Solution to problem no. 4

Entropy of the box increases; entropy of the water decreases because of (a) cooling and (b) decreasing amount of water. On evaporation the fastest molecules leave the liquid phase and carry away their energy, leaving behind the slower molecules; the liquid phase therefore cools down.


The picture shows the entropy changes (arbitrary units) on evaporation. While the entropy of the whole system increases, the entropy of the water decreases. Overall entropy goes up, of course.

Entropy is an extensive quantity, that is, if the quantity of matter is doubled, entropy is also doubled.

This system is an isolated one; neither the exchange of matter nor of energy with its surroundings are of interest.

Looking at the liquid water alone, we have an open system. It exchanges both matter and heat with the vapour part, until equilibrium is reached.


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