Kelvin’s principle

As defined by (4.19) or (4.21), it is easy to recognize that TK is an absolute (strictly non-negative) quantity. Furthermore, one can see from (4.19) that the highest possible efficiency ( —> 1) is achievable only at the absolute zero of the Kelvin scale (7"cK —> 0). In addition, the lowest efficiency of converting heat to work ( —> 0) occurs when the two reservoirs approach the same temperature (7j —> 7"cK), consistent with the statement of Kelvin s principle in Section 4.4. Such limits on engine efficiency can be used to paraphrase the three laws of thermodynamics in somewhat whimsical form as follows (the ultimate formulation of the no free lunch principle) ... 

We consider two equivalent physical expressions of the second law, one based on Kelvin s principle and the other a generalization of Clausius postulate. 

Titulaer, U.M., van Kampen, N.G. On the deduction of Caratheodory s axiom from Kelvin s principle. Physica31, 1029-1032 (1965)... 

Thomsen regarded the heat evolved in a reaction or the decrease of energy E as a measure of the affinity. The true position was first clearly stated by Lord Rayleigh, and is based on Lord Kelvin s principle of dissipation of energy, that only those changes occur spontaneously which involve the conversion of... 

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. 

THEORETICAL LIMITS ON PERPETUAL MOTION KELVIN S AND CLAUSIUS PRINCIPLES... 

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. 

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. 

The main purpose of this book is to present a rigorous and logical discussion of the fundamentals of thermodynamics and to develop in a coherent fashion the application of the basic principles to a number of systems of interest to chemists. The concept of temperature is carefully discussed, and special emphasis is placed on the appropriate method for the introduction of molecular weights into thermodynamics. A new treatment of the second law of thermodynamics is presented which demonstrates that Caratheodory s principle is a necessary and sufficient consequence of the physical statements of Clausius and Kelvin. 

Assuming that H(Y X) < 0 [information variant of Kelvin s formulation of the 11. Principle of Thermodynamics for irreversible cyclical transfer O when the respective relation (34) is valid], we also have the information variant of the second part of Carnot s theorem... 

There can be little doubt that at the root of Kelvin s objections to Joule s theory lay his conviction that the whole science of heat rested on what since 1783 had been the basic axiom of conservation. If that were rejected what would happen to the impressive structure of experimental knowledge and theoretical development that had been built up by the labours of men like Delaroche and Berard, Fourier, Dulong and Petit, Poisson, Victor Regnault and many others Thus he quoted Carnot as saying, of the axiom of conservation, that To deny it would be to overturn the whole theory of heat, in which it is the fimdamental principle. And he himself adds the comment that if the axiom of conservation is rejected . .. we meet with innumerable other difficulties - insuperable without further experimental investigation, and an entire reconstruction of the theory of heat from its foundation. " (Cardwell, p.244)... 

What kind of solution was expected from physicists As we have seen, many chemists, from Lavoisier on, expected that fundamental chemical problems would be accessible to mathematical solution, meaning not just precise quantification or geometrical explanation but algebraic formulation on mechanical principles. 32 For all the resentment of statements by Kelvin or Boltzmann that chemistry could be reduced to vortex atoms or the kinetics of atoms,33 many nineteenth-century chemists shared Kekule s vague presentiment... 

The most important modem system of units is the SI system, which is based around seven primary units time (second, abbreviated s), length (meter, m), temperature (Kelvin, K), mass (kilogram, kg), amount of substance (mole, mol), current (Amperes, A) and luminous intensity (candela, cd). The candela is mainly important for characterizing radiation sources such as light bulbs. Physical artifacts such as the platinum-iridium bar mentioned above no longer define most of the primary units. Instead, most of the definitions rely on fundamental physical properties, which are more readily reproduced. For example, the second is defined in terms of the frequency of microwave radiation that causes atoms of the isotope cesium-133 to absorb energy. This frequency is defined to be 9,192,631,770 cycles per second (Hertz) —in other words, an instrument which counts 9,192,631,770 cycles of this wave will have measured exactly one second. Commercially available cesium clocks use this principle, and are accurate to a few parts in 1014. 

In other words, you make an observation, develop a hypothesis, and perform experiments. The observations and results from the experimental procedure allow the scientist to review the hypothesis and plan new experiments. The interpretations of the results from many experiments can classify the observation as a theory or law. A law explains what happens. For example, Charles s Law (see Lesson 7) explains that temperature and volume, at constant pressure, are proportional. If the Kelvin temperature of a gas doubles, then its volume doubles correspondingly. A law is a statement based on many experiments that produced the same result and conclusion. A principle would explain a more specific set of relationships of a law. 

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