Thermodynamics

by Haddad, Wassim M.

• ISBN13: 9780691123271
• ISBN10: 0691123276
• Format: Hardcover
• Copyright: 2005-07-05
• Publisher: Princeton Univ Pr

Summary

This book places thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, the authors develop a novel formulation of thermodynamics that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics. The authors' theory is motivated by the fact that a discipline as cardinal as thermodynamics--entrusted with some of the most perplexing secrets of our universe--demands far more than physical mathematics as its underpinning. Even though many great physicists, such as Archimedes, Newton, and Lagrange, have humbled us with their mathematically seamless eurekas over the centuries, this book suggests that a great many physicists and engineers who have developed the theory of thermodynamics seem to have forgotten that mathematics, when used rigorously, is the irrefutable pathway to truth. This book uses system theoretic ideas to bring coherence, clarity, and precision to an extremely important and poorly understood classical area of science.

Author Biography

VijaySekhar Chellaboina is Associate Professor in the Department of Mechanical, Aerospace, and Biomedical Engineering at the University of Tennessee.

Table of Contents

Preface	ix
Chapter 1. Introduction	1	(16)
1.1 An Overview of Thermodynamics	1	(10)
1.2 System Thermodynamics	11	(3)
1.3 A Brief Outline of the Monograph	14	(3)
Chapter 2. Dynamical System Theory	17	(28)
2.1 Notation, Definitions, and Mathematical Preliminaries	17	(3)
2.2 Stability Theory for Nonnegative Dynamical Systems	20	(7)
2.3 Reversibility, Irreversibility, Recoverability, and Irrecoverability	27	(7)
2.4 Reversible Dynamical Systems, Volume-Preserving Flows, and Poincaré Recurrence	34	(11)
Chapter 3. A Systems Foundation for Thermodynamics	45	(58)
3.1 Introduction	45	(1)
3.2 Conservation of Energy and the First Law of Thermodynamics	46	(9)
3.3 Entropy and the Second Law of Thermodynamics	55	(17)
3.4 Ectropy	72	(9)
3.5 Semistability, Energy Equipartition, Irreversibility, and the Arrow of Time	81	(8)
3.6 Entropy Increase and the Second Law of Thermodynamics	89	(2)
3.7 Interconnections of Thermodynamic Systems	91	(7)
3.8 Monotonicity of System Energies in Thermodynamic Processes	98	(5)
Chapter 4. Temperature Equipartition and the Kinetic Theory of Gases	103	(12)
4.1 Semistability and Temperature Equipartition	103	(7)
4.2 Boltzmann Thermodynamics	110	(5)
Chapter 5. Work, Heat, and the Carnot Cycle	115	(16)
5.1 On the Equivalence of Work and Heat: The First Law Revisited	115	(11)
5.2 The Carnot Cycle and the Second Law of Thermodynamics	126	(5)
Chapter 6. Thermodynamic Systems with Linear Energy Exchange	131	(10)
6.1 Linear Thermodynamic System Models	131	(5)
6.2 Semistability and Energy Equipartition in Linear Thermodynamic Models	136	(5)
Chapter 7. Continuum Thermodynamics	141	(28)
7.1 Conservation Laws in Continuum Thermodynamics	141	(7)
7.2 Entropy and Ectropy for Continuum Thermodynamics	148	(12)
7.3 Semistability and Energy Equipartition in Continuum Thermodynamics	160	(9)
Chapter 8. Conclusion	169	(6)
Bibliography	175	(10)
Index	185