# Carnot's theorem (thermodynamics)

**Carnot's theorem**, also called "Carnot's rule" is a principle which sets a limit on the maximum amount of efficiency any possible engine can obtain, which thus solely depends on the difference between the hot and cold temperature reservoirs. Carnot's theorem states:cquote|No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs.The rule was an essential stepping stone towards the formulation of the

second law of thermodynamics . When transformingthermal energy intomechanical energy , the thermal efficiency of aheat engine is the percentage of energy that is transformed into work. Thermal efficiency is defined as:$eta\_\{th\}\; equiv\; frac\{W\_\{out\{Q\_\{in$,

requires $Q\_H\; =\; Q\_C\; +\; W,!$Thesecond law of thermodynamics requires $frac\{Q\_H\}\{T\_H\}\; =\; frac\{Q\_C\}\{T\_C\}$Thethird law of thermodynamics requires the use of anabsolute temperature scale. Together they imply a maximum heat-to-work efficiency of: $eta\; equiv\; frac\{W\_\{out\{Q\_\{in\; =\; frac\{Delta\; T\}\; \{T\_H\}$] Carnot showed that the maximum efficiency possible by any sort of engine has a limit defined by the following efficiency $eta$::$eta=frac\{W\}\{Q\_H\}=frac\{T\_H\}\{T\_H\}-frac\{T\_C\}\{T\_H\}\; =\; frac\{Delta\; T\}\; \{T\_H\}$where:

: $W$ is the work done by the system (energy exiting the system as work),: $Q\_H$ is the heat put into the system (heat energy entering the system),: $T\_C$ is the

absolute temperature of the cold reservoir, and : $T\_H$ is the absolute temperature of the hot reservoir.Carnot's theorem sets essential limitations on the yield of a cyclic heat engine such as

steam engine s orinternal combustion engine s, which operate on theCarnot Cycle . They can extract only a certain proportion of mechanical energy from the heat of the working fluid, and this maximal amount is realized by the idealCarnot heat engine .

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**carnot's theorem**— noun or carnot s principle Usage: usually capitalized C Etymology: translation of French principe de Carnot, after N.L.S. Carnot, its formulator : a principle in thermodynamics: an engine working in a reversible cycle is at least as efficient as… … Useful english dictionary**Carnot**— is the name of a celebrated French family in politics and science with the following members:*Lazare Nicolas Marguerite Carnot (1753 1823), mathematician and politician. *Nicolas Léonard Sadi Carnot (1796 1832), mathematician and eldest son of… … Wikipedia**Thermodynamics**— Annotated color version of the original 1824 Carnot heat engine showing the hot body (boiler), working body (system, steam), and cold body (water), the letters labeled according to the stopping points in Carnot cycle … Wikipedia**Carnot cycle**— The Carnot cycle is a particular thermodynamic cycle, modeled on the hypothetical Carnot heat engine, proposed by Nicolas Léonard Sadi Carnot in 1824 and expanded upon by Benoit Paul Émile Clapeyron in the 1830s and 40s. Every thermodynamic… … Wikipedia**Non-equilibrium thermodynamics**— Thermodynamics … Wikipedia**Clausius theorem**— Thermodynamics … Wikipedia**Endoreversible thermodynamics**— Thermodynamics … Wikipedia**Third law of thermodynamics**— Thermodynamics … Wikipedia**Material properties (thermodynamics)**— Thermodynamics … Wikipedia**Nicolas Léonard Sadi Carnot**— For the 1887–1894 president of France and nephew of Nicolas Léonard, see Marie François Sadi Carnot. Sadi Carnot Nicolas Léonard Sadi Carnot (1796 1832) in the dress uniform of a student of the École Polytechnique … Wikipedia