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1st Edition - August 19, 2015

**Author:** Robert Floyd Sekerka

Paperback ISBN:

9 7 8 - 0 - 1 2 - 8 0 3 3 0 4 - 3

eBook ISBN:

9 7 8 - 0 - 1 2 - 8 0 3 3 3 7 - 1

In Thermal Physics: Thermodynamics and Statistical Mechanics for Scientists and Engineers, the fundamental laws of thermodynamics are stated precisely as postulates and… Read more

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In Thermal Physics: Thermodynamics and Statistical Mechanics for Scientists and Engineers, the fundamental laws of thermodynamics are stated precisely as postulates and subsequently connected to historical context and developed mathematically. These laws are applied systematically to topics such as phase equilibria, chemical reactions, external forces, fluid-fluid surfaces and interfaces, and anisotropic crystal-fluid interfaces.

Statistical mechanics is presented in the context of information theory to quantify entropy, followed by development of the most important ensembles: microcanonical, canonical, and grand canonical. A unified treatment of ideal classical, Fermi, and Bose gases is presented, including Bose condensation, degenerate Fermi gases, and classical gases with internal structure. Additional topics include paramagnetism, adsorption on dilute sites, point defects in crystals, thermal aspects of intrinsic and extrinsic semiconductors, density matrix formalism, the Ising model, and an introduction to Monte Carlo simulation.

Throughout the book, problems are posed and solved to illustrate specific results and problem-solving techniques.

- Includes applications of interest to physicists, physical chemists, and materials scientists, as well as materials, chemical, and mechanical engineers
- Suitable as a textbook for advanced undergraduates, graduate students, and practicing researchers
- Develops content systematically with increasing order of complexity
- Self-contained, including nine appendices to handle necessary background and technical details

Advanced undergraduate and graduate students in physics and chemical and engineering sciences; researchers in academia and industry working in these areas

- Dedication
- About the Cover
- Preface
- Part I: Thermodynamics
- 1: Introduction
- Abstract
- 1.1 Temperature
- 1.2 Thermodynamics Versus Statistical Mechanics
- 1.3 Classification of State Variables
- 1.4 Energy in Mechanics
- 1.5 Elementary Kinetic Theory

- 2: First Law of Thermodynamics
- Abstract
- 2.1 Statement of the First Law
- 2.2 Quasistatic Work
- 2.3 Heat Capacities
- 2.4 Work Due to Expansion of an Ideal Gas
- 2.5 Enthalpy

- 3: Second Law of Thermodynamics
- Abstract
- 3.1 Statement of the Second Law
- 3.2 Carnot Cycle and Engines
- 3.3 Calculation of the Entropy Change
- 3.4 Combined First and Second Laws
- 3.5 Statistical Interpretation of Entropy

- 4: Third Law of Thermodynamics
- Abstract
- 4.1 Statement of the Third Law
- 4.2 Implications of the Third Law

- 5: Open Systems
- Abstract
- 5.1 Single Component Open System
- 5.2 Multicomponent Open Systems
- 5.3 Euler Theorem of Homogeneous Functions
- 5.4 Chemical Potential of Real Gases, Fugacity
- 5.5 Legendre Transformations
- 5.6 Partial Molar Quantities
- 5.7 Entropy of Chemical Reaction

- 6: Equilibrium and Thermodynamic Potentials
- Abstract
- 6.1 Entropy Criterion
- 6.2 Energy Criterion
- 6.3 Other Equilibrium Criteria
- 6.4 Summary of Criteria

- 7: Requirements for Stability
- Abstract
- 7.1 Stability Requirements for Entropy
- 7.2 Stability Requirements for Internal Energy
- 7.3 Stability Requirements for Other Potentials
- 7.4 Consequences of Stability Requirements
- 7.5 Extension to Many Variables
- 7.6 Principles of Le Chatlier and Le Chatlier-Braun

- 8: Monocomponent Phase Equilibrium
- Abstract
- 8.1 Clausius-Clapeyron Equation
- 8.2 Sketches of the Thermodynamic Functions
- 8.3 Phase Diagram in the v, p Plane

- 9: Two-Phase Equilibrium for a van der Waals Fluid
- Abstract
- 9.1 van der Waals Equation of State
- 9.2 Thermodynamic Functions
- 9.3 Phase Equilibrium and Miscibility Gap
- 9.4 Gibbs Free Energy

- 10: Binary Solutions
- Abstract
- 10.1 Thermodynamics of Binary Solutions
- 10.2 Ideal Solutions
- 10.3 Phase Diagram for an Ideal Solid and an Ideal Liquid
- 10.4 Regular Solution
- 10.5 General Binary Solutions

- 11: External Forces and Rotating Coordinate Systems
- Abstract
- 11.1 Conditions for Equilibrium
- 11.2 Uniform Gravitational Field
- 11.3 Non-Uniform Gravitational Field
- 11.4 Rotating Systems
- 11.5 Electric Fields

- 12: Chemical Reactions
- Abstract
- 12.1 Reactions at Constant Volume or Pressure
- 12.2 Standard States
- 12.3 Equilibrium and Affinity
- 12.4 Explicit Equilibrium Conditions
- 12.5 Simultaneous Reactions

- 13: Thermodynamics of Fluid-Fluid Interfaces
- Abstract
- 13.1 Planar Interfaces in Fluids
- 13.2 Curved Interfaces in Fluids
- 13.3 Interface Junctions and Contact Angles
- 13.4 Liquid Surface Shape in Gravity

- 14: Thermodynamics of Solid-Fluid Interfaces
- Abstract
- 14.1 Planar Solid-Fluid Interfaces
- 14.2 Anisotropy of γ
- 14.3 Curved Solid-Fluid Interfaces
- 14.4 Faceting of a Large Planar Face
- 14.5 Equilibrium Shape from the ξ-Vector
- 14.6 Herring Formula
- 14.7 Legendre Transform of the Equilibrium Shape
- 14.8 Remarks About Solid-Solid Interfaces

- 1: Introduction
- Part II: Statistical Mechanics
- 15: Entropy and Information Theory
- Abstract
- 15.1 Entropy as a Measure of Disorder
- 15.2 Boltzmann Eta Theorem

- 16: Microcanonical Ensemble
- Abstract
- 16.1 Fundamental Hypothesis of Statistical Mechanics
- 16.2 Two-State Subsystems
- 16.3 Harmonic Oscillators
- 16.4 Ideal Gas
- 16.5 Multicomponent Ideal Gas

- 17: Classical Microcanonical Ensemble
- Abstract
- 17.1 Liouville’s Theorem
- 17.2 Classical Microcanonical Ensemble

- 18: Distinguishable Particles with Negligible Interaction Energies
- Abstract
- 18.1 Derivation of the Boltzmann Distribution
- 18.2 Two-State Subsystems
- 18.3 Harmonic Oscillators
- 18.4 Rigid Linear Rotator

- 19: Canonical Ensemble
- Abstract
- 19.1 Three Derivations
- 19.2 Factorization Theorem
- 19.3 Classical Ideal Gas
- 19.4 Maxwell-Boltzmann Distribution
- 19.5 Energy Dispersion
- 19.6 Paramagnetism
- 19.7 Partition Function and Density of States

- 20: Classical Canonical Ensemble
- Abstract
- 20.1 Classical Ideal Gas
- 20.2 Law of Dulong and Petit
- 20.3 Averaging Theorem and Equipartition
- 20.4 Virial Theorem
- 20.5 Virial Coefficients
- 20.6 Use of Canonical Transformations
- 20.7 Rotating Rigid Polyatomic Molecules

- 21: Grand Canonical Ensemble
- Abstract
- 21.1 Derivation from Microcanonical Ensemble
- 21.2 Ideal Systems: Orbitals and Factorization
- 21.3 Classical Ideal Gas with Internal Structure
- 21.4 Multicomponent Systems
- 21.5 Pressure Ensemble

- 22: Entropy for Any Ensemble
- Abstract
- 22.1 General Ensemble
- 22.2 Summation over Energy Levels

- 23: Unified Treatment of Ideal Fermi, Bose, and Classical Gases
- Abstract
- 23.1 Integral Formulae
- 23.2 The Functions h
_{ν}(λ,a) - 23.3 Virial Expansions for Ideal Fermi and Bose Gases
- 23.4 Heat Capacity

- 24: Bose Condensation
- Abstract
- 24.1 Bosons at Low Temperatures
- 24.2 Thermodynamic Functions
- 24.3 Condensate Region

- 25: Degenerate Fermi Gas
- Abstract
- 25.1 Ideal Fermi Gas at Low Temperatures
- 25.2 Free Electron Model of a Metal
- 25.3 Thermal Activation of Electrons
- 25.4 Pauli Paramagnetism
- 25.5 Landau Diamagnetism
- 25.6 Thermionic Emission
- 25.7 Semiconductors

- 26: Quantum Statistics
- Abstract
- 26.1 Pure States
- 26.2 Statistical States
- 26.3 Random Phases and External Influence
- 26.4 Time Evolution
- 26.5 Density Operators for Specific Ensembles
- 26.6 Examples of the Density Matrix
- 26.7 Indistinguishable Particles

- 27: Ising Model
- Abstract
- 27.1 Ising Model, Mean Field Treatment
- 27.2 Pair Statistics
- 27.3 Solution in One Dimension for Zero Field
- 27.4 Transfer Matrix
- 27.5 Other Methods of Solution
- 27.6 Monte Carlo Simulation

- 15: Entropy and Information Theory
- A: Stirling’s Approximation
- A.1 Elementary Motivation of Eq. A.1
- A.2 Asymptotic Series

- B: Use of Jacobians to Convert Partial Derivatives
- B.1 Properties of Jacobians
- B.2 Connection to Thermodynamics

- C: Differential Geometry of Surfaces
- C.1 Alternative Formulae for ξ Vector
- C.2 Surface Differential Geometry
- C.3 ξ Vector for General Surfaces
- C.4 Herring Formula

- D: Equilibrium of Two-State Systems
- E: Aspects of Canonical Transformations
- E.1 Necessary and Sufficient Conditions
- E.2 Restricted Canonical Transformations

- F: Rotation of Rigid Bodies
- F.1 Moment of Inertia
- F.2 Angular Momentum
- F.3 Kinetic Energy
- F.4 Time Derivatives
- F.5 Rotating Coordinate System
- F.6 Matrix Formulation
- F.7 Canonical Variables
- F.8 Quantum Energy Levels for Diatomic Molecule

- G: Thermodynamic Perturbation Theory
- G.1 Classical Case
- G.2 Quantum Case

- H: Selected Mathematical Relations
- H.1 Bernoulli Numbers and Polynomials
- H.2 Euler-Maclaurin Sum Formula

- I: Creation and Annihilation Operators
- I.1 Harmonic Oscillator
- I.2 Boson Operators
- I.3 Fermion Operators
- I.4 Boson and Fermion Number Operators

- References
- Index
- Physical_constants

- No. of pages: 610
- Language: English
- Published: August 19, 2015
- Imprint: Elsevier
- Paperback ISBN: 9780128033043
- eBook ISBN: 9780128033371

RS

Robert Floyd Sekerka is University Professor Emeritus, Physics and Mathematics, Carnegie Mellon University. He received his bachelor’s degree summa cum laude in physics from the University of Pittsburgh in 1960 and his AM (1961) and PhD (1965) degrees from Harvard University where he was a Woodrow Wilson Fellow. He worked as a senior engineer at Westinghouse Research Laboratories until 1969 when he joined the faculty of Carnegie Mellon in the Materials Science and Engineering Department; he was promoted to Professor in 1972 and was Department Head from 1976–82. He served as Dean of the Mellon College of Science from 1982 through 1991. Subsequently he was named University Professor of Physics and Mathematics with a courtesy appointment in Materials Science and Engineering. He retired in 2011 but continues to do scientific research and writing. He is a Fellow of the American Society for Metals, the American Physical Society, and the Japanese Society for the Promotion of Science, and he has been a consultant to NIST for over forty years. Honors include the Phillip M. McKenna Award, the Frank Prize of the International Organization for Crystal Growth (President for six years) and the Bruce Chalmers Award of TMS. Please see http://sekerkaweb.phys.cmu.edu for further information and publications.

Affiliations and expertise

University Professor Emeritus, Physics and Mathematics, Carnegie Mellon University, Pittsburgh, PA, USA