An Introduction to Thermal Physics

Preface

Part I: Fundamentals

Chapter 1: Energy in Thermal Physics

1.1
Thermal Equilibrium
1.2
The Ideal Gas
Microscopic Model of an Ideal Gas
1.3
Equipartition of Energy
1.4
Heat and Work
1.5
Compression Work
Compression of an Ideal Gas [problems]
1.6
Heat Capacities
Latent Heat; Enthalpy
1.7
Rates of Processes
Heat Conduction; Conductivity of an Ideal Gas; Viscosity; Diffusion
Chapter 2: The Second Law
2.1
Two-State Systems
The Two-State Paramagnet
2.2
The Einstein Model of a Solid
2.3
Interacting Systems
2.4
Large Systems
Very Large Numbers; Stirling's Approximation;
Multiplicity of a Large Einstein Solid;
Sharpness of the Multiplicity Function
2.5
The Ideal Gas
Multiplicity of a Monatomic Ideal Gas; Interacting Ideal Gases
2.6
Entropy
Entropy of an Ideal Gas; Entropy of Mixing;
Reversible and Irreversible Processes
Chapter 3: Interactions and Implications
3.1
Temperature
A Silly Analogy; Real-World Examples
3.2
Entropy and Heat
Predicting Heat Capacities; Measuring Entropies;
The Macroscopic View of Entropy
3.3
Paramagnetism
Notation and Microscopic Physics; Numerical Solution;
Analytic Solution
3.4
Mechanical Equilibrium and Pressure
The Thermodynamic Identity; Entropy and Heat Revisited
3.5
Diffusive Equilibrium and Chemical Potential
3.6
Summary and a Look Ahead
Part II: Thermodynamics
Chapter 4: Engines and Refrigerators

4.1
Heat Engines
The Carnot Cycle
4.2
Refrigerators
4.3
Real Heat Engines
Internal Combustion Engines; The Steam Engine
4.4
Real Refrigerators
The Throttling Process; Liquefaction of Gases;
Toward Absolute Zero
Chapter 5: Free Energy and Chemical Thermodynamics
5.1
Free Energy as Available Work
Electrolysis, Fuel Cells, and Batteries; Thermodynamic Identities
5.2
Free Energy as a Force toward Equilibrium
Extensive and Intensive Quantities; Gibbs Free Energy
and Chemical Potential
5.3
Phase Transformations of Pure Substances
Diamonds and Graphite; The Clausius-Clapeyron Relation;
The van der Waals Model
5.4
Phase Transformations of Mixtures
Free Energy of a Mixture; Phase Changes of a Miscible Mixture;
Phase Changes of a Eutectic System
5.5
Dilute Solutions
Solvent and Solute Chemical Potentials; Osmotic Pressure;
Boiling and Freezing Points
5.6
Chemical Equilibrium
Nitrogen Fixation; Dissociation of Water; Oxygen Dissolving
in Water; Ionization of Hydrogen
Part III: Statistical Mechanics
Chapter 6: Boltzmann Statistics

6.1
The Boltzmann Factor
The Partition Function; Thermal Excitation of Atoms
6.2
Average Values
Paramagnetism; Rotation of Diatomic Molecules
6.3
The Equipartition Theorem
6.4
The Maxwell Speed Distribution
6.5
Partition Functions and Free Energy
6.6
Partition Functions for Composite Systems
6.7
Ideal Gas Revisited
The Partition Function; Predictions
Chapter 7: Quantum Statistics
7.1
The Gibbs Factor
An Example: Carbon Monoxide Poisoning
7.2
Bosons and Fermions
The Distribution Functions
7.3
Degenerate Fermi Gases
Zero Temperature; Small Nonzero Temperatures;
The Density of States; The Sommerfeld Expansion
7.4
Blackbody Radiation
The Ultraviolet Catastrophe; The Planck Distribution; Photons;
Summing over Modes; The Planck Spectrum; Total Energy;
Entropy of a Photon Gas; The Cosmic Background Radiation;
Photons Escaping through a Hole; Radiation from Other Objects;
The Sun and the Earth
7.5
Debye Theory of Solids
7.6
Bose-Einstein Condensation
Real-World Examples; Why Does it Happen?
Chapter 8: Systems of Interacting Particles
8.1
Weakly Interacting Gases
The Partition Function; The Cluster Expansion;
The Second Virial Coefficient
8.2
The Ising Model of a Ferromagnet
Exact Solution in One Dimension; The Mean Field Approximation;
Monte Carlo Simulation
* * *
Appendix A: Elements of Quantum Mechanics

A.1
Evidence for Wave-Particle Duality
The Photoelectric Effect; Electron Diffraction
A.2
Wavefunctions
The Uncertainty Principle; Linearly Independent Wavefunctions
A.3
Definite-Energy Wavefunctions
The Particle in a Box; The Harmonic Oscillator;
The Hydrogen Atom
A.4
Angular Momentum
Rotating Molecules; Spin
A.5
Systems of Many Particles
A.6
Quantum Field Theory
Appendix B: Mathematical Results
B.1
Gaussian Integrals
B.2
The Gamma Function
B.3
Stirling's Approximation
B.4
Area of a d-Dimensional Hypersphere
B.5
Integrals of Quantum Statistics
Suggested Reading

Reference Data
Index
Further topics covered in the problems include:

Thermal expansion coefficients
The exponential atmosphere
The virial expansion for nonideal gases
Gas escaping through a hole (effusion)
Speed of sound in an ideal gas
Convection in earth's atmosphere (adiabatic lapse rate)
Climbing Mt. Ogden
Temperature and heat capacity of a star
One-dimensional random walk and diffusion
Entropy and temperature of a black hole
Thermodynamics of computing
Heat capacity of an Einstein solid
A simple model of a rubber band
Chemical potential in a gravitational field
Thermal pollution
Maximizing the power of a Carnot engine
Heat pump
Absorption refrigerator
Carnot's theorem
Efficiency of the Otto and Diesel cycles
The Stirling engine
Efficiency of steam and refrigeration cycles
Limits on magnetic cooling and laser cooling
Glucose metabolism and muscle contraction
Maxwell relations and their applications
Magnetic work and magnetic analogues of H and G
The grand free energy
Efficiency of an ice engine
The helium-3 phase diagram
The calcite-aragonite phase diagram
The aluminosilicate phase diagram
Equilibrium in a solid-solid reaction
Integrating the Clausius-Clapeyron equation
Condensation and cloud formation
Wet adiabatic lapse rate
Nucleation of water droplets
Magnetic analogue of the Clausius-Clapeyron relation
Helmholtz free energy of a van der Waals fluid
Critical exponents of a van der Waals fluid
A simple model of mixing energy
Purifying nitrogen and oxygen
Phase diagrams for systems with azeotropes
Phase diagram for a peritectic system
Desalination by reverse osmosis
Temperature dependence of equilibrium constants
Acid rain, with and without sulfates
Rotational excitations of interstellar CN molecules
Protons and neutrons in the early universe
Orthohydrogen and parahydrogen at low temperature
Molecules escaping from an atmosphere
Relativistic ideal gas
Cooperative binding in hemoglobin
Relativistic electron gas
White dwarfs and neutron stars
Two-dimensional Fermi gas
Fermi gas at intermediate temperatures
Semiconductors
Electrons, positrons, and neutrinos in the early universe
Efficiency of an incandescent light
Hawking radiation from black holes
Measuring stellar radii
The greenhouse effect
Debye theory of a two-dimensional solid
Magnons
Bose-Einstein condensation of rubidium-87 vapor
Superfluid helium
Heat capacity of a Bose gas
Bose-Einstein condensation in a harmonic trap
Second virial coefficient of an ideal quantum gas
Second virial coefficient of nitrogen
Energy and heat capacity of a weakly interacting gas
Ising model with an external magnetic field
Lattice gas interpretation of the Ising model
Critical exponents of the Ising model
Heat capacity and magnetization of a two-dimensional Ising model
Block spin transformations of the Ising model
The cosmological constant