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A Student's Guide to Entropy

Book Description

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.

Table of Contents

  1. Coverpage
  2. A Student’s Guide to Entropy
  3. Title page
  4. Copyright page
  5. Contents
  6. Preface
  7. 1 Thermodynamic entropy
    1. 1.1 Thermodynamics and entropy
    2. 1.2 Reversible and irreversible processes
    3. 1.3 The second law of thermodynamics
    4. 1.4 Entropy and irreversibility
    5. 1.5 Quantifying irreversibility
    6. 1.6 The Carnot efficiency and Carnot’s theorem
    7. 1.7 Absolute or thermodynamic temperature
    8. 1.8 Consequences of the second law
    9. 1.9 Equations of state
    10. 1.10 The third law of thermodynamics
    11. Problems
  8. 2 Statistical entropy
    1. 2.1 Boltzmann and atoms
    2. 2.2 Microstates and macrostates
    3. 2.3 Fundamental postulate
    4. 2.4 Statistical entropy and multiplicity
    5. 2.5 Maxwell’s demon
    6. 2.6 Relative versus absolute entropy
    7. Problems
  9. 3 Entropy of classical systems
    1. 3.1 Ideal gas: volume dependence
    2. 3.2 Ideal gas: volume and energy dependence
    3. 3.3 Imposing extensivity
    4. 3.4 Occupation numbers
    5. 3.5 Ideal classical gas
    6. 3.6 Ideal classical solid
    7. 3.7 Boltzmann’s tomb
    8. Problems
  10. 4 Entropy of quantized systems
    1. 4.1 Quantum conditions
    2. 4.2 Quantized harmonic oscillators
    3. 4.3 Einstein solid
    4. 4.4 Phonons
    5. 4.5 Third law
    6. 4.6 Paramagnetism
    7. 4.7 Negative absolute temperature
    8. Problems
  11. 5 Entropy of a non-isolated system
    1. 5.1 Beyond the fundamental postulate
    2. 5.2 The Gibbs entropy formula
    3. 5.3 Canonical ensemble
    4. 5.4 Partition functions
    5. 5.5 Entropy metaphors
    6. Problems
  12. 6 Entropy of fermion systems
    1. 6.1 Symmetries and wave functions
    2. 6.2 Intrinsic semiconductors
    3. 6.3 Ideal Fermi gas
    4. 6.4 Average energy approximation
    5. Problems
  13. 7 Entropy of systems of bosons
    1. 7.1 Photons
    2. 7.2 Blackbody radiation
    3. 7.3 Ideal Bose gas
    4. 7.4 Bose–Einstein condensate
    5. 7.5 Modeling the ideal gas
    6. Problems
  14. 8 Entropy of information
    1. 8.1 Messages and message sources
    2. 8.2 Hartley’s information
    3. 8.3 Information and entropy
    4. 8.4 Shannon entropy
    5. 8.5 Fano code
    6. 8.6 Data compression and error correction
    7. 8.7 Missing information and statistical physics
    8. Problems
  15. Epilogue
  16. Appendix I Physical constants and standard definitions
  17. Appendix II Formulary
  18. Appendix III Glossary
  19. Appendix IV Time line
  20. Appendix V Answers to problems
  21. Appendix VI Annotated further reading
  22. Index