Carnot’s principle

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. 

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

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... 

According to Thomson s principle, no machine can convert heat to useful work unless some of that heat is transferred to a colder reservoir. This implies that no quantity of heat can be converted to work at a single temperature. It also implies that heat is a less useful form of energy, because some of it must always be thrown away by transfer to a lower temperature. Because the falsity of Carnot s principle would imply easy violations of Thomson s principle (which are never observed), we conclude that Carnot s principle must be valid. 

Still another contradiction with experience can be deduced from the assumed existence of any C device that falsifies Carnot s principle. Let us again suppose that the old Carnot cycle is operated as a heat pump C, now coupled to the improved C device through the work (w = w ), as follows ... 

Again we conclude that Carnot s principle must be true, because devices that contradict the principle of Clausius are never observed. 

Kelvin first suggested how the Carnot efficiency (4.9) might be used to define an absolute temperature scale. As Carnot s principle asserts, the efficiency... 

Carnot s principle in Kelvin form (4.19) makes clear that the usefulness of a certain quantity of heat energy q depends on its temperature. Thus, a quantity of high-7" heat intrinsically carries greater work capacity than the equivalent quantity of low-7" heat. Even if the first law tells us that a quantity of heat q and work w are energetically equivalent, the second law restricts what fraction can actually be extracted from q as useful work, depending on its temperature. 

Following Le Chatelier s principle (or Carnot s principle), the global heat demand of the section decreases when the maximal loop temperature increases. However, no sensible decrease is pointed out above 840°C. Thus, increasing the maximal temperature in the cycle is not useful beyond ca. 840°C. Two antagonist phenomena can explain the levelling off ... 

Jaynes, E. T., The evolution of Carnot s Principle. In G. J. Erickson and C. R. Smith (eds.), Maximum-Entropy and Bayesian Methods in Science and Engineering, volume 1. Dordrecht Kluwer (1988). 

Sadi Carnot s principle. Generalization of this principle by Clausius.— In 1824 di Carnot published a short work on the mechanical effects of heat depending on the one hand upon the impossibility of perpetual motion, on the other hand upon the principle, then accepted without question, that aroimd a closed cycle a i stem undergoes losses and absorptions of heat which exactly compensate each other, he demonstrated a theorem of the greatest importance both for the theory of heat and for the applications of this science to heat-engines. 

According to Meyerson, Carnot s principle concerning the irreversibility of time is factually true but irrational in that rational science follows the principle of causality that pre-supposes reversibility and the identity of antecedent and consequent science thus tends to the elimination of time. Carnot s principle asserts reality as it resists, from without, our scientific attempts at rationalizing it (cf. Meyerson 1930, 278, 286, 317). According to Meyerson, Carnot s principle signifies a limit of science. 

Jaynes, E. T., 1988, The evolution of Carnot s principle, in Maximum Entropy and... 

Carnot cycle The idealized reversible cycle of four operations occurring in a perfect heat engine. These are the successive adiabatic compression, isothermal expansion, adiabatic expansion, and isothermal compression of the working substance. The cycle returns to its initial pressure, volume, and temperature, and transfers energy to or from mechanical work. The efficiency of the Carnot cycle is the maximum attainable in a heat engine. It was published in 1824 by the French physicist Nicolas L. S. Carnot (1796-1832). See Carnot s principle. 

Carnot s principle (Carnot theorem) The efficiency of any heat engine cannot be greater than that of a reversible heat engine operating over the same temperature range. Carnot s principle follows directly from the second law of thermodynamics, and means that all reversible heat engines have the same efficiency, independent of... 

Rudolf Julius Emanuel Clausius (1822-1888), a German physicist and mathematician, was one of the founders of thermodynamics. By his restatement of Carnot s principle, he put the theory of heat on a sounder basis. His most important paper On the mechanical theory of heat (1850) first stated the ideas of the second law of thermodynamics. In 1865, he introduced the concept of entropy. He also contributed to the kinetic theory of gases by including translational, rotational, and vibrational molecular motions, and introduced the mean free path of a particle. Clausius deduced the Clausius-Cla-peyron relation - see Eq. (3.1.45) below - based on thermodynamic considerations. This law on phase transition had originally been developed in 1834 by Emile Clapeyron. 

Benoit Paul Emile Clapeyron (1799-1864) A French engineer and physicist and one of the founders of thermodynamics. In 1843, Clapeyron further developed the idea of a reversible process, already suggested by Carnot, and made a definitive statement of Carnot s principle, which is now known as the second law of thermodynamics. Clapeyron also worked on the characterization of perfect gases, the calculation of the statics of continuous beams, and on phase transitions, Eq. (3.1.45). 

Jaynes, E. T. Evolution of Carnot s Principle. Reprinted in Ericksen Smith. 1988, 1, 267-282. 

H. L. Callendar The Caloric Theory of Heat and Carnot s Principle Proc. Phys. Soc. of London, 23(1911)153... 

When Gibbs first turned his attention to thermodynamics in the early 1870 s, the subject had already achieved a certain level of maturity. The essential step had been taken in 1850 by Rudolf Clausius, when he argued that two laws are needed to reconcile Carnot s principle about the motive power of heat with the law of energy transformation and conservation. Efforts to understand the second of the two laws finally led Clausius in 1865 to his most concise and ultimately most fruitful analytical formulation. In effect, two basic quantities, internal energy and entropy, are defined by the two laws of thermodynamics. The internal energy U is that function of the state of the system whose differential is given by the equation expressing the first law,... 

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