Statistical Thermodynamics

This textbook introduces chemistry and chemical engineering students to molecular descriptions of thermodynamics, chemical systems, and biomolecules.

• Equips students with the ability to apply the method to their own systems, as today's research is microscopic and molecular and articles are written in that language

• Provides ample illustrations and tables to describe rather difficult concepts

• Makes use of plots (charts) to help students understand the mathematics necessary for the contents

• Includes practice problems and answers

Autorentext

IWAO TERAOKA, PHD, is a professor of chemistry at Tandon School of Engineering of NYU. His current research areas include photonic sensors and liquid chromatography, but in early years he worked on physical chemistry of polymer solutions. He is a recipient of the 1994 NSF Young Investigator Award. Professor Teraoka is also the author of Polymer Solutions: An Introduction to Physical Properties and more than 100 original papers and 6 book chapters.

Klappentext
Discusses the basics and applications of statistical thermodynamics to chemical systems This textbook introduces chemistry and chemical engineering students to molecular descriptions of thermodynamics, chemical systems, and biomolecules. It focuses on topics such as adsorption, mixture, and chemical equilibria, which are integral to their grasping of the subject. It teaches readers how to apply the tools of statistical mechanics to different thermodynamic systems and provides chapter-end practice problems to aide in their understanding. Statistical Thermodynamics: Basics and Applications to Chemical Systems addresses topics that are most applicable to the interests of chemistry and chemical engineering students. These topics include: probability; energy and interactions; statistical mechanics; harmonic oscillators; ideal gas; imperfect gas; heat capacities of gas; rubber elasticity; conformation of polymers; surface adsorption; law of mass action; Ising model; helical polymers; helix-coil transition; and liquid mixture.

• Focuses on applications of statistical mechanics to chemistry, biochemistry, and biology
• Equips students with the ability to apply the method to their own systems, as today's research is microscopic and molecular and articles are written in that language
• Provides ample illustrations and tables to describe rather difficult concepts
• Makes use of plots (charts) to help students understand the mathematics necessary for the contents
• Includes practice problems and answers Statistical Thermodynamics is an ideal text for undergraduate and graduate students studying chemistry, chemical engineering, materials science, and other related programs.

Inhalt
Preface xiii

Acknowledgments xvii

About the Companion Website xix

Symbols and Constants xxi

1 Introduction 1

1.1 Classical Thermodynamics and Statistical Thermodynamics 1

1.2 Examples of Results Obtained from Statistical Thermodynamics 2

1.2.1 Heat Capacity of Gas of Diatomic Molecules 2

1.2.2 Heat Capacity of a Solid 3

1.2.3 Blackbody Radiation 3

1.2.4 Adsorption 4

1.2.5 HelixCoil Transition 5

1.2.6 Boltzmann Factor 6

1.3 Practices of Notation 6

2 Review of Probability Theory 9

2.1 Probability 9

2.2 Discrete Distributions 11

2.2.1 Binomial Distribution 12

2.2.2 Poisson Distribution 13

2.2.3 Multinomial Distribution 14

2.3 Continuous Distributions 15

2.3.1 Uniform Distribution 19

2.3.2 Exponential Distribution 19

2.3.3 Normal Distribution 21

2.3.4 Distribution of a Dihedral Angle 21

2.4 Means and Variances 22

2.4.1 Discrete Distributions 22

2.4.2 Continuous Distributions 26

2.4.3 Central Limit Theorem 27

2.5 Uncertainty 28

Problems 31

3 Energy and Interactions 35

3.1 Kinetic Energy and Potential Energy of Atoms and Ions 35

3.1.1 Kinetic Energy 35

3.1.2 Gravitational Potential 36

3.1.3 Ion in an Electric Field 36

3.1.4 Total Energy of Atoms and Ions 37

3.2 Kinetic Energy and Potential Energy of Diatomic Molecules 37

3.2.1 Kinetic Energy (Translation, Rotation, Vibration) 37

3.2.2 Dipolar Potential 42

3.2.2.1 Potential of a Permanent Dipole 42

3.2.2.2 Potential of an Induced Dipole 44

3.3 Kinetic Energy of Polyatomic Molecules 46

3.3.1 Linear Polyatomic Molecule 46

3.3.2 Nonlinear Polyatomic Molecule 48

3.4 Interactions Between Molecules 50

3.4.1 Excluded-Volume Interaction 52

3.4.2 Coulomb Interaction 52

3.4.3 DipoleDipole Interaction 53

3.4.4 van der Waals Interaction 54

3.4.5 Lennard-Jones Potential 55

3.5 Energy as an Extensive Property 57

3.6 Kinetic Energy of a Gas Molecule in Quantum Mechanics 58

3.6.1 Quantization of Translational Energy 58

3.6.2 Quantization of Rotational Energy 61

3.6.3 Quantization of Vibrational Energy 63

3.6.4 Electronic Energy Levels 65

3.6.5 Comparison of Energy Level Spacings 66

Problems 67

4 Statistical Mechanics 69

4.1 Basic Assumptions, Microcanonical Ensembles, and Canonical Ensembles 69

4.1.1 Basic Assumptions 69

4.1.2 Microcanonical Ensembles 73

4.1.3 Canonical Ensembles 75

4.2 Probability Distribution in Canonical Ensembles and Partition Functions 77

4.2.1 Probability Distribution 77

4.2.2 Partition Function for a System with Discrete States 79

4.2.3 Partition Function for a System with Continuous States 81

4.2.4 Energy Levels and States 83

4.3 Internal Energy 88

4.4 Identification of 𝛽 89

4.5 Equipartition Law 91

4.6 Other Thermodynamic Functions 93

4.7 Another View of Entropy 97

4.8 Fluctuations of Energy 99

4.9 Grand Canonical Ensembles 100

4.10 Cumulants of Energy 107

Problems 110

5 Canonical Ensemble of Gas Molecules 113

5.1 Velocity of Gas Molecules 113

5.2 Heat Capacity of a Classical Gas 116

5.2.1 Point Mass 117

5.2.2 Rigid Dumbbell 117

5.2.3 Elastic Dumbbell 118

5.3 Heat Capacity of a Quantum-Mechanical Gas 120

5.3.1 General Formulas 120

5.3.2 Translation 122

5.3.3 Rotation 124

5.3.4 Vibration 127

5.3.5 Comparison with Classical Models 128 5.4 Distribution of Rotational...