Carnot principle

Carnot principle States that no engine can be more efficient than a reversible engine when both operate between the same temperature limits. 

A third version of the Second Law, called the Carnot principle after the French engineer, Sadi Carnot, also deals with engine performance. It states that ... 

The Clausius and Kelvin-Planck statements and the Carnot principle reflect a historical interest in increasing the efficiency of engines. While the... 

Discussions on how to increase the hydrogen generation efficiency therefore often focus on how to maximise the temperature that can be used by the process, whether by maximising the HTR outlet helium temperature or by reducing pinches in heat exchangers. On the lower end of the secondary helium temperature spectrum, the importance of the helium return temperature is often overlooked. However, as a component of the average heat source temperature, it must, according to the Carnot principle, have an influence on the efficiency. 

Since Qi is equal to Q2 — TF, and Q[ is equal to Q2 — TF it follows that Qi — Q is equal to W — W, so that the heat absorbed at Ti is equal to the work done by the engine. That is to say, the combmed hypothetical, reversible machine, functioning in cycles, is able to convert completely into work the whole oif the heat taken up from a reservoir at the temperature T1, without leaving changes elsewhere. This is contrary to the second law of thermodynamics, and so it must be concluded that the two reversible mar chines I and II cannot have different efficiencies. The Carnot principle... 

Carnot principle, a fraction Tf, — Tg)/Ti, of the total amount of heat supplied. For the amount of heat Qh supplied, the corresponding amount of work available is Qh [(7h—7o)/7h]- If the amount of heat rejected by the separation device is Qi at temperature T(, then the amount of work one could get out of this heat, from the Carnot principle, is Qe [ Te — To)/Te, where Tg is the lowest temperature heat sink (Figure 10.1.3). Therefore the highest amount of work one can get out from an amount of heat Qi, supplied to the separation device at Ti, and an amount of heat Q< rejected by the separation device at T( is as follows ... 

Carnot cycle A thermodynamic cycle used in a heat engine and comprises four distinct steps isothermal expansion, adiabatic expansion, isothermal compression, and then adiabatic compression (see Fig. 11). According to the Carnot principle, the efficiency of a heat... 

The industrial economy depends heavily on electrochemical processes. Electrochemical systems have inherent advantages such as ambient temperature operation, easily controlled reaction rates, and minimal environmental impact (qv). Electrosynthesis is used in a number of commercial processes. Batteries and fuel cells, used for the interconversion and storage of energy, are not limited by the Carnot efficiency of thermal devices. Corrosion, another electrochemical process, is estimated to cost hundreds of millions of dollars aimuaUy in the United States alone (see Corrosion and CORROSION control). Electrochemical systems can be described using the fundamental principles of thermodynamics, kinetics, and transport phenomena. 

The second law as it left the hands of Carnot required no explanation. On the caloric theory then prevalent, it was a necessary consequence of a hydrodynamical analogy—the mechanical explanation was in fact, as Carnot s words show, the source of the principle. When the caloric theory was thrown down, the analogy and explanation fell with it, and the reconstruction of Carnot s principle by Clausius and Kelvin resulted in a law of experience. 

This conclusion was arrived at, from considerations based on Carnot s principle alone, by James Thomson in 1849. He also calculated the magnitude of the effect, in the case of ice, by means of a cyclic process. Since the reasoning is the same for both cases, we shall deal with both together, giving appropriate diagrams. 

To summarize, the Carnot cycle or the Caratheodory principle leads to an integrating denominator that converts the inexact differential 8qrev into an exact differential. This integrating denominator can assume an infinite number of forms, one of which is the thermodynamic (Kelvin) temperature T that is equal to the ideal gas (absolute) temperature. The result is... 

France was a center for the development of thermodynamics, the study of heat and its conversion to other forms of energy. A few years before Ril-lieux s arrival in Paris, the French physicist Sadi Carnot had published his studies of steam engines and described the principles that became the second law of thermodynamics, placing fundamental limits on how efficiently heat can be used. Within a few years, James Prescott Joule of England would lay the basis for the first law of thermodynamics stating the equivalence of heat and energy. 

One hundred fifty years ago, the two classic laws of thermodynamics were formulated independently by Kelvin and by Clausius, essentially by making the Carnot theorem and the Joule-Mayer-Helmholtz principle of conservation of energy concordant with each other. At first the physicists of the middle 1800s focused primarily on heat engines, in part because of the pressing need for efficient sources of power. At that time, chemists, who are rarely at ease with the calculus, shied away from... 

A principle stating that for any engine working between the same two temperatures, maximum efficiency will occur by a engine working reversibly between those same two temperatures. Thus, all reversible engines have the same efficiency between the same temperatures and that efficiency is dependent only on those temperatures and not on the nature of the substance being acted upon. See Efficiency Thermodynamics, Laws of Carnot Cycle... 

Sadi Carnot (full name Nicolas Leonard Sadi Carnot, Sadi after a Persian poet) was bom into one of the most emdite and influential families of the turbulent Napoleonic period. Sadi s father, Lazare Carnot, was a leading scientist and mathematician of his time, as well as a noted military commander who achieved high ministerial office under Napoleon. The father s profound intellectual influence on Sadi is apparent from parallels between Lazare s 1803 treatise, Fundamental Principles of Equilibrium and Movement, and Sadi s famous 1824 monograph, Reflections on the Motive Power of Fire (Reflexions sur la puissance motrice du feu), which applied similarly general and abstract analysis to purely mechanical and thermomechanical devices, respectively. Among other accomplishments of this remarkable family, Sadi s younger brother, Hippolyte, became a noted writer and statesman, and the latter s eldest son, Marie Francois Sadi Carnot, later became a president of the Third Republic. 

Clausius great paper of 1850 can be recognized as a landmark in the development of thermodynamics. As remarked by Thomson in 1851, the merit of first establishing [Carnot s theorem] upon correct principles is entirely due to Clausius. In his 1889 eulogy of Clausius, Gibbs praised the 1850 paper in the following terms ... 

Carnot s principle can be summarized as an inequality that limits the possible efficiency reai of any real engine ... 

The simple inequality (4.10) captures the essence of the second law. Its general consistency with universal inductive experience will be established in Section 4.4, and its further consequences (culminating in the final form of the second law as expressed by Clausius) will be developed in Sections 4.5-4.7. Thus, Carnot s remarkable principle provides virtually complete answers to the questions posed at the beginning of this chapter, although the relationship of (4.10) to these broader issues will certainly not become obvious until the following section. 

To explore the rich consequences of Carnot s principle (4.10), let us begin by adopting the following alternative schematic representation of a Carnot cycle C ... 

Carnot s principle (4.10) may not seem particularly compelling from experience. However, we can easily derive some consequences from (4.10) that are indeed more obvious statements about the irreversibility of natural events, and hence provide compelling inductive proof of the truth of Carnot s principle. These derivative principles were first obtained by Thomson (Kelvin) and Clausius. 

The derivations presented below illustrate the logical technique of proof by contradiction. In this method of proof, we begin by assuming that Carnot s principle is untrue, then demonstrate that we could easily produce crazy consequences that contradict experience if this assumption were valid. That is, we conclude that Carnot s principle must be true, because the contrary assumption leads to inconsistencies with inductive experience. 

Let us therefore begin by assuming that Carnot s principle is false, i.e., that there exists some new and improved model C whose efficiency exceeds that of the reversible Carnot cycle. The hypothetical C engine can be represented as... 

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