Contents -- I: Preliminaries -- 1 Introduction -- 1.1 What is a mole? -- 1.2 The thermodynamic limit -- 1.3 The ideal gas -- 1.4 Combinatorial problems -- 1.5 Plan of the book -- Exercises -- 2 Heat -- 2.1 A definition of heat -- 2.2 Heat capacity -- Exercises -- 3 Probability -- 3.1 Discrete probability distributions -- 3.2 Continuous probability distributions -- 3.3 Linear transformation -- 3.4 Variance -- 3.5 Linear transformation and the variance -- 3.6 Independent variables -- Further reading -- Exercises -- 4 Temperature and the Boltzmann factor -- 4.1 Thermal equilibrium -- 4.2 Thermometers -- 4.3 The microstates and macrostates -- 4.4 A statistical definition of temperature -- 4.5 Ensembles -- 4.6 Canonical ensemble -- 4.7 Applications of the Boltzmann distribution -- Further reading -- Exercises -- II: Kinetic theory of gases -- 5 The Maxwell-Boltzmann distribution -- 5.1 The velocity distribution -- 5.2 The speed distribution -- 5.3 Experimental justification -- Exercises -- 6 Pressure -- 6.1 Molecular distributions -- 6.2 The ideal gas law -- 6.3 Dalton's law -- Exercises -- 7 Molecular effusion -- 7.1 Flux -- 7.2 Effusion -- Exercises -- 8 The mean free path and collisions -- 8.1 The mean collision time -- 8.2 The collision cross-section -- 8.3 The mean free path -- Exercises -- III: Transport and thermal diffusion -- 9 Transport properties in gases -- 9.1 Viscosity -- 9.2 Thermal conductivity -- 9.3 Diffusion -- 9.4 More-detailed theory -- Further reading -- Exercises -- 10 The thermal diffusion equation -- 10.1 Derivation of the thermal diffusion equation -- 10.2 The one-dimensional thermal diffusion equation -- 10.3 The steady state -- 10.4 The thermal diffusion equation for a sphere -- 10.5 Newton's law of cooling -- 10.6 The Prandtl number -- 10.7 Sources of heat -- Exercises -- IV: The first law -- 11 Energy.

11.1 Some definitions -- 11.2 The first law of thermodynamics -- 11.3 Heat capacity -- Exercises -- 12 Isothermal and adiabatic processes -- 12.1 Reversibility -- 12.2 Isothermal expansion of an ideal gas -- 12.3 Adiabatic expansion of an ideal gas -- 12.4 Adiabatic atmosphere -- Exercises -- V: The second law -- 13 Heat engines and the second law -- 13.1 The second law of thermodynamics -- 13.2 The Carnot engine -- 13.3 Carnot's theorem -- 13.4 Equivalence of Clausius and Kelvin statements -- 13.5 Examples of heat engines -- 13.6 Heat engines running backwards -- 13.7 Clausius' theorem -- Further reading -- Exercises -- 14 Entropy -- 14.1 Definition of entropy -- 14.2 Irreversible change -- 14.3 The first law revisited -- 14.4 The Joule expansion -- 14.5 The statistical basis for entropy -- 14.6 The entropy of mixing -- 14.7 Maxwell's demon -- 14.8 Entropy and probability -- Exercises -- 15 Information theory -- 15.1 Information and Shannon entropy -- 15.2 Information and thermodynamics -- 15.3 Data compression -- 15.4 Quantum information -- Further reading -- Exercises -- VI: Thermodynamics in action -- 16 Thermodynamic potentials -- 16.1 Internal energy, U -- 16.2 Enthalpy, H -- 16.3 Helmholtz function, F -- 16.4 Gibbs function, G. -- 16.5 Availability -- 16.6 Maxwell's relations -- Exercises -- 17 Rods, bubbles and magnets -- 17.1 Elastic rod -- 17.2 Surface tension -- 17.3 Paramagnetism -- Exercises -- 18 The third law -- 18.1 Different statements of the third law -- 18.2 Consequences of the third law -- Exercises -- VII: Statistical mechanics -- 19 Equipartition of energy -- 19.1 Equipartition theorem -- 19.2 Applications -- 19.3 Assumptions made -- 19.4 Brownian motion -- Exercises -- 20 The partition function -- 20.1 Writing down the partition function -- 20.2 Obtaining the functions of state -- 20.3 The big idea.

20.4 Combining partition functions -- Exercises -- 21 Statistical mechanics of an ideal gas -- 21.1 Density of states -- 21.2 Quantum concentration -- 21.3 Distinguishability -- 21.4 Functions of state of the ideal gas -- 21.5 Gibbs paradox -- 21.6 Heat capacity of a diatomic gas -- Exercises -- 22 The chemical potential -- 22.1 A definition of the chemical potential -- 22.2 The meaning of the chemical potential -- 22.3 Grand partition function -- 22.4 Grand potential -- 22.5 Chemical potential as Gibbs function per particle -- 22.6 Many types of particle -- 22.7 Particle number conservation laws -- 22.8 Chemical potential and chemical reactions -- Further reading -- Exercises -- 23 Photons -- 23.1 The classical thermodynamics of electromagnetic radiation -- 23.2 Spectral energy density -- 23.3 Kirchhoff's law -- 23.4 Radiation pressure -- 23.5 The statistical mechanics of the photon gas -- 23.6 Black body distribution -- 23.7 Cosmic Microwave Background radiation -- 23.8 The Einstein A and B coefficients -- Further reading -- Exercises -- 24 Phonons -- 24.1 The Einstein model -- 24.2 The Debye model -- 24.3 Phonon dispersion -- Further reading -- Exercises -- VIII: Beyond the ideal gas -- 25 Relativistic gases -- 25.1 Relativistic dispersion relation for massive particles -- 25.2 The ultrarelativistic gas -- 25.3 Adiabatic expansion of an ultrarelativistic gas -- Exercises -- 26 Real gases -- 26.1 The van der Waals gas -- 26.2 The Dieterici equation -- 26.3 Virial expansion -- 26.4 The law of corresponding states -- Exercises -- 27 Cooling real gases -- 27.1 The Joule expansion -- 27.2 Isothermal expansion -- 27.3 Joule-Kelvin expansion -- 27.4 Liquefaction of gases -- Exercises -- 28 Phase transitions -- 28.1 Latent heat -- 28.2 Chemical potential and phase changes -- 28.3 The Clausius-Clapeyron equation -- 28.4 Stability & metastability.

28.5 The Gibbs phase rule -- 28.6 Colligative properties -- 28.7 Classification of phase transitions -- Further reading -- Exercises -- 29 Bose-Einstein and Fermi-Dirac distributions -- 29.1 Exchange and symmetry -- 29.2 Wave functions of identical particles -- 29.3 The statistics of identical particles -- Further reading -- Exercises -- 30 Quantum gases and condensates -- 30.1 The non-interacting quantum fluid -- 30.2 The Fermi gas -- 30.3 The Bose gas -- 30.4 Bose-Einstein condensation (BEC) -- Further reading -- Exercises -- IX: Special topics -- 31 Sound waves -- 31.1 Sound waves under isothermal conditions -- 31.2 Sound waves under adiabatic conditions -- 31.3 Are sound waves in general adiabatic or isothermal? -- 31.4 Derivation of the speed of sound within fluids -- Further reading -- Exercises -- 32 Shock waves -- 32.1 The Mach number -- 32.2 Structure of shock waves -- 32.3 Shock conservation laws -- 32.4 The Rankine-Hugoniot conditions -- Further reading -- Exercises -- 33 Brownian motion and fluctuations -- 33.1 Brownian motion -- 33.2 Johnson noise -- 33.3 Fluctuations -- 33.4 Fluctuations and the availability -- 33.5 Linear response -- 33.6 Correlation functions -- Further reading -- Exercises -- 34 Non-equilibrium thermodynamics -- 34.1 Entropy production -- 34.2 The kinetic coefficients -- 34.3 Proof of the Onsager reciprocal relations -- 34.4 Thermoelectricity -- 34.5 Time reversal and the arrow of time -- Further reading -- Exercises -- 35 Stars -- 35.1 Gravitational interaction -- 35.2 Nuclear reactions -- 35.3 Heat transfer -- Further reading -- Exercises -- 36 Compact objects -- 36.1 Electron degeneracy pressure -- 36.2 White dwarfs -- 36.3 Neutron stars -- 36.4 Black holes -- 36.5 Accretion -- 36.6 Black holes and entropy -- 36.7 Life, the Universe and Entropy -- Further reading -- Exercises -- 37 Earth's atmosphere.

37.1 Solar energy -- 37.2 The temperature profile in the atmosphere -- 37.3 The greenhouse effect -- Further reading -- Exercises -- A: Fundamental constants -- B: Useful formulae -- C: Useful mathematics -- C.1 The factorial integral -- C.2 The Gaussian integral -- C.3 Stirling's formula -- C.4 Riemann zeta function -- C.5 The polylogarithm -- C.6 Partial derivatives -- C.7 Exact differentials -- C.8 Volume of a hypersphere -- C.9 Jacobians -- C.10 The Dirac delta function -- C.11 Fourier transforms -- C.12 Solution of the diffusion equation -- C.13 Lagrange multipliers -- D: The electromagnetic spectrum -- E: Some thermodynamical definitions -- F: Thermodynamic expansion formulae -- G: Reduced mass -- H: Glossary of main symbols -- I: Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.