Statistical Thermodynamics

Table of contents

1. Cover
2. Preface
3. Acknowledgments
4. About the Companion Website
5. Symbols and Constants
   1. Reference
6. 1 Introduction
   1. 1.1 Classical Thermodynamics and Statistical Thermodynamics
   2. 1.2 Examples of Results Obtained from Statistical Thermodynamics
   3. 1.3 Practices of Notation
7. 2 Review of Probability Theory
   1. 2.1 Probability
   2. 2.2 Discrete Distributions
   3. 2.3 Continuous Distributions
   4. 2.4 Means and Variances
   5. 2.5 Uncertainty
   6. Problems
8. 3 Energy and Interactions
   1. 3.1 Kinetic Energy and Potential Energy of Atoms and Ions
   2. 3.2 Kinetic Energy and Potential Energy of Diatomic Molecules
   3. 3.3 Kinetic Energy of Polyatomic Molecules
   4. 3.4 Interactions Between Molecules
   5. 3.5 Energy as an Extensive Property
   6. 3.6 Kinetic Energy of a Gas Molecule in Quantum Mechanics
   7. Problems
9. 4 Statistical Mechanics
   1. 4.1 Basic Assumptions, Microcanonical Ensembles, and Canonical Ensembles
   2. 4.2 Probability Distribution in Canonical Ensembles and Partition Functions
   3. 4.3 Internal Energy
   4. 4.4 Identification of β
   5. 4.5 Equipartition Law
   6. 4.6 Other Thermodynamic Functions
   7. 4.7 Another View of Entropy
   8. 4.8 Fluctuations of Energy
   9. 4.9 Grand Canonical Ensembles
   10. 4.10 Cumulants of Energy
   11. Problems
10. 5 Canonical Ensemble of Gas Molecules
    1. 5.1 Velocity of Gas Molecules
    2. 5.2 Heat Capacity of a Classical Gas
    3. 5.3 Heat Capacity of a Quantum‐Mechanical Gas
    4. 5.4 Distribution of Rotational Energy Levels
    5. 5.5 Conformations of a Molecule
    6. Problems
11. 6 Indistinguishable Particles
    1. 6.1 Distinguishable Particles and Indistinguishable Particles
    2. 6.2 Partition Function of Indistinguishable Particles
    3. 6.3 Condition of Nondegeneracy
    4. 6.4 Significance of Division by N!
    5. 6.5 Indistinguishability and Center‐of‐Mass Movement
    6. 6.6 Open System of Gas
    7. Problems
12. 7 Imperfect Gas
    1. 7.1 Virial Expansion
    2. 7.2 Molecular Expression of Interaction in the Canonical Ensemble
    3. 7.3 Second Virial Coefficients in Different Models
    4. 7.4 Joule–Thomson Effect
13. 8 Rubber Elasticity
    1. 8.1 Rubber
    2. 8.2 Polymer Chain in One Dimension
    3. 8.3 Polymer Chain in Three Dimensions
    4. 8.4 Network of Springs
    5. Problems
14. 9 Law of Mass Action
    1. 9.1 Reaction of Two Monatomic Molecules
    2. 9.2 Decomposition of Homonuclear Diatomic Molecules
    3. 9.3 Isomerization
    4. 9.4 Method of the Steepest Descent
    5. Problems
15. 10 Adsorption
    1. 10.1 Adsorption Phenomena
    2. 10.2 Langmuir Isotherm
    3. 10.3 BET Isotherm
    4. 10.4 Dissociative Adsorption
    5. 10.5 Interaction Between Adsorbed Molecules
    6. Problems
16. 11 Ising Model
    1. 11.1 Model
    2. 11.2 Partition Function
    3. 11.3 Mean‐Field Theories
    4. 11.4 Exact Solution of 1D Ising Model
    5. 11.5 Variations of the Ising Model
    6. Problems
17. 12 Helical Polymer
    1. 12.1 Helix‐Forming Polymer
    2. 12.2 Optical Rotation and Circular Dichroism
    3. 12.3 Pristine Poly(n‐hexyl isocyanate)
    4. 12.4 Variations to the Helical Polymer
    5. Problems
18. 13 Helix–Coil Transition
    1. 13.1 Historical Background
    2. 13.2 Polypeptides
    3. 13.3 Zimm–Bragg Model
    4. Problems
19. 14 Regular Solutions
    1. 14.1 Binary Mixture of Equal‐Size Molecules
    2. 14.2 Binary Mixture of Molecules of Different Sizes
    3. Problems
20. Appendix A: Mathematics
    1. A.1 Hyperbolic Functions
    2. A.2 Series
    3. A.3 Binomial Theorem and Trinomial Theorem
    4. A.4 Stirling's formula
    5. A.5 Integrals
    6. A.6 Error Functions
    7. A.7 Gamma Functions
21. References
22. Index
23. End User License Agreement