Contents

• Course details and how to use these notes
  • PC 2352: THERMAL AND STATISTICAL PHYSICS
  
  
• 1. Classical Thermodynamics: the first law
  • 1.1 The First Law of Thermodynamics
    • James Joule
  • 1.2 The First Law for Small Changes
    • Notation for finite and infinitesimal changes
  • 1.3 Cycles
  • 1.4 Work
    • Work during free and reversible expansions
    • Example of calculation of work
  • 1.5 Temperature
  
  
• 2. Classical Thermodynamics: The second law
  • 2.1 Heat Engines and Refrigerators
    • Introduction to engines
    • Example: The Otto cycle
    • Details of the Otto cycle
  • 2.2 The Second Law of Thermodynamics
    • Equivalence of Kelvin and Clausius statements of 2nd law.
  • 2.3 Carnot cycles
    • Carnot wins
    • Efficiency of ideal gas Carnot cycle
    • Reversible processes
    • Heat engine examples
  • 2.4 Thermodynamic Temperature
    • Construction of thermodynamic temperature
  • 2.5 Entropy
    • Proof of Clausius's theorem
    • Increase of entropy
  • 2.6 Examples of entropy changes
    • Ex. 1
    • Ex. 2
    • Ex. 3
    • Ex. 4
    • Ex. 5
  • 2.7 The Fundamental Thermodynamic Relation
  • 2.8 Thermodynamic potentials
  • 2.9 The approach to equilibrium
    • Derivation of availability
  • 2.10 Use of Gibbs Free Energy: Phase Transitions
    • Proof of equality of Gibbs free energy at a phase coexistence line
    • The Clausius-Clapeyron Equation
    • Boiling point on Everest
  • 2.11 Available work
    • Example of available work
  • 2.12 Maxwell's Relations
    • The rules of partial differentiation
  • 2.13 Heat Capacities
    • Entropy changes
  • 2.13b Joule-Thomson Expansion
  • 2.14 Systems with more than one component
  • 2.15 Chemical reactions
    • Chemical equilibrium
  
  
• 3. The statistical theory of thermodynamics
  • 3.1 Microstates and Macrostates
    • Ensembles
    • Microstates
  • 3.2 The statistical basis of entropy
    • Equilibrium on the checkerboard
  • 3.3 The spin-half paramagnet
  • 3.4 From entropy to temperature
    • Deriving temperature etc
    • The isolated spin-half paramagnet in a magnetic field
    • The ideal gas, first attempt
  
  
• 4. Statistical Physics of Non-isolated Systems
  • 4.1 The Boltzmann Distribution
    • Derivation of the Boltzmann distribution
  • 4.2 The Partition Function
    • Fluctuations
  • 4.3 Entropy, Helmholtz Free Energy and the Partition Function
    • Entropy in a non-isolated system
  • 4.4 The paramagnet at fixed temperature
    • The N-particle partition function for distinguishable particles
    • Details of the paramagnet calculation
    • Hyperbolic Trigonometry
  • 4.5 Adiabatic demagnetisation and the third law of thermodynamics
    • The real paramagnet
  • 4.6 Vibrational and rotational energy of a diatomic molecule
  • 4.7 Translational energy of a molecule in an ideal gas
    • The Density of States
  • 4.8 The Equipartition Theorem
    • The heat capacity of a crystal
  • 4.9 The ideal gas
    • The N particle partition function for indistinguishable particles.
    • Factorisation of the partition function for independent modes.
  • 4.10 The Maxwell-Boltzmann Distribution
  
  
• 5. Systems with variable particle number
  • 5.1 The Gibbs Distribution
    • The grand potential
  • 5.2 Two examples of the Gibbs Distribution
  • 5.3 Bosons and Fermions
  • 5.4 The ideal gas of bosons or fermions: beyond the classical approximation
  • 5.5 The classical approximation again
  • 5.6 Electrons in a metal
  • 5.7 Black-body radiation
  
  
• Glossary
• Ideal Gas: Recap
• Tutorial Examples sheets
  • PC2352 Examples 1
  • PC2352 Examples 2
  • PC2352 Examples 3
  • PC2352 Examples 4
  • PC2352 Examples 5&6
  • PC2352 Examples 7
  • PC2352 Examples 8
  • PC2352 Examples 9&10
  
  
• Index