1 How to use this book
1.1 For the student
1.2 For the teacher
2 Introducing thermodynamics
3 A survey of thermodynamic ideas
3.1 Energy and entropy
3.2 Concepts and terminology
3.2.1 System
3.2.2 State
3.2.3 Extensive, intensive
3.2.4 Thermodynamic equilibrium
3.2.5 Temperature
3.2.6 Quasistatic
3.2.7 Reversible and irreversible
3.2.8 Adiathermal, isentropic, adiabatic, isothermal
3.2.9 Expansion coefficients, heat capacities
3.2.10 Thermal reservoir
3.3 The laws of thermodynamics
3.4 Where we are heading
Exercises
4 Some general knowledge
4.1 Density, heat capacity
4.2 Moles
4.3 Boltzmann constant, gas constant
4.4 Pressure and STP
4.5 Latent heat
4.6 Magnetic properties
5 Mathematical tools
5.1 Working with partial derivatives
5.1.1 Reciprocal and reciprocity theorems
5.1.2 Integrating
5.1.3 Mixed derivatives
5.2 Proper and improper differentials, function of state
5.2.1 Integrating factor
5.3 Some further observations
5.3.1 Alternative derivation of reciprocal and reciprocity theorems
5.3.2 Integration in general
Exercises
6 Zeroth law, equation of state
6.1 Empirical temperature
6.1.1 Equation of state
6.1.2 Algebraic argument ()
6.2 Some example equations of state
6.2.1 Ideal gas
6.2.2 Thermal radiation
6.2.3 Solids and wires
6.2.4 Paramagnetic material
6.2.5 Equations of state for other properties
6.3 Thermometry
Exercises
7 First law, internal energy
7.1 Defining internal energy
7.1.1 Heat and work
7.2 Work by compression
7.3 Heat capacities
7.3.1 Energy equation
7.3.2 Relation of compressibilitiesand heat capacities
7.4 Solving thermodynamic problems
7.5 Expansion
7.5.1 Free expansion of ideal gas
7.5.2 Adiabatic expansion of ideal gas
7.5.3 Adiabatic atmosphere
7.5.4 Fast and yet adiabatic?
Exercises
8 The second law and entropy
8.1 Heat engines and the Carnot cycle
8.1.1 Heat pumps and refrigerators
8.1.2 Two impossible things (equivalence of Kelvin and Clausius statements)
8.2 Carnot's theorem and absolute temperature
8.2.1 Carnot's theorem: reversible engines are equally, and the most, efficient
8.2.2 Existence of an absolute temperature measure
8.2.3 Hot heat is more valuable than cold heat
8.3 Clausius' theorem and entropy
8.4 The first and second laws together
8.5 Summary
Exercises
9 Understanding entropy
9.1 Examples
9.1.1 Entropy content
9.1.2 Entropy production and entropy flow
9.2 But what is it?
9.2.1 Entropy increase in a free expansion
9.3 Gibbs' paradox
9.3.1 Entropy of mixing
9.3.2 Reversible mixing
9.4 Specific heat anomalies
9.5 Maxwell's daemon
9.5.1 Szilard engine
9.5.2 The Feynman–Smoluchowski ratchet
9.6 The principle of detailed balance
9.7 Adiabatic surfaces ()
9.8 Irreversibility in the universe
Exercises
10 Heat flow and thermal relaxation
10.1 Thermal conduction; diffusion equation
10.1.1 Steady state
10.1.2 Time-dependent
10.2 Relaxation time
10.3 Speed of sound ()
10.3.1 Ultra-relativistic gas
Exercises
11 Practical heat engines
11.1 The maximum work theorem
11.1.1 Imperfections
11.2 Otto cycle
Exercises
12 Introducing chemical potential
12.1 Chemical potential of anideal gas
12.1.1 Example: the isothermal atmosphere
12.2 Saha equation ()
Exercises
13 Functions and methods
13.1 The fundamental relation
13.1.1 Euler relation, Gibbs–Duhem relation
13.2 Thermodynamic potentials
13.2.1 Free energy as a form of potential energy
13.2.2 Natural variables and thermodynamic potentials
13.2.3 Maxwell relations
13.2.4 Obtaining one potential function from another
13.3 Basic results for closed systems
13.3.1 Relating internal energy to equation of state
13.3.2 Sackur–Tetrode equation
13.3.3 Complete thermodynamic information
Exercises
14 Elastic bands, rods, bubbles, magnets
14.1 Expressions for work
14.2 Rods, wires, elastic bands
14.3 Surface tension
14.4 Paramagnetism
14.4.1 Ideal paramagnet
14.4.2 Cooling by adiabatic demagnetization
14.5 Electric and magnetic work ()
14.5.1 Dielectrics and polarization
14.5.2 Magnetic work
14.6 Introduction to the partition function ()
Exercises
15 Modelling real gases
15.1 van der Waals gas
15.1.1 Phase change
15.1.2 Critical parameters and the law of corresponding states
15.2 Redlich–Kwong, Dieterici, and Peng–Robinson gas
Exercises
16 Expansion and flow processes
16.1 Expansion coefficients
16.2 U: free expansion
16.2.1 Deriving the equation of state of an ideal gas
16.3 H: throttle process: Joule–Kelvin expansion
16.3.1 Bernoulli equation
16.3.2 Cooling and liquification of gases
16.4 General flow process
16.4.1 S and H: the gas turbine
Exercises
17 Stability and free energy
17.1 Isolated system: maximum entropy
17.1.1 Equilibrium condition with internal restrictions
17.1.2 The minimum energy principle
17.1.3 Stability
17.2 Phase change
17.3 Free energy and availability
17.3.1 Free energy and equilibrium
Exercises
18 Reinventing the subject
18.1 Some basic derivations from maximum entropy
18.2 Carathéodory formulation of the second law ()
18.3 Negative temperature ()
19 Thermal radiation
19.1 Some general observations about thermal radiation
19.1.1 Black body radiation: a first look
19.2 Basic thermodynamic arguments
19.2.1 Equation of state and Stefan–Boltzmann law
19.2.2 Comparison with ideal gas
19.2.3 Adiabatic expansion and Wien's laws ()
19.3 Cosmic microwave background radiation
Exercises
20 Radiative heat transfer
20.1 The greenhouse effect
Exercises
21 Chemical reactions
21.1 Basic considerations
21.1.1 Reaction rate
21.2 Chemical equilibrium and the law of mass action
21.2.1 Van 't Hoff equation
21.2.2 Chemical terminology
21.3 The reversible electric cell ()
Exercises
22 Phase change
22.1 General introduction
22.1.1 Phase diagram
22.1.2 Some interesting phase diagrams
22.2 Basic properties of first-order phase transitions
22.3 Clausius–Clapeyron equation
22.3.1 Vapour–liquid and liquid–solid coexistence lines
22.3.2 Gibbs phase rule
22.3.3 Behaviour of the chemical potential
22.4 The type-I superconducting transition ()
Exercises
23 The third law
23.1 Response functions
23.2 Unattainability theorem
23.3 Phase change
23.4 Absolute entropy and chemical potential
24 Phase change, nucleation, and solutes
24.1 Treatment of surface effects
24.2 Metastable phases
24.2.1 Nucleation
24.3 Colligative properties
24.3.1 Osmotic pressure
24.3.2 Influence of dissolved particles on phase transitions
24.4 Chapter summary
Exercises
25 Continuous phase transitions
25.1 Order parameter
25.2 Critical exponents
25.3 Landau mean field theory
25.3.1 Application to ferromagnetism
25.4 Binary mixtures
Exercises
26 Self-gravitation and negative heat capacity
26.1 Negative heat capacity
26.1.1 Jeans length
26.2 Black holes and Hawking radiation
Exercises
27 Fluctuations
27.1 Probability of a departure from the maximum entropy point
27.1.1 Is there a violation of the second law?
27.2 Calculating the fluctuations
27.2.1 More general constraints
27.2.2 Some general observations
27.3 Internal flows
27.4 Fluctuation as a function of time
27.5 Johnson noise
Exercises
28 Thermoelectricity and entropy flow
28.1 Thermoelectric effects
28.1.1 Thomson's treatment
28.2 Entropy gradients and Onsager's reciprocal relations
28.2.1 Derivation of Onsager's reciprocal relation
28.2.2 Application
28.2.3 Entropy current, entropy production rate
Exercises
Appendix A Electric and magnetic work
Appendix B More on natural variables and free energy
Appendix C Some mathematical results
Bibliography
Index