Freezer and the second law

Problem

A student claims: “A freezer decreases the entropy of the water when it turns it into ice, so it violates the second law of thermodynamics.” Explain why this claim is wrong, indicating where and how the overall entropy increases.

Solution

The mistake lies in applying the second law to a system that is not isolated. The form $\Delta S \ge 0$ holds only for an ISOLATED system, i.e. for the universe as a whole, not for the water alone.

A freezer is a refrigeration machine: it absorbs electrical work $L$ and, in order to remove heat $Q_\text{f}$ from the water being frozen, discharges to the environment (through the rear coil) a heat $Q_\text{c} = Q_\text{f} + L > Q_\text{f}$ greater than the amount drawn from the water.

It is true that the water decreases its own entropy by freezing ($\Delta S_\text{water} < 0$), but the environment receives a larger amount of heat, at a relatively low temperature, and its entropy grows more than the water’s falls: $\Delta S_\text{environment} > |\Delta S_\text{water}|$ The overall balance is therefore $\ev{\Delta S_\text{tot} > 0}$ No violation of the second law: the order created locally (water turning into ordered ice) is paid for by a larger increase in disorder in the environment.

Linked atoms

Topics: Entropia e secondo principio Concepts: Entropia · Secondo principio della termodinamica · Frigorifero e pompa di calore Skills: Bilancio entropico Objects: Frigorifero