§ DICTIONARY · CONCEPT

Kelvin–Planck statement

No cyclic engine can turn heat from a single reservoir entirely into work with no other effect.

§ 01

Definition

The KelvinPlanck statement of the second law asserts that no process is possible whose sole result is the complete conversion of heat drawn from a single reservoir into work. Every heat engine must reject some heat to a colder reservoir; a perfectly efficient engine is impossible.

This is why a heat engine needs two reservoirs, not one. An engine that ran by cooling the ocean alone would conserve energy perfectly yet still be impossible — it would be a perpetual-motion machine of the second kind. The cold sink is mandatory.

The statement is equivalent to the Clausius statement and to the Clausius inequality; the three are interchangeable expressions of the second law, each easiest to apply in a different setting.

§ 02

History

William Thomson (Lord Kelvin) gave the original form in 1851; Max Planck sharpened it into its modern wording in the 1880s and 1890s, which is why the combined name has stuck.