Thermal Physics

Gases, Entropy and the Statistics of Many Particles in 16 chapters — from “Temperature, pressure and the kinetic theory of gases” to “Photons and phonons: blackbody radiation and the heat capacity of solids”.

Chapters

  1. Temperature, pressure and the kinetic theory of gases
    • The ideal gas law per particle
    • Pressure from wall collisions
    • Temperature as mean kinetic energy
    • Equipartition of energy
    • The velocity distribution function
    • The Maxwell-Boltzmann speed distribution
    • Characteristic speeds of a gas
    • Problems
  2. Collisions, mean free path and transport in gases
    • The mean free path
    • Collision rate and collision time
    • Effusion through a small hole
    • The transport coefficient
    • Viscosity and thermal conductivity of a dilute gas
    • The self-diffusion coefficient
    • Problems
  3. The first law: work, heat and internal energy
    • Internal energy as a state function
    • Work and heat as energy in transit
    • Partial derivatives and heat capacities
    • Isothermal and quasistatic adiabatic processes
    • Two cycles of quasistatic work
    • Problems
  4. Heat engines, refrigerators and the Carnot cycle
    • Heat engine efficiency
    • The Kelvin and Clausius statements
    • The Carnot cycle on an ideal gas
    • Carnot's theorem and the thermodynamic temperature scale
    • Refrigerators and the coefficient of performance
    • Problems
  5. Internal-combustion cycles and indicator diagrams
    • The indicator diagram of a real engine
    • The air-standard idealisation
    • The Otto cycle and the compression ratio
    • The Diesel cycle and the cut-off ratio
    • Problems
  6. The second law, entropy and irreversibility
    • The Clausius inequality
    • Entropy as a state function
    • The entropy of the ideal gas
    • The reversible-path method
    • The entropy increase principle and lost work
    • Three entropy ledgers with lost work
    • The thermodynamic identity
    • Temperature as an entropy derivative
    • Problems
  7. Thermodynamic potentials, Legendre transforms and Maxwell relations
    • Natural variables of a potential
    • Exact differentials and mixed partials
    • The Legendre transform
    • Enthalpy, Helmholtz and Gibbs free energies
    • The four Maxwell relations
    • The free energy minimum principle
    • The energy equation of a gas
    • Problems
  8. Chemical potential, open systems and chemical equilibrium
    • The chemical potential
    • Direction of particle flow
    • Chemical potential of the ideal gas
    • Chemical potential in an external field
    • The entropy of mixing
    • The law of mass action
    • Osmotic pressure
    • Problems
  9. Phase coexistence and the Clausius-Clapeyron relation
    • Reading the phase diagram
    • The phase coexistence condition
    • The Clausius-Clapeyron relation
    • The vapour-pressure curve
    • First-order transitions and metastability
    • The Gibbs phase rule
    • The mixture phase diagram
    • Problems
  10. Probability, random walks and the statistics of large numbers
    • Probability as ensemble frequency
    • Mean and variance of a sum
    • The binomial distribution
    • Stirling's approximation for large factorials
    • The Gaussian limit of the binomial
    • The one over root N rule
    • The random walk and diffusion
    • Problems
  11. Microstates, multiplicity and the statistical entropy
    • Microstate, macrostate and multiplicity
    • Equal a priori probabilities
    • The most probable macrostate of two solids
    • Boltzmann entropy and temperature
    • The Gibbs entropy formula
    • State counting in a box
    • Identical particles and the Gibbs paradox
    • Problems
  12. The Boltzmann factor, the canonical ensemble and the partition function
    • The reservoir and the Boltzmann factor
    • The partition function and what it counts
    • Mean energy from the partition function
    • Free energy from the partition function
    • Factorisation of the partition function
    • Equipartition from the Boltzmann factor
    • Speed distribution from the Boltzmann factor
    • Problems
  13. Two-level systems, paramagnets and the Einstein solid
    • The two-level system
    • The Schottky anomaly
    • The two-state paramagnet and Curie's law
    • Negative temperature
    • The Einstein heat capacity
    • Freezing out of degrees of freedom
    • Problems
  14. The classical ideal gas from the partition function
    • The single-particle partition function
    • The N-particle partition function
    • The ideal gas from the partition function
    • The Sackur-Tetrode entropy
    • The chemical potential from the partition function
    • Internal degrees of freedom
    • The classical limit condition
    • Problems
  15. The grand canonical ensemble, ensemble equivalence and fluctuations
    • The Gibbs factor
    • The grand partition function and grand potential
    • Energy fluctuations
    • Number fluctuations
    • Ensemble equivalence
    • The Langmuir isotherm
    • Problems
  16. Photons and phonons: blackbody radiation and the heat capacity of solids
    • The Planck oscillator mean energy
    • Mode counting in a cavity
    • The Planck spectrum and its limits
    • The photon gas chemical potential
    • Stefan-Boltzmann law and Wien displacement law
    • Stefan-Boltzmann law for the Sun and the planets
    • Phonons and the Debye model
    • Problems