Thermal Physics: Thermodynamics and Statistical Mechanics for Scientists and Engineers

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
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 hν(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
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