Heat Engines and the Caloric Theory of Heat

  • Hans U. Fuchs


This chapter will present an alternative route to the thermodynamics of simple fluids at a slightly higher mathematical level, allowing for a generalization of the subject of thermodynamics of uniform fluids. The most important difference to the previous development has to do with what we assume to know about the nature of heat. By introducing the law of balance of heat, and the relation between currents of heat and energy in heating (Equation (13) of Chapter 1), we have directly identified heat with entropy, and have made the relation between entropy and energy the cornerstone of our development. This approach has afforded us a great simplification which is important in an introductory course on the foundations of thermodynamics. Still, it somewhat oversimplifies the matter in that it assumes too much about the nature of heat at the start, and it leaves open the question as to the historical development of the subject. In this chapter, we will therefore not assume any knowledge of the relation between heat and energy. Rather, we will start with what is known as Carnot’s Axiom (an assumption about the power of heat in ideal engines), and with a statement about the existence of a heat function. On this basis we will be able to derive the relation between heat and energy.


Heat Capacity Latent Heat Heat Function Heat Engine Mechanical Theory 
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    S. Carnot (1824): Reflections on the Motive Power of Fire. Google Scholar
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    In his work, The Tragicomical History of Thermodynamics,C. Truesdell gave a detailed and critical account of the historical development of thermodynamics (Truesdell, 1980). He and Bharatha worked out the logical foundations of classical thermodynamics (The Concepts and Logic of Classical Thermodynamics,1977), where the nature of heat is left to be determined almost up to the end. Following their reasoning, you can see what is needed to make heat a quantity of energy. If you take a slightly different approach, however, heat turns out to be entropy. This line of reasoning was demonstrated in a paper by Callendar (1911).Google Scholar
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    See Truesdell (1979) for a discussion of this matter.Google Scholar
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    That heat can be transferred is the fundamental assumption underlying both the caloric and the mechanical theories of heat. The caloric theory, however, also assumes the existence of a heat function. We may interpret this graphically as meaning that heat also resides in bodies. Therefore, in the context of the caloric theory, we are justified in speaking of a quantity of heat for which a law of balance must hold. Researchers in Carnot’s time never expressed their assumption in this way.Google Scholar
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    Since our assumptions will lead to the identification of caloric with entropy, we shall use the symbol S for heat.Google Scholar
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    The problem is not quite so simple, however. For example, for a given empirical scale, F(T) is independent of the particular fluid used. We cannot be sure, however, that we get the same function F for other scales as well. Then, the axioms and equations should be independent of the particular scale used; they should be invariant under transformation from one scale to another. (This imposes some restrictions on what kind of fluids can be used for thermometry: water is unsuitable.) Finally, Carnot’s function may not vanish; otherwise, the absolute scale chosen above does not make any sense.Google Scholar
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    Note that we do not include in the general properties of caloric its conservation or nonconservation. Historically, however, caloric was assumed to be a conserved quantity.Google Scholar
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    Using the symbol dH/dt for the heating leaves room for misunderstandings. Is it the rate of flow of heat across the surface of the body, or is it the rate of change of the heat content? In the mechanical theory of heat, there is no “heat content.” There, heating may mean only the rate of flow of heat. In the caloric theory of heat, on the other hand, there is a heat content, but heat might not be conserved.Google Scholar
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    C. Truesdell (1980), Chapter 8.Google Scholar
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    S. Carnot: quoted from C. Truesdell (1980), p. 81.Google Scholar
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    R. Clausius: quoted from C. Truesdell (1980), p. 187.Google Scholar
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    Indeed, it is wrong in the mechanical theory of heat, since there heat may not be thought of as residing in bodies. Clausius’ results contradict the very prejudice they were built upon.Google Scholar
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    See Stacey(1992), p. 305 and appendixes therein.Google Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Hans U. Fuchs
    • 1
  1. 1.Department of PhysicsTechnikum WinterthurWinterthurSwitzerland

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