Second Law of Thermodynamics
The second law of thermodynamics states that the total entropy of an isolated system never decreases over time, remaining constant only for idealised reversible processes. Equivalent classical forms are the Clausius statement (heat cannot spontaneously flow from a colder to a hotter body) and the Kelvin–Planck statement (no cyclic process can convert heat from a single reservoir entirely into work), which together limit every heat engine to at most the Carnot efficiency 1 − Tc/Th.
Curious
A hot cup of tea cools to room temperature; it never spontaneously gets hotter by drawing heat from the cooler air, even though that would not violate energy conservation. The second law is the rule that picks out which direction things go. Its measure is entropy, roughly the amount of spread-out, disordered energy, and in an isolated system it only increases.
One practical consequence: every engine that turns heat into work, from a car engine to a power station, must dump some heat into a cooler surrounding. A refrigerator can move heat from cold to hot, but only by using work, so the total entropy still rises.
Exploring
| Statement | Originator | Forbids |
|---|---|---|
| Clausius statement (1850, 1854) | Rudolf Clausius | Spontaneous heat flow from cold to hot |
| Kelvin–Planck statement (1851) | William Thomson (Lord Kelvin), Max Planck | A cyclic engine converting all heat into work |
| Entropy statement (1865) | Clausius | Decrease of total entropy of an isolated system |
| Carnot theorem (1824) | Sadi Carnot | Any engine more efficient than a reversible one |
Deep Dive
Formal statement. For any process, dS ≥ δQ/T (the Clausius inequality), with equality only for reversible processes; for an isolated system δQ = 0, so dS ≥ 0. Carnot's 1824 analysis of reversible engines, reinterpreted by Clausius and Kelvin, shows that all reversible engines between the same two reservoirs have the same efficiency, which lets Kelvin define an absolute thermodynamic temperature scale independent of any material (see Temperature).
Statistical meaning. Boltzmann showed that entropy measures the number of microscopic arrangements W compatible with a macroscopic state, S = kB ln W (see Ludwig Boltzmann). The second law then becomes overwhelmingly probable rather than absolutely certain: for macroscopic systems, entropy-decreasing fluctuations are so improbable as never to be observed, while for very small systems they are measurable, as quantified by fluctuation theorems confirmed experimentally since the early 2000s.
Open questions. Why entropy was so low in the early universe, which gives time its arrow, is not explained by the second law itself and is a question in cosmology and philosophy of physics (see History, Philosophy & Foundations). Maxwell's demon, a thought experiment that seemed to violate the law, was resolved by recognising that erasing information carries an entropy cost (Landauer's principle, at least kBT ln 2 per bit), confirmed experimentally in 2012.
Concept Relationship Map
Requires: first law, temperature
Enables: entropy, Carnot cycle, third law
Commonly confused with: a ban on any local increase in order
Sources
- Carnot, S. (1824). Réflexions sur la puissance motrice du feu. Paris: Bachelier.
- Clausius, R. (1850). Annalen der Physik, 79, 368–397, 500–524.
- Thomson, W. (1851). “On the Dynamical Theory of Heat.” Transactions of the Royal Society of Edinburgh, 20, 261–288.
- Bérut, A., et al. (2012). “Experimental verification of Landauer's principle linking information and thermodynamics.” Nature, 483, 187–189.