E-Book, Englisch, 252 Seiten, Web PDF
Giles / Sneddon / Stark Mathematical Foundations of Thermodynamics
1. Auflage 2016
ISBN: 978-1-4831-8491-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
International Series of Monographs on Pure and Applied Mathematics
E-Book, Englisch, 252 Seiten, Web PDF
ISBN: 978-1-4831-8491-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Mathematical Foundations of Thermodynamics details the core concepts of the mathematical principles employed in thermodynamics. The book discusses the topics in a way that physical meanings are assigned to the theoretical terms. The coverage of the text includes the mechanical systems and adiabatic processes; topological considerations; and equilibrium states and potentials. The book also covers Galilean thermodynamics; symmetry in thermodynamics; and special relativistic thermodynamics. The book will be of great interest to practitioners and researchers of disciplines that deal with thermodynamics, such as physics, engineering, and chemistry.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Mathematical Foundations of Thermodynamics;6
3;Copyright Page;7
4;Table of Contents;8
5;Preface;12
6;Introduction;16
7;CHAPTER 1. FUNDAMENTAL CONCEPTS;24
7.1;1.1. The Structure of a Physical Theory;24
7.2;1.2. Primitive Observers;27
7.3;1.3. The Classical Formulations of Thermodynamics;29
7.4;1.4. Systems and States;31
7.5;1.5. Relations between States;37
7.6;1.6. The Axioms;42
8;CHAPTER 2. FORMAL PROCESSES;45
8.1;2.1. Definitions and Axioms;45
8.2;2.2. Addition of Processes;47
8.3;2.3. Ordering of Processes;47
8.4;2.4. Further Properties of Processes;49
9;CHAPTER 3. COMPONENTS OF CONTENT;52
9.1;3.1. Definition;52
9.2;3.2. Existence of Components of Content;54
10;CHAPTER 4. IRREVERSIBILITY;56
10.1;4.1. Irreversibility Functions;56
10.2;4.2. The Construction of an Irreversibility Function;58
10.3;4.3. Irreversibility and Entropy;60
11;CHAPTER 5. MECHANICAL SYSTEMS AND ADIABATIC PROCESSES;63
11.1;5.1. Physical Considerations;63
11.2;5.2. Mechanical States and Processes;67
11.3;5.3. Adiabatic Processes;68
12;CHAPTER 6. ENTROPY;71
12.1;6.1. Entropy Functions;71
12.2;6.2. The Construction of an Entropy Function;72
13;CHAPTER 7. TOPOLOGICAL CONSIDERATIONS;75
13.1;7.1. Components of Content;75
13.2;7.2. Entropy;79
14;CHAPTER 8. THERMODYNAMIC SPACE;87
14.1;8.1. Definitions;87
14.2;8.2. The Case of Finite Dimension;89
14.3;8.3. Mathematical Commentary;92
15;CHAPTER 9. EQUILIBRIUM STATES AND POTENTIAL;97
15.1;9.1. Equilibrium States;97
15.2;9.2. Components of Potential;99
16;CHAPTER 10. PERFECT EQUILIBRIUM STATES;105
16.1;10.1. Motivation;105
16.2;10.2. Properties of Perfect Equilibrium States;106
16.3;10.3. Perfect Thermodynamic Systems;108
17;CHAPTER 11. THERMODYNAMICS OF A RIGIDLY ENCLOSED SYSTEM;111
17.1;11.1. General Discussion;111
17.2;11.2. A Pathological Example;116
17.3;11.3. The Construction of an Energy Function;120
17.4;11.4. The Construction of an Entropy Function;123
18;CHAPTER 12. SYSTEMS OF VARIABLE VOLUME;127
18.1;12.1. Volume and Pressure;127
18.2;12.2. Simple Systems;131
19;CHAPTER 13. ELECTRIC AND MAGNETIC SYSTEMS;134
19.1;13.1. Electrostatic Systems;134
19.2;13.2. Magnetic Systems;139
19.3;13.3. Hysteresis;141
20;CHAPTER 14. GALILEAN THERMODYNAMICS;145
20.1;14.1. The Components of Content;146
20.2;14.2. Galilean Transformations;149
20.3;14.3. The Equilibrium Surface;150
20.4;14.4. Properties of Equilibrium States;151
20.5;14.5. Thermodynamic Particles;152
20.6;] 4.6. Local Properties in an Eqilibrium State;153
20.7;14.7. Some Special Cases;156
20.8;14.8. The Centrifugal Effect;159
21;CHAPTER 15. SYMMETRY IN THERMODYNAMICS;164
21.1;15.1. Introduction;164
21.2;15.2. The Principle of Equivalence;167
21.3;15.3. An Example;168
21.4;15.4. The Symmetry Group;170
21.5;15.5. The Transformation of States;172
21.6;15.6. The Transformation of Functions of State;174
22;CHAPTER 16. SPECIAL RELATIVISTIC THERMODYNAMICS;178
22.1;16.1. The Inhomogeneous Lorentz Group;179
22.2;16.2. The Components of Content;183
22.3;16.3. Rest Mass and Spin;186
22.4;16.4. The Representation of States in Space-Time;187
22.5;16.5. Centre of Mass and Spin Angular Momentum;188
22.6;16.6. The Transformation of Entropy;190
22.7;16.7. Equilibrium States and Temperature;192
22.8;16.8. Local Properties of an Equilibrium State;195
22.9;16.9. Conclusion;203
23;APPENDIX A. THE FORMAL THEORY;206
23.1;A . l . Notation;207
23.2;A.2. States and Processes;207
23.3;A. 3. Components of Content;210
23.4;A.4. Quasi-Entropy;214
23.5;A.5. The Duality Principle;220
23.6;A.6. Boundedness;221
23.7;A.7. Equilibrium States;223
23.8;A.8. Potentials;225
23.9;A.9. Absolute Entropy;226
24;APPENDIX B. SUBADDITIVE FUNCTIONS ON A GROUP;230
24.1;B.l. Partially Ordered Sets;230
24.2;B.2. Subadditive Functions;231
24.3;B.3. The Extension Theorem;234
25;APPENDIX C. THE PHYSICAL BASIS FOR THE ADJOINT REPRESENTATION;238
25.1;C.l. The Case of Special Relativity;238
25.2;C.2. The General Case;241
26;REFERENCES;244
27;INDEX;246
28;SYMBOL INDEX;252
