A Student's Guide to Entropy

✍ Scribed by Don S. Lemons

• Publisher: Cambridge University Press
• Year: 2013
• Tongue: English
• Leaves: 194
• Category: Library

✦ Synopsis

Striving to explore the subject in as simple a manner as possible, this book helps readers understand the elusive concept of entropy. Innovative aspects of the book include the construction of statistical entropy from desired properties, the derivation of the entropy of classical systems from purely classical assumptions, and a statistical thermodynamics approach to the ideal Fermi and ideal Bose gases. Derivations are worked through step-by-step and important applications are highlighted in over 20 worked examples. Around 50 end-of-chapter exercises test readers' understanding. The book also features a glossary giving definitions for all essential terms, a time line showing important developments, and list of books for further study. It is an ideal supplement to undergraduate courses in physics, engineering, chemistry and mathematics.

Focuses on foundations and illustrative examples to help readers understand the origin and purposes of the concept of entropy
Treats entropy across a range of topics, from thermodynamics, classical and quantum statistical mechanics, and information theory
Gives expanded derivations, taking readers through each one step by step

✦ Table of Contents

Preface
1 Thermodynamic entropy
1.1 Thermodynamics and entropy
1.2 Reversible and irreversible processes
Thermodynamic reversibility
Loschmidt’s paradox
Example 1.1 Reversible or irreversible?
1.3 The second law of thermodynamics
Heat reservoirs
The second law and irreversibility
1.4 Entropy and irreversibility
Entropy difference
1.5 Quantifying irreversibility
Applying additivity
Entropy generation in a two-reservoir isolated system
Reversible heating and cooling
Summary
Example 1.2 Joule expansion
Example 1.3 Humpty Dumpty
1.6 The Carnot efi ciency and Carnot’s theorem
1.7 Absolute or thermodynamic temperature
Temperature
Absolute temperature scales
The entropy increment
The universality and simplicity of absolute temperatures
1.8 Consequences of the second law
Entropy and stability
Example 1.4 Automobile engine efi ciency
Example 1.5 The entropy generator
1.9 Equations of state
Reversible work
Fluid systems
An example
Working backwards
A summary
Example 1.6 Modifying the ideal gas
1.10 The third law of thermodynamics
An illustration
Example 1.7 The third law and blackbody radiation
Problems
1.1 Compressing a l uid
1.2 Derivation
1.3 Heat capacity
1.4 Isothermal compression of ideal gas
1.5 Entropy increment
1.6 Valid and invalid equations of state
1.7 Entropy function
1.8 Room-temperature solid
1.9 Valid and invalid entropy functions
2 Statistical entropy
2.1 Boltzmann and atoms
2.2 Microstates and macrostates
Generalizations
Distinguishable classical particles
2.3 Fundamental postulate
Multiplicity
Limitations and counter-examples
Thermodynamic systems
Improbable macrostates
Example 2.1 Uniform density
2.4 Statistical entropy and multiplicity
Dependence of entropy on macrostate multiplicity
Additivity
Independence
Exploiting derivatives
The meaning of “constant”
The statistical entropy of an isolated system
Alternate forms
The entropy of a non-isolated system
The limits of classical statistical thermodynamics
Example 2.2 Joule expansion
Example 2.3 A paradox
Example 2.4 Entropy of mixing
2.5 Maxwell’s demon
The entropy of a non-equilibrium system
2.6 Relative versus absolute entropy
Problems
2.1 Probabilities
2.2 Playing card multiplicities
2.3 Stirling’s approximation
2.4 The art of counting
2.5 Rubber elasticity
3 Entropy of classical systems
3.1 Ideal gas: volume dependence
3.2 Ideal gas: volume and energy dependence
Discretizing phase space
The multiplicity
Summary
3.3 Imposing extensivity
Example 3.1 Extensivity of blackbody radiation
3.4 Occupation numbers
Maximizing the entropy
Single-particle partition function
Eliminating
Maxwell–Boltzmann distribution
Summary
3.5 Ideal classical gas
3.6 Ideal classical solid
Equipartition theorem
The entropy of an ideal classical solid
Example 3.2 Average kinetic energy
3.7 Boltzmann’s tomb
Problems
3.1 Room temperature density
3.2 Van der Waals equations of state
3.3 Ideal gas of diatomic molecules
3.4 Mixing of ideal gases
3.5 Extensivity of ideal solid
3.6 Room temperature speed of N 2 molecules
4 Entropy of quantized systems
4.1 Quantum conditions
4.2 Quantized harmonic oscillators
Oscillator energy quantized
Oscillator phase space quantized
Oscillator entropy
Three-dimensional oscillators
Example 4.1 Correspondence principle
4.3 Einstein solid
4.4 Phonons
Indistinguishable particles and distinguishable places
4.5 Third law
Planck’s convention
Constructing the entropy
Example 4.2 Shottky defect
4.6 Paramagnetism
Entropy
Energy equation of state
4.7 Negative absolute temperature
Experimental realization
Problems
4.1 Oscillator entropy
4.2 Nitrogen molecules
4.3 Correspondence principle
4.4 Two-level system
4.5 Entropy maximum
4.6 Third law limit
4.7 Chemical potential
4.8 Frequency of paramagnet orientations
4.9 Heat capacity of a paramagnet
4.10 Curie’s law
5 Entropy of a non-isolated system
5.1 Beyond the fundamental postulate
Ensembles
5.2 The Gibbs entropy formula
Random variables
Eponymy
5.3 Canonical ensemble
5.4 Partition functions
5.5 Entropy metaphors
Problems
5.1 Canonical ensemble of Shottky defects
5.2 The Gibbs entropy formula
6 Entropy of fermion systems
6.1 Symmetries and wave functions
The spin-statistics theorem and the Pauli principle
6.2 Intrinsic semiconductors
Entropy
6.3 Ideal Fermi gas
The multiplicity of distinguishable particles
The multiplicity of an ideal Fermi gas
The entropy
Low occupancy regime
Equations of state
Low temperature regime
Ground state
6.4 Average energy approximation
Example 6.1 conduction electrons nuclei and white dwarfs
Problems
6.1 Extensivity
6.2 De Broglie wavelength
6.3 Heat capacity
6.4 Laser fusion
6.5 White dwarfs
7 Entropy of systems of bosons
7.1 Photons
Photons
Complementarity
7.2 Blackbody radiation
Example 7.1 Stefan–Boltzmann law and the radiation constant
7.3 Ideal Bose gas
The multiplicity of an ideal Bose gas
The entropy
Low occupancy regime
Equations of state
Low temperature regime
Ground state
Thermodynamic instability
7.4 Bose–Einstein condensate
Two-phase regime
7.5 Modeling the ideal gas
Average energy approximation
Quantum and classical descriptions
Problems
7.1 Radiation pressure
7.2 Radiation pressure at the center of the Sun
7.3 Maximum radiation
7.4 Number of photons
7.5 Two-phase energy
7.6 Photon condensate?
7.7 Heat capacity of ideal Bose gas and condensate
8 Entropy of information
8.1 Messages and message sources
8.2 Hartley’s information
An application
The symbol H
Example 8.1 Shufl ed deck
8.3 Information and entropy
Missing information
Example 8.2 Missing information
8.4 Shannon entropy
Constructing the Shannon entropy
Reduction to expected results
Example 8.3 Two symbols
Example 8.4 Entropy of English text
8.5 Fano code
8.6 Data compression and error correction
Lossy data compression
Error correction
8.7 Missing information and statistical physics
Microcanonical ensemble
Canonical ensemble
The information theoretic approach to statistical mechanics
Problems
8.1 Deriving the logarithm
8.2 Information content
8.3 Block coding
8.4 Information from a grade?
8.5 Impossible outcome
8.6 Efi cient Fano code
8.7 Hamming error correction
Epilogue What is entropy?
Appendix I Physical constants and standard dei nitions
Appendix II Formulary
Appendix III Glossary
Appendix IV Time line
Appendix V Answers to problems
Appendix VI Annotated further reading
Index

✦ Subjects

Физика;Термодинамика, молекулярная и статистическая физика;