forcing the system to have more surface area requires energy (because some bonds are relatively unsatisfied) that initially comes from the thermal energy. The water thus cools down until heat transfer with the environment brings it back to room temperature. (During that process, the surrounding air necessarily cools down temporarily as well.)

The surface energy of water is about 0.072 J/m² at room temperature, which—in conjunction with the heat capacity—can help you estimate the magnitude of the resulting cooling.

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