Summary
This article reviews modern theories of irreversible thermodynamics. It is known that the second law of thermodynamics is not a unique statement defined by precise rules. On the contrary, there are various versions of the second law and, likewise, also various degrees of generality to which these are exploited. All these laws express some notion of irreversibility and the implications drawn from them necessarily differ from each other. In this article we discuss these versions. They are motivated from the balance law of entropy. It is shown how the Clausius-Duhem theory, the entropy free thermodynamics of Meixner and the theory of Müller naturally follow from such a balance law. The approaches of irreversible thermodynamics and that of rational thermodynamics are compared using a simple heat conducting fluid. Müller's version of the second law, which appears to be the most general form of it, is discussed in detail. It is shown that whereever it has been applied already, its implications are farther reaching than other theories permit. Finally we discuss some criticism that has been raised against one or the other theory. — Physical arguments are emphasized and on the mathematical side the reader need only be familiar with basic calculus.
Zusammenfassung
In diesem Artikel werden die modernen Theorien der irreversiblen Thermodynamik dargestellt. Es ist wohlbekannt, daß der zweite Hauptsatz der Thermodynamik keine wohldefinierte Aussage ist. Im Gegenteil, es gibt verschiedene Versionen des zweiten Hauptsatzes und ebenso auch verschiedenen Grade der Allgemeinheit, wie diese Gesetze auszuschöpfen sind. All diese zweiten Hauptsätze beinhalten leicht abweichende Aussagen der Irreversibilität, und die Folgerungen, die man aus ihnen ziehen kann, sind nicht notwendigerweise identisch. In dieser Arbeit werden diese Versionen besprochen und aus dem Bilanzsatz der Entropie heraus motiviert. Es wird gezeigt, wie die Clausius-Duhem-Theorien, die entropiefreie Thermodynamik von Meixner und Day und die Theorie von Müller in natürlicher Weise aus dieser Bilanzaussage „abgeleitet” werden können. Es wird anhand einer einfachen wärmeleitenden Flüssigkeit verglichen, inwieweit sich die Methoden der irreversiblen Thermodynamik von jenen der rationalen Thermodynamik unterscheiden. Müller's Fassung des zweiten Hauptsatzes der Thermodynamik, die allgemeiner als alle anderen zu sein scheint, wird im Detail diskutiert. Es wird gezeigt, daß diese Theorie für alle bisher durchgerechneten Fälle auf weiterreichende Schlußfolgerungen führt, als dies bei allen anderen Formulierungen der Fall zu sein scheint. Schließlich wird auf Kritiken eingegangen, die von der einen oder anderen Seite gegen die verschiedenen Theorien erhoben wurden. — Physikalische Argumentationen stehen im Vordergrund, und mathematisch wird vom Leser nur Kenntnis der grundlegenden Analysis verlangt.
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This article is an extended version in the English language of the “Habilitationsvortrag” at the Technical University in Vienna, held to receive thevenia legendi in mechanics. I am grateful to Professor Heinz Parkus for his encouragement and his invitation to write this review article for Acta Mechanica. I further wish to thank him for making available to me an unpublished paper due to Day which has been used in the manuscript. Professor I. Müller has read and criticized and earlier version of this paper. His effor is gratefully acknowledged. Last but not least I wish to thank Professor D. Vischer, Director of the Laboratory of Hydraulics, Hydrology and Glaciology for his permission to work for the habilitation degree and for his approval that made this piece of work possible at the above mentioned establishment.
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Hutter, K. The foundations of thermodynamics, its basic postulates and implications. A review of modern thermodynamics. Acta Mechanica 27, 1–54 (1977). https://doi.org/10.1007/BF01180075
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DOI: https://doi.org/10.1007/BF01180075