Thermodynamics

Thermodynamics & Statistical Mechanics in 10 chapters — from “Temperature, Heat, and the Zeroth Law” to “Beyond: Toward Statistical Mechanics”.

Chapters

  1. Temperature, Heat, and the Zeroth Law
    • Thermal Equilibrium and the Zeroth Law
    • Defining Temperature Operationally
    • Temperature Scales: Celsius and Kelvin
    • Heat as Energy Transfer
    • Heat Capacity and Calorimetry
  2. Equations of State and Kinetic Theory
    • The Ideal Gas: Empirical Observations
    • Kinetic Theory: Derivation of the Ideal Gas Law
    • The Equipartition Theorem
    • Real Gases and the Van der Waals Equation
    • Equations of State for Other Systems
    • Worked Examples and Applications
  3. The First Law of Thermodynamics
    • Energy Conservation and the First Law
    • Heat and Work Are Path-Dependent
    • Work in Reversible Processes
    • Heat Capacities and Internal Energy
    • Cyclic Processes and the First Law
  4. Heat Engines and the Carnot Cycle
    • Heat Engines: Converting Heat to Work
    • The Carnot Cycle
    • Carnot's Theorem and the Second Law
    • Refrigerators and Heat Pumps
    • Real Engines and Practical Limits
  5. Entropy: Definition and the Clausius Inequality
    • Motivation: Why the Carnot Efficiency Points to a State Function
    • Definition of Entropy
    • The Clausius Inequality
    • The Second Law as Entropy Increase
    • Calculating Entropy Changes for Ideal Gases
    • Worked Example: Free Expansion into Vacuum
    • Entropy and Irreversibility
  6. The Boltzmann Interpretation: Entropy as a Count
    • Macrostates, Microstates, and the Multiplicity Function
    • The Boltzmann Formula: S=kB​lnΩ
    • The Spin-1/2 Paramagnet
    • The Two-State Schottky System
    • The Third Law of Thermodynamics
    • The Meaning of Equilibrium: Maximum Multiplicity
  7. Helmholtz and Gibbs Free Energies
    • Why We Need New Potentials
    • The Helmholtz Free Energy
    • Enthalpy
    • The Gibbs Free Energy
    • Applications: Spontaneity and Equilibrium Criteria
  8. The Canonical Ensemble and the Partition Function
    • The Canonical Ensemble: A System in Thermal Contact
    • The Partition Function Z
    • Thermodynamic Quantities from Z
    • Example: The Quantum Harmonic Oscillator
    • Example: The Two-State System
    • Fluctuations and Higher Moments
    • Summary and the Road Ahead
  9. Phase Transitions and the Clausius-Clapeyron Relation
    • Phases of Matter and the Gibbs Phase Rule
    • First-Order Phase Transitions
    • Worked Example: The Phase Diagram of Water
    • The Triple Point and Critical Point
    • Second-Order Phase Transitions
    • Limitations and Extensions
  10. Beyond: Toward Statistical Mechanics
    • The Bridge from Thermodynamics to Statistical Mechanics
    • Quantum Statistics: When Identity Matters
    • The Grand Canonical Ensemble
    • Phase Transitions and the Ising Model
    • The Renormalisation Group: Zooming Out
    • Beyond Equilibrium
    • Where to Go from Here