The consequences of the second law

Behind the dry notation $\Delta S_\text{tot} \geq 0$ lies a list of everyday facts that the first law, on its own, could never explain. These are all transformations that energy would allow to be reversed, but that entropy forbids.

• Heat flows spontaneously from hot to cold, never the other way round. A cold teaspoon dipped in tea warms up; no teaspoon ever cools down by itself while giving up heat to an already-hot tea.
• The free expansion of a gas into a vacuum never spontaneously reverses. The molecules, once spread throughout the container, never gather back into one half of it by themselves.
• Two bodies at different temperatures move towards thermal equilibrium, never separating on their own into a hot part and a cold part.

In all three cases energy would still be conserved in the reverse process: a tea that warms an already-hot teaspoon, a gas that compresses itself, two lukewarm bodies that split into hot and cold would not violate the first law. What makes them impossible is that they would decrease the entropy of the universe, and this the second law forbids.

Principle — Possible vs probable

The first law says what is possible (in terms of energy). The second law says what is probable (which direction things go in).

This pair of sentences is the most compact way to remember the division of labour between the two laws. The first law is a constraint of balance: energy is neither created nor destroyed. The second is a constraint of direction: among all the transformations that the energy balance allows, only those that lead towards more probable macrostates — that is, with more microstates — actually occur. The irreversibility of the macroscopic world is nothing but the statistical expression of this simple fact: there are incomparably more ways of being “mixed” than of being “separated”.

Collegamenti

Argomenti: Entropy and the second law Concetti: Second law of thermodynamics · Entropy Competenze: Micro–macro interpretation

Esercizi collegati: Worked exercise — the coffee cools down · Hot shower: ΔS of the universe · Heat from hot to cold: proof