Thermal Physics Thermodynamics and Statistical Mechanics for Scientists and Engineers

Thermal Physics
 
Author:
Robert F. Sekerka
Publisher: Elsevier
ISBN No: 978-0-12-803304-3
Release at: 2015
Pages: 610
Edition:
First Edition
File Size: 8 MB
File Type: pdf
Language: English



Content of Thermal Physics Thermodynamics and Statistical Mechanics for Scientists and Engineers



PART  I  Thermodynamics

1 Introduction 3

1.1  Temperature 3

1.2  Thermodynamics Versus Statistical Mechanics 5

1.3  Classification of State Variables 6

1.4  Energy in Mechanics 8

1.5  Elementary Kinetic Theory 12

2  First Law of Thermodynamics 15

2.1  Statement of the First Law 15

2.2  Quasistatic Work 17

2.3  Heat Capacities 19

2.4  Work Due to Expansion of an Ideal Gas 24

2.5  Enthalpy 28

3  Second Law of Thermodynamics 31

3.1  Statement of the Second Law 32

3.2  Carnot Cycle and Engines 35

3.3  Calculation of the Entropy Change 39

3.4  Combined First and Second Laws 41

3.5  Statistical Interpretation of Entropy 47

4  Third Law of Thermodynamics  49

4.1  Statement of the Third Law  49

4.2  Implications of the Third Law  50

5  Open Systems  53

5.1  Single Component Open System  53

5.2  Multicomponent Open Systems  55

5.3  Euler Theorem of Homogeneous Functions  59

5.4  Chemical Potential of Real Gases, Fugacity  64

5.5  Legendre Transformations  67

5.6  Partial Molar Quantities  71

5.7  Entropy of Chemical Reaction  75

6  Equilibrium and Thermodynamic Potentials  79

6.1  Entropy Criterion  79

6.2  Energy Criterion  84

6.3  Other Equilibrium Criteria  88

6.4  Summary of Criteria  92

7  Requirements for Stability  95

7.1  Stability Requirements for Entropy  95

7.2  Stability Requirements for Internal Energy  100

7.3  Stability Requirements for Other Potentials  102

7.4  Consequences of Stability Requiremen ts  105

7.5  Extension to Many Variables  106

7.6  Principles of Le Charlier and Le Charlier-Braun  107

8  Monocomponent  Phase Equi librium  109

8.1  Clausius-Clapeyron Equation  110

8.2  Sketches of the Thermodynamic  Function s  115

8.3  Phase Diagram in the  v,  p  Plane  118

9  Two-Phase Equilibrium for a van der Waals Fluid  121

9.1  van der Waals Equation of State  121

9.2  Thermodynamic Functions  124

9.3  Phase Equilibrium and Miscibility Gap  127

9.4  Gibbs Free Energy  131

10  Binary Solutions  137

10.1  Thermodynamics of Binary Solutions  137

10.2  Ideal Solutions  142

10.3  Phase Diagram for an Ideal Solid and an Ideal Liquid  145

10.4  Regular Solution  148

10.5  General Binary Solutions  153

11  Externa l Forces and Rotating Coordinate Systems  155

11.1  Conditions for Equilibrium  155

11.2  Uniform Gravitational Field  157

11.3  Non-Uniform Gravitational Field  164

11.4  Rotating Systems  164

11.5  Electric Fields  166

12  Chemical Reactions  167

12.1  Reactions at Constant Volume or Pressure  168

12.2  Standard States  171

12.3  Equilibrium and Affinity  173

12.4  Explicit Equilibrium Conditions  175

12.5  Simultaneous Reactions  182

13  Thermodynamics of Fluid-Fluid Interfaces  185

13.1  Planar Interfaces in Fluids  186

13.2  Curved Interfaces in Fluids  197

13.3  Interface Junctions and Contact Angles  202

13.4  Liquid Surface Shape in Gravity  205

14  Thermodynamics of Solid-Flu iid Interfaces  215

14.1  Planar Solid-Fluid Interfaces  216

14.2  Anisotropy of  y  221

14.3  Curved Solid-Fluid Interfaces  227

14.4  Faceting of a Large Planar Face  233

14.5  Equilibrium Shape from the~ -Vector  236

14.6  Herring Formula  240

14.7  Legendre Transform of the Equilibrium Shape  241

14.8  Remarks About Solid-Solid Interfaces  242

PART II  Statistical Mechanics  245

15  Entropy and Information Theory  247

15.1  Entropy as a Measure of Disorder  247

15.2  Boltzmann Eta Theorem  251

16  Microcanonical Ensemble  257

16.1  Fundamental Hypothesis of Statistical Mechanics  258

16.2  Two-State Subsystems  261

16.3  Harmonic Oscillators  265

16.4  Ideal Gas  267

16.5  Multicomponent Ideal Gas  273

17  Classical Microcanonical Ensemble  277

17.1  Liouville's Theorem  278

17.2  Classical Microcanonical Ensemble  280

18  Distinguishable Particles with Negligible

Interaction Energies  285

18.1  Derivation of the Boltzmann Distribution  285

18.2  Two-State Subsystems  289

18.3  Harmonic Oscillators  293

18.4  Rigid Linear Rotator  303

19  Canonical Ensemble  305

19.1  Three Derivations  305

19.2  Factorization Theorem  312

19.3  Classical Ideal Gas  313

19.4  Maxwell-Boltzmann Distribution  317

19.5  Energy Dispersion  320

19.6  Paramagnetism  321

19.7  Partition Function and Density of States  330

20  Classical Canonical Ensemble  337

20.1  Classical Ideal Gas  338

20.2  Law of Dulong and Petit  342

20.3  Averaging Theorem and Equipartition  343

20.4  Virial Theorem  346

20.5  Virial Coefficients  348

20.6  Use of Canonical Transformations  354

20.7  Rotating Rigid Polyatomic Molecules  356

21  Grand Canonical Ensemble  359

21.1  Derivation from Microcanonical Ensemble  360

21.2  Ideal Systems: Orbitals and Factorization  368

21.3  Classical Ideal Gas with Internal Structure  380

21.4  Multicomponent Systems  388

21.5  Pressure Ensemble  389

22  Entropy for Any Ensemble  397

22.1  General Ensemble  397

22.2  Summation over Energy Levels  402

23  Unified Treatment of Ideal Fermi, Bose, and Classical Gases  405

23.1  Integral Formulae  406

23.2  The Functions  HV(A,  a)  408

23.3  Virial Expansions for Ideal Fermi and Bose Gases  410

23.4  Heat Capacity  412

24  Bose Condensation  413

24.l  Bosons at Low Temperatures  413

24.2  Thermodynamic Functions  416

24.3  Condensate Region  421

25  Degenerate Fermi Gas  425

25.1  Ideal Fermi Gas at Low Temperatures  425

25.2  Free Electron Model of a Metal  428

25.3  Thermal Activation of Electrons  429

25.4  Pauli Paramagnetism  433

25.5  Landau Diamagnetism  436

25.6  Thermionic Emission  439

25.7  Semiconductors  442

26  Quantum Statistics  451

26.1  Pure States  451

26.2  Statistical States  453

26.3 Random Phases and External Influence  454

26.4 Time Evolution 455

26.5 Densit y Operators for Specific Ensembles  456

26.6 Examples of the Density Matrix  459

26.7 Indistinguishable Particles  465

27  Ising Model  469

27.1 Ising Model, Mean Field Treatment  470

27.2 Pair Statistics  477

27.3 Solution in One Dimension for Zero Field  479

27.4 Transfer Matrix  480

27.5 Other Methods of Solution  483

27.6 Monte Carlo Simulation  484

PART III  Appendices  495

A  Stirling 's Approximation  497

A.l  Elementary Motivation ofEq. (A.l)  498

A.2  Asymptotic Series  499

B  Use of Jacobians to Convert Partial Derivatives  503

B.l  Properties of Jacobians  503

B.2  Connection to Thermodynamics  504

C  Differential Geometry of Surfaces  509

C.l  Alterna tive Formulae for ~ Vector  509

C.2  Surface Differential Geometry  511

C.3  ~  Vector for Genera l Surfaces  516

C.4  Herring Formula  518

D  Equilibrium of Two-State Systems  523

E Aspects of Canonical Transformations 529

E.1  Necessary and Sufficient Conditions 530

E.2  Restricted Canonical Transformations 534

F Rotation of Rigid Bodies 537

F.1  Moment of inertia 537

F.2  Angular Momentum 539

F.3  Kinetic Energy 540

F.4  Time Derivatives 540

F.5  Rotating Coordinate System 541

F.6  Matrix Formulation 544

F.7  Canonical Variables 546

F.8  Quantum Energy Levels for Diatomic Molecule 547

G  Thermodynamic Perturbation Theory 549

G .1  Classical Case 549

G.2  Quantum Case 550

H  Selected Mathematical Relations 553

H.1  Bernoulli Numbers and Polynomials 553

H.2  Euler-Maclaur in Sum Formula 554

Creation and Annihilation Operators 559

1.1  Harmonic Oscillator 559

1.2  Boson Operators 560

1.3  Fermion Operators 562

1.4  Boson and Fermion Number Operators 563

References 565

Index 569

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