Freezer and life

Problem

A classmate of yours observes: “A refrigerator decreases the entropy of the water that freezes; therefore the second law is violated.” And also: “An embryo that becomes an adult organism decreases entropy (the cells organise themselves); therefore life violates the second law.” Refute both statements by distinguishing the entropy of the system from that of the universe, and specifying where the entropy produced ends up.

Solution

Both statements make the same mistake: they apply the second law in the form $\Delta S \ge 0$ to a system that is NOT isolated. That form holds only for an isolated system, i.e. for the entire thermodynamic universe. The refrigerator and the living organism are instead OPEN systems, which continuously exchange energy and matter with the environment.

Refrigerator: the water that freezes decreases its own entropy, $\Delta S_\text{acqua} < 0$. But the machine absorbs electrical work and pours into the environment, through the condenser coil, the heat removed from the water PLUS the dissipated work. The environment thus gains more entropy than the water loses.

Living organism: the developing, self-organising embryo lowers its own internal entropy. To do so it consumes food (ordered, low-entropy molecules) and returns to the environment metabolic heat, $\mathrm{CO}_2$, water and disordered waste: it emits more entropy into the environment than it reduces within itself.

In both cases the overall balance respects the second law: $\ev{\Delta S_\text{universo} > 0}$ The order created locally (ice, organised tissue) is always paid for by a larger increase in disorder in the surrounding environment.

Collegamenti

Argomenti: Entropy and the second law Concetti: Entropy · Second law of thermodynamics · Refrigerator and heat pump Competenze: Micro–macro interpretation · Entropy balance Oggetti: Refrigerator