Thermal physics

The second law of thermodynamics

The second law sets the direction of natural processes: total entropy does not decrease in an isolated system, even though energy is conserved.

The first law gives an energy balance but not which processes occur spontaneously. The second law adds an arrow of time: heat flows spontaneously from hot to cold; the reverse requires external intervention.

System and surroundings

The system's entropy alone may decrease if it releases heat; the second law applies to the system plus its surroundings. A reversible process keeps total entropy constant; an irreversible process produces positive entropy.

Quick check

A useful way to see entropy's role is to let two bodies at different temperatures exchange a small amount of heat $delta Q$. The hot body loses heat and changes entropy by about $-delta Q/T_h$; the cooler body gains it and changes entropy by $+delta Q/T_c$. Since $T_c<T_h$, their total entropy change is positive: spontaneous heat transfer increases the entropy of the isolated pair. To move heat in the reverse direction, a refrigerator must receive work from outside; energy is not violated, but the surroundings' entropy also changes. A reversible process leaves total entropy unchanged, while real friction, diffusion, and heat transfer across a finite temperature difference generate entropy. The second law therefore does not say that energy disappears. It explains why no cyclic engine can convert all heat taken from a single reservoir into work.

A system can decrease its entropy if it releases heat or is cooled, provided the surroundings gain more entropy. When two reservoirs at the same temperature exchange heat reversibly, total entropy stays constant; a finite temperature difference makes total entropy increase. To determine the spontaneous direction, include both system and surroundings.