CLASSICAL THERMODYNAMICS AND QUANTUM STATISTICS

This is a basic textbook of thermodynamics and statistical physics suitable for a one-semester upper-undergraduate course. This book is based on my lectures read four times since 2009 at Lehman College of the City University of New York. I opted for a conceptually more transparent quantum-mechanical approach to statistical physics dealing with discrete states from the very beginning. Classical statistics appears as a limiting case of quantum statistics or, in some cases, as an alternative approach at the level of a recipe, to make a comparison with the quantum approach. Elements of quantum mechanics that are needed are introduced in the text. For the sake of simplicity, only the most important building elements of thermodynamics and statistical physics are included in this small book. Still, this most important material is considered in great detail and even illustrated by numerical solutions for the magnetic systems in the mean-field approximation and for the Bose- and Fermi gases. This textbook is also suitable for graduate students and researchers who wish to recuperate the basics of thermodynamics and statistical physics before advancing to more specialized topics.

Contents:

• Preface
• About the Author
• Thermodynamics:
  • Definitions of Thermodynamics
  • Temperature
  • Equation of State
  • Thermodynamic Coefficients
  • Work and Internal Energy
  • Heat and the First Law of Thermodynamics
  • Heat Capacity
  • Adiabatic Process of the Ideal Gas
  • Problems
  • Heat Machines
  • Entropy and Thermodynamic Potentials
  • Problems
  • The Third Law of Thermodynamics
  • Second Law of Thermodynamics: Carnot's Theorem
  • Entropy Maximum, Thermodynamic Equilibrium, Phase Transitions
• Molecular Theory of Ideal Gases:
  • Basic Assumptions of the Molecular Theory
  • Characteristic Lengths of the Gas
  • Velocity Distribution Function of Molecules
  • Molecular Flux
  • Gas Pressure on the Walls
  • Molecular Interpretation of Temperature and Equipartition of Energy
  • Heat Capacity of the Ideal Gas
  • Maxwell–Boltzmann Distribution Function
  • Characteristic Speeds of Gas Molecules
  • Effusion
  • Problems
• Statistical Physics:
  • Microstates and Macrostates
  • Two-State Particles (Coin Tossing)
  • Stirling Formula and Thermodynamic Probability at Large N
  • Many-State Particles
  • Thermodynamic Probability and Entropy
  • Boltzmann Distribution and Connection with Thermodynamics
  • Quantum States and Energy Levels
  • Statistical Thermodynamics of the Ideal Gas
  • Statistical Thermodynamics of Harmonic Oscillators
  • Statistical Thermodynamics of Rotators
  • Statistical Physics of Vibrations in Solids
  • Problems
  • Spins in Magnetic Field
  • Phase Transitions and the Mean-Field Approximation
  • 1D Ising Model
  • Problems
  • The Grand Canonical Ensemble
  • Statistics of Noninteracting Indistinguishable Particles
  • Bose–Einstein Gas
  • Fermi–Dirac Gas
  • Electromagnetic Radiation (Photon Gas)
  • Problems
• Index

Readership: Undergraduate students in: Physics, Physical Chemistry, Engineering (Mechanical, Chemical, Materials) and Applied Mathematics (with physics electives). Lecturers and instructors teaching: Introductory thermodynamics/statistical physics courses, and one-semester survey courses in thermal and statistical physics. Researchers and professionals seeking: A concise review of foundational thermodynamics and quantum statistics and a structured reference for interdisciplinary applications. Self-learners and enthusiasts with: A strong mathematical/physics background looking to grasp core thermal physics concepts in a single semester structure.