Foundations of Thermodynamics

In Chapter 1 mathematical facts are dealt with exclusively. Now we are going to the physics of it. We may mention several important preliminaries, usually treated shabbily. We start to talk with the term energy and use the term system in this chapter without having it defined before. However, the term system is discussed soon afterward. Thus, we do not talk about the individual terms here in an axiomatic way. An axiomatic introduction into thermodynamics is, if it is possible at all, quite more difficult to understand. It is unnecessary to say that there are many impressive textbooks in thermodynamics [1-6]. 

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Gibbs, J.W. (1902) Elementary Principles in Statistical Mechanics, Developed with Special Reference to the Rational Foundations of Thermodynamics (Yale University Press, New Haven). 

Fig. 6.1), who helped to lay the foundations of thermodynamics, believed that work resulted from the flow of caloric, just as the flow of water turns a water wheel. Some of Carnot s conclusions survive, but we now know that there is no such substance as caloric. About 25 years after Carnot proposed his ideas in the early nineteenth century, the English physicist James Joule showed that both heat and work are forms of energy (Fig. 6.2). 

In contrast to mechanics, electromagnetic field theory, or relativity, where the names of Newton, Maxwell, and Einstein stand out uniquely, the foundations of thermodynamics originated from the thinking of over half a dozen individuals Carnot, Mayer, Joule, Helmholtz, Rankine, Kelvin, and Clausius [1]. Each person provided cmcial steps that led to the grand synthesis of the two classic laws of thermodynamics. 

MSN.62. I. Prigogine, Dynamic foundations of thermodynamics and statistical mechanics, in A Critical Review of Thermodynamics, E. B. Stuart, B. Gal-Or, and A. Brainard, eds., Mono Book Corp., Baltimore, 1970, pp. 1-18. 

In carrying out the procedure for determining mechanisms that is presented here, one obtains a set of independent chemical reactions among the terminal species in addition to the set of reaction mechanisms. This set of reactions furnishes a fundamental basis for determination of the components to be employed in Gibbs phase rule, which forms the foundation of thermodynamic equilibrium theory. This is possible because the specification of possible elementary steps to be employed in a system presents a unique a priori resolution of the number of components in the Gibbs sense. 

Except for some addenda of very recent date, the whole foundation of thermodynamics was laid before the middle of the nineteenth century. .. Next came the task of building up from these cardinal principles a great body of thermodynamic theorems. .. especially [by]... 

It is noteworthy that Gibbs himself was acutely aware of the qualitative failures of 19th-century molecular theory (as revealed, for example, by erroneous classical predictions of heat capacities Sidebar 3.8). In the preface to his Elementary Principles in Statistical Mechanics, Developed with Especial Reference to the Rational Foundation of Thermodynamics (published in the last year of his life), Gibbs wrote ... 

These four laws form the foundation of thermodynamics and have never been known to be violated. These laws govern the physical behaviors that we observe every day. These laws can also be seen as goals toward which we must strive in order to make our technological world more thermodynamically efficient and more sustainable for future generations. 

Gibbs, J.W. Elementary principles in statistical mechanics, developed with essential reference to the rational foundation of thermodynamics. N.Y. (1902). 

J. B. Serrin, Lectures at NSF-CBMS Regional Conference on Mathematical Foundations of Thermodynamics, July 1978, Ball State University. 

The power of thermodynamics lies in its generality It rests on no particnlar model of the structure of matter. In fact, if the entire atomic theory of matter were to be found invalid and discarded (a very unlikely event ), the foundations of thermodynamics would remain nnshaken. Nonetheless, thermodynamics has some important limitations. Thermodynamics asserts that snbstances have specific mea-snrable macroscopic properties, but it cannot explain why a particular substance has particular numerical values for these properties. Thermodynamics can determine whether a process is possible, but it cannot say how rapidly the process will occur. For example, thermodynamics predicts that diamond is an unstable substance at atmospheric pressure and will eventually become graphite, but cannot predict how long this process will take. 

Bradshaw, J. A., Historical Background and Foundations of Thermodynamics, in Thermodynamics, Vol. 5D, p. 1, AIChE Modular Instruction Series, American Institute of Chemical Engineers, New York, 1984. 

The notion of an on,scmble was first suggested by Gibbs in a remarkably insightful manner. In the preface of his book Elementary Principles in Statistical Mechanics Developed with Special Reference to the Rational Foundation of Thermodynamics Gibbs writes [29] ... 

The principles that form the foundation of thermodynamics are embodied in several laws referred to as the laws of thermodynamics. In addition, thermodynamic functions, which interrelate the various properties of a system, are derived on the basis of these laws. A system refers to a part of space under consideration through whose boundaries energy in its different forms, as well as mass, may be transferred. 

Tribus, Myron Evans, Robert B. The Probability Foundation of Thermodynamics, Applied Mechanics Reviews, October 1965 ... 

The foundations of thermodynamics rest on two laws. The first law of thermodynamics defines a function of state, the energy, and restricts the region of conceivable processes to those in which the energy is conserved. The second law determines the direction in which the possible processes will proceed in a given system. These laws represent the formalization of a large number of experimental observations. No violations of these laws have been observed, and it is clear, from microscopic statistical mechanical considerations, that the occurrence of such violations is so improbable that they may be considered to be impossible. 

Giles, R. Mathematical Foundations of Thermodynamics, International Series of Monographs on Pure and Applied Mathematics, vol. 53. Pergamon Press, Oxford (1964) Landsberg, P.T. Thermodynamics and Statistical Mechanics. Dover Pubhcations, New York (1990)... 

Owen, D.R. A First Course in the Mathematical Foundations of Thermodynamics. Undergraduate Texts in Mathematics. Springer-Verlag, New York (1984)... 

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