New Perspectives in Thermodynamics

Paperback (Softcover reprint of the original 1st ed. 1986)
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Product Details

  • ISBN-13: 9783540159315
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 5/22/1986
  • Edition description: Softcover reprint of the original 1st ed. 1986
  • Edition number: 1
  • Pages: 262
  • Product dimensions: 6.69 (w) x 9.61 (h) x 0.59 (d)

Table of Contents

I Foundations of Thermodynamics.- 1. An Outline of Thermodynamical Structure.- 1.1 Introduction.- 1.2 Classical Thermal Structure.- 1.3 The Formal Structure of Thermodynamics.- 1.4 The First Law.- 1.5 The Second Law.- 1.6 State Structure and Potentials.- 1.7 Reversible Processes.- 1.8 Special Systems.- 1.9 Concluding Remarks.- References.- 2. Foundations of Continuum Thermodynamics.- 2.1 Introduction.- 2.2 Work, Heat, and Empirical Temperature.- 2.3 The First Law of Thermodynamics.- 2.4 The Second Law of Thermodynamics.- References.- 3. Foundations of the Clausius-Duhem Inequality.- 3.1 Introduction.- 3.2 Thermodynamical Theories.- 3.3 The Existence of Specific Entropy Functions and Thermodynamic Temperature Scales.- 3.4 Properties of the Set of Clausius-Duhem Temperatures Scales.- 3.5 Properties of the Set of Specific Entropy Functions.- 3.6 Concluding Remark.- References.- 4. Recent Research on the Foundations of Thermodynamics.- References.- 5. A Third Line of Argument in Thermodynamics.- List of Sources.- 6. The Laws of Thermodynamics for Non-Cyclic Processes.- 6.1 Basic Definitions.- 6.2 The First Law and Energy.- 6.3 The Second Law and Entropy.- 6.4 Deterministic State Structures.- References.- II The Thermodynamics of Gibbs and Carathéodory.- What Did Gibbs and Carathéodory Leave Us About Thermodynamics?.- Apology.- 7.1 The Words.- 7.2 Statics and Dynamics: the Catenary.- 7.3 The Thermostatics of Gibbs.- 7.4 Gibbs on Thermodynamics.- 7.5 The Thermodynamics of Planck.- 7.6 Gibbs’s Rational Foundations of Thermodynamics: Gibbsian Statistical Mechanics.- 7.7 Bryan’s Rational Thermodynamics.- 7.8 Carathéodory’s Axioms.- 7.9 Carathéodory’s Legacy.- 7.10 Colophon.- 8. Structure and Dynamical Stability of Gibbsian States.- 8.1 Introduction.- 8.2 Preliminaries and Motivation.- 8.3 Gibbsian States: Necessary Conditions and Comparison Principles.- 8.4 Gibbsian States: Sufficient Conditions and Structure.- 8.5 Equivalent Problems of Thermostatics.- 8.6 Dynamical Stability.- References.- 9. Genericity and Gibbs’s Conjecture on the Maximum Number of Coexistent Phases.- 9.1 Gibbs’s Conjecture and the First Phase Rule.- 9.2 Counterexamples.- 9.3 Naive Reformulation of the Gibbs Conjecture for Substances.- 9.4 The Set of Gibbs Surfaces G.- 9.5 Strong and Weak Topologies on G.- 9.6 The Criterion.- 9.7 The Rule-Abiding Gibbs Surfaces. Denseness.- 9.8 Difficulty and Refinement of the Naive Reformulation.- 9.9 The Remaining Paradox.- References.- III Special Material Systems.- 10. Thermodynamics and the Constitutive Relations for Second Sound in Crystals.- Summary.- 10.1 Introduction.- 10.2 Derivation of Thermodynamical Relations.- References.- 11. Interstitial Working and a Nonclassical Continuum Thermodynamics.- 11.1 Introduction.- 11.2 Classical Continuum Thermodynamics: A Limitation.- 11.3 A Nonclassical Continuum Thermodynamics: Interstitial Work Flux.- 11.4 Forms and Effects of the Interstitial Work Flux.- 11.5 Materials of Korteweg Type.- 11.6 An Application: Rules Like Maxwell’s.- References.- 12. Phase Transformations and Non-Elliptic Free Energy Functions.- 12.1 Introduction.- 12.2 Kinematics of Co-Existence.- 12.3 Non-Elliptic Free Energy Functions for Materials Which Change Phase.- 12.4 Significance of Points of Convexity of the Free Energy.- 12.5 Geometry of the Domain of the Free Energy.- 12.6 Special Analysis for the Case of a Cubic Parent Phase.- References.- 13. Dynamic Changes of Phase in a van der Waals Fluid.- 13.1 Introduction.- 13.2 Basic Equations.- 13.3 The Hugoniot Curve.- 13.4 Existence of Compressive Shock Layers.- References.

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