Physics104 Statistical

Table of contents

1. CHAPTER 1 Characteristic Features of Macroscopic Systems
2. CHAPTER 2 Basic Probability Concepts
3. CHAPTER 3 Statistical Description of Systems of Particles
4. CHAPTER 4 Thermal Interaction
5. CHAPTER 5 Microscopic Theory and Macroscopic Measurements
6. CHAPTER 6 Canonical Distribution in the Classical Approximation
7. CHAPTER 7 General Thermodynamic Interaction
8. CHAPTER 8 Elementary Kinetic Theory of Transport Processes
9. Appendix
10. Mathematical Notes

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CHAPTER 1 Characteristic Features of Macroscopic Systems

• Fluctuations in Equilibrium
• Irreversibility and the Approach to Equilibrium
• Further Illustrations
• Properties of the Equilibrium Situation
• Heat and Temperature
• Typical Magnitudes
• Important Problems of Macroscopic Physics
• Summary of Defnitions
• Suggestions for Supplementary Reading
• Problems

CHAPTER 2 Basic Probability Concepts

• Statistical Ensembles
• Elementary Relations among Probabilities
• The Binomial Distribution
• Mean Values
• Calculation of Mean Values for a Spin System
• Continuous Probability Distributions
• Summary of Deinitions
• Important Relations
• Suggestions for Supplementary Reading
• Problems

CHAPTER 3 Statistical Description of Systems of Particles

• Specification of the State of a System
• Statistical Ensemble
• Statistical Postulates
• Probability Calculations
• Number of States Accessible to a Macroscopic System
• Constraints, Equilibrium, and Irreversibility
• Interaction between Systems
• Summary of Definitions
• Important Relations
• Suggestions for Supplementary Reading
• Problems

CHAPTER 4 Thermal Interaction

• Distribution of Energy between Macroscopic Systems
• The Approach to Thermal Equilibrium
• Temperature
• Small Heat Transfer
• System in Contact with a Heat Reservoir
• Paramagnetism
• Mean Energy of an ldeal Gas
• Mean Pressure of an Ideal Gas
• Summary of Defnitions
• Important Relations
• Suggestions for Supplementary Reading
• Problems

CHAPTER 5 Microscopic Theory and Macroscopic Measurements

• Determination of the Absolute Temperature
• High and Low Absolute Temperatures
• Work, Internal Energy, and Heat
• Heat Capacity
• Entropy
• Intensive and Extensive Parameters
• Summary of Defnitions
• Important Relations
• Suggestions for Supplementary Reading
• Problems

CHAPTER 6 Canonical Distribution in the Classical Approximation

• The Classical Approximation
• Maxwell Velocity Distribution
• Discussion of the Maxwell Distribution
• Effusion and Molecular Beams
• The Equipartition Theorem
• Applications of the Equipartition Theorem
• The Specific Heat of Solids
• Summary of Definitions
• Important Relations
• Suggestions for Supplementary Reading
• Problems

CHAPTER 7 General Thermodynamic Interaction

• Dependence of the Number of States on the External Parameters
• General Relations Valid in Equilibrium
• Applications to an Ideal Gas
• Basic Statements of Statistical Thermdynamics
• Equilibrium Conditions
• Equilibrium between Phases
• The Transformation of Randomness into Order
• Summary of Definitions
• Important Relations
• Suggestions for Supplementary Reading
• Problems

CHAPTER 8 Elementary Kinetic Theory of Transport Processes

• Mean Free Path
• Viscosity and Transport of Momentum
• Thermal Conductivity and Transport of Energy
• Self-diffusion and Transport of Molecules
• Electrical Conductivity and Transport of Charge
• Summary of Definitions
• Important Relations
• Suggestions for Supplementary Reading
• Problems

Appendix

• Gaussian Distribution
• Poisson Distribution
• Magnitude of Energy Fluctuations
• Molecular Impacts and Pressure in a Gas

Mathematical Notes

• The Summation Notation
• Sum of a Geometric Series
• Derivative of in n! for large n
• Value of in n! for large n
• The Inequality lnx≤x-1
• Evaluation of the Integral
• Evaluation of Integrals of the Form