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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Carnot's theorem (thermodynamics) ： ウィキペディア英語版 Carnot's theorem (thermodynamics) Carnot's theorem, developed in 1824 by Nicolas Léonard Sadi Carnot, also called Carnot's rule, is a principle that specifies limits on the maximum efficiency any heat engine can obtain, which thus solely depends on the difference between the hot and cold temperature reservoirs. Carnot's theorem states: *All heat engines between two heat reservoirs are less efficient than a Carnot heat engine operating between the same reservoirs. *Every Carnot heat engine between a pair of heat reservoirs is equally efficient, regardless of the working substance employed or the operation details. The formula for this maximum efficiency is :$\backslash eta\_\}\; =\; 1\; -\; \backslash frac$ where ''TC'' is the absolute temperature of the cold reservoir, ''TH'' is the absolute temperature of the hot reservoir, and the efficiency $\backslash eta$ is the ratio of the work done by the engine to the heat drawn out of the hot reservoir. Based on modern thermodynamics, Carnot's theorem is a result of the second law of thermodynamics. Historically, however, it was based on contemporary caloric theory and preceded the establishment of the second law.〔 〕 ==Proof== The proof of the Carnot theorem is a proof by contradiction, or reductio ad absurdum, as illustrated by the figure showing two heat engines operating between two reservoirs of different temperature. The heat engine with more efficiency ($\backslash eta\_M$) is driving a heat engine with less efficiency ($\backslash eta\_L$), causing the latter to act as a heat pump. This pair of engines receives no outside energy, and operates solely on the energy released when heat is transferred from the hot and into the cold reservoir. However, if $\backslash eta\_M>\backslash eta\_L$, then the net heat flow would be backwards, i.e., into the hot reservoir: :. It is generally agreed that this is impossible because it violates the second law of thermodynamics. We begin by verifying the values of work and heat flow depicted in the figure. First, we must point out an important caveat: the engine with less efficiency ($\backslash eta\_L$) is being driven as a heat pump, and therefore must be a ''reversible'' engine. If the less efficient engine ($\backslash eta\_L$) is not reversible, then the device could be built, but the expressions for work and heat flow shown in the figure would not be valid. By restricting our discussion to cases where engine ($\backslash eta\_L$) has less efficiency than engine ($\backslash eta\_M$), we are able to simplify notation by adopting the convention that all symbols, $Q$ and $W$ represent non-negative quantities (since the direction of energy flow never changes sign in all cases where $\backslash eta\_L\backslash leqslant\backslash eta\_M$). Conservation of energy demands that for each engine, the energy which enters, $E\_$, must equal the energy which exits, $E\_$: :$E\_^\; =\; Q\; =\; (1-\backslash eta\_M)Q\; +\; \backslash eta\_M\; Q\; =\; E\_^$, :$E\_^\; =\; \backslash eta\_M\; Q\; +\; \backslash eta\_M\; Q\; \backslash left(\backslash fracQ\; =\; E\_^$, The figure is also consistent with the definition of efficiency as $\backslash eta=W/Q\_h$ for both engines: :$\backslash eta\_M=\; \backslash frac=\backslash frac=\backslash eta\_M$, :$\backslash eta\_L=\backslash frac=\backslash fracQ\}=\backslash eta\_L$. It may seem odd that a hypothetical heat pump with low efficiency is being used to violate the second law of thermodynamics, but the figure of merit for refrigerator units is not efficiency, $W/Q\_h$, but the coefficient of performance (COP), which is $Q\_c/W$. A reversible heat engine with low thermodynamic efficiency, $W/Q\_h$ delivers more heat to the hot reservoir for a given amount of work when it is being driven as a heat pump. Having established that the heat flow values shown in the figure are correct, Carnot's theorem may be proven for irreversible and the reversible heat engines.〔(【引用サイトリンク】title=Lecture 10: Carnot theorem )〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Carnot's theorem (thermodynamics)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.