Energy and Entropy: An Intimate Relationship — © 2020 Harvey S. Leff

What is this website?

This website serves two purposes:

(1) To explain and illuminate energy and entropy, their history in the context of thermodynamics, and their applicability to real-world phenomena. To navigate to the Introduction, please click
HERE. The Overview, Essays, Publications, and Resources are accessible using the top menu bar.

(2) To serve as a communication channel for my monograph,
Energy and Entropy: A Dynamic Duo. Information about this book is below this message. If you wish to report an error or to otherwise communicate with me, please click HERE or on the Contact Me link at the bottom of this (and every) page.

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Energy and Entropy

A Dynamic Duo


ISBN 9780367349066
August 1, 2020
Forthcoming by CRC Press
328 Pages - 180 B/W Illustrations


From the back cover

Energy is typically regarded as understandable, despite its multiple forms of storage and transfer. Entropy, however, is an enigma, in part because of the common view that it represents disorder. That view is flawed and hides entropy’s connection with energy. In fact, macroscopic matter stores
internal energy, and that matter’s entropy is determined by how the energy is stored. Energy and entropy are intimately linked.

Energy and Entropy: A Dynamic Duo illuminates connections between energy and entropy for students, teachers, and researchers. Conceptual understanding is emphasised where possible through examples, analogies, figures, and key points.

Features:
• Qualitative demonstration that entropy is linked to spatial and temporal energy spreading, with equilibrium corresponding to the most equitable distribution of energy, which corresponds to maximum entropy
• Analysis of energy and entropy of matter and photons, with examples ranging from rubber bands, cryogenic cooling, and incandescent lamps to Hawking radiation of black holes
• Unique coverage of numerical entropy, the 3rd law of thermodynamics, entropic force, dimensionless entropy, free energy, and fluctuations, from Maxwell's demon to Brownian ratchets, plus attempts to violate the second law of thermodynamics.

Purchase:
This book can be purchased HERE.


Table of Contents
Chapter 1 Energy is Universal
1.1 MYSTERIOUS INVISIBLE ENERGY
   1.1.1 Internal energy
   1.1.2 Brownian motion
1.2 CALORIC: A SEDUCTIVE IDEA
1.3 ENERGY TRANSFERS: WORK, HEAT, MASS
1.4 IMAGINED SYSTEMS WITH E = CONSTANT
   1.4.1 Rigid bodies
   1.4.2 Frictionless surfaces
1.5 DILUTE GAS MODEL: IDEAL GAS
1.6 ENERGY DEFINITIONS, UNITS
1.7 ENERGY TRANSFORMATION EXAMPLES
Chapter 2 Energy is not Enough
2.1 THE WORK-ENERGY THEOREM
   2.1.1 Conservation of energy
   2.1.2 Inadequacy of work-energy theorem
2.2 HEAT DEFINED IN TERMS OF WORK
2.3 ENERGY IS NOT SUFFICIENT
2.4 DISSIPATION, ENERGY SPREADING, EQUITY
   2.4.1 Energy exchanges & equity
   2.4.2 Carnot cycle & reversibility
2.5 AN OVERVIEW OF TEMPERATURE
   2.5.1 International temperature scale
   2.5.2 What is temperature?
2.6 CONNECTING ENERGY & ENTROPY
   2.6.1 Clausius’s main contributions
   2.6.2 Clausius entropy & entropy increase
   2.6.3 Systems not in equilibrium
   2.6.4 Disgregation
   2.6.5 Entropy as missing information
   2.6.6 Confusion about entropy
Chapter 3 Entropy: Energy’s Needed Partner
3.1 COMPOSITE SYSTEMS
3.2 ENTROPY & PROBABILITY
   3.2.1 Why probabilities?
   3.2.2 Boltzmann, probability & entropy
3.3 ENTROPY VS. ENERGY GRAPHS
   3.3.1 Concavity
   3.3.2 Reflections on the entropy vs. energy curve
   3.3.3 Equity revisited
3.4 BOLTZMANN RESERVOIR & PROBABILITY
  3.4.1 Boltzmann reservoir
  3.4.2 Boltzmann factor
  3.4.3 Statistical mechanics
3.5 HELMHOLTZ FREE ENERGY
   3.5.1 Understanding free energy
   3.5.2 Available energy and exergy
   3.5.3 Available energy with finite reservoirs
   3.5.4 Entropic force
Chapter 4 Gases, Solids, Polymers
4.1 IDEAL GAS SACKUR-TETRODE ENTROPY
   4.1.1 Quantum ideal gases
4.2 NONIDEAL GASES & THE VIRIAL EXPANSION
   4.2.1 Liquid-vapour phase transition
   4.2.2 Clausius–Clapeyron equation
   4.2.3 Van der Waals gas
   4.2.4 Virial expansion
4.3 MIXING, & MIXING ENTROPY FUNCTION
   4.3.1 Mixing or expansion?
   4.3.2 Mixing entropy function
   4.3.3 Gibbs paradox & information
   4.3.4 The role of information
4.4 MODELS OF SOLIDS
   4.4.1 Einstein model
   4.4.2 Debye solid
4.5 PARAMAGNETS & FERROMAGNETS
   4.5.1 Ideal paramagnet
   4.5.2 Negative temperature
   4.5.3 Ferromagnets
4.6 RUBBER BANDS
   4.6.1 Rubber band experiment
   4.6.2 Model of a rubber band
4.7 NUCLEAR BINDING ENERGY, FISSION, FUSION
4.8 JARZYNSKI FREE ENERGY EQUALITY
   4.8.1 Examples of the Jarzynski equality
Chapter 5 Radiation & Photons
5.1 EM RADIATION & TEMPERATURE
5.2 BLACKBODY RADIATION
5.3 PHOTONS & THE PHOTON GAS
   5.3.1 What is a photon gas?
   5.3.2 Photon gas equations & graphs
   5.3.3 Photon gas processes
5.4 KIRCHHOFF’S & PLANCK’S LAWS
   5.4.1 Incandescent lamps
   5.4.2 Cosmic microwave background radiation
   5.4.3 Hawking radiation from black holes
   5.4.4 What you see is not always what you get
Chapter 6 Numerical Entropy
6.1 NUMERICAL ENTROPY
6.2 ENTROPY OF ELEMENTS & COMPOUNDS
6.3 THIRD LAW OF THERMODYNAMICS
   6.3.1 Nuances of entropy
   6.3.2 Three statements of the third law
   6.3.3 Metastable states and residual entropy
   6.3.4 Comparison of the third and other laws of thermodynamics
   6.3.5 The third law and model systems ENTROPY UNITS, DIMENSIONLESS ENTROPY
6.4 ENTROPY UNITS, DIMENSIONLESS ENTROPY
   6.4.1 Entropy’s weird dimensions
   6.4.2 Dimensionless entropy
   6.4.3 Numerics
   6.4.4 Physical interpretation of tempergy
Chapter 7 Language & Philosophy of Thermodynamics
7.1 THE LANGUAGE OF WORK & HEAT
   7.1.1 Thing vs. process
7.1.2 Analogy: bank transactions & W, Q, E
   7.1.3 More about defining heating energy
   7.1.4 Isothermal, reversible volume changes
   7.1.5 Work and heat for friction processes LINKS BETWEEN THERMODYNAMICS LAWS
7.2 LINKS BETWEEN THERMODYNAMICS LAWS
   7.2.1 Thermal equilibrium & zeroth law
   7.2.2 Heating & direction of energy flow
   7.2.3 Linkage between first and second laws
7.3 THE LANGUAGE OF ENTROPY
   7.3.1 More about metaphors
Chapter 8 Working, Heating, Cooling
8.1 THE VALUE OF CYCLES
   8.1.1 What is a cycle?
   8.1.2 How Clausius used cycles
   8.1.3 Implications of cycles for entropy
   8.1.4 PV & TS diagrams
8.2 EXAMPLES OF CYCLES
   8.2.1 Reversible Carnot cycles
   8.2.2 E
ciency measures
   8.2.3 Reversible & irreversible Otto cycles
   8.2.4 Reversible & irreversible Stirling cycles
   8.2.5 Irreversible Carnot engine
8.3 IRREVERSIBILITY & 2ND LAW EFFICIENCY
8.4 COMBINED-CYCLE HEAT ENGINES
8.5 LORD KELVIN’S HEAT PUMP
8.6 COOLING & CRYOGENICS
   8.6.1 Cooling techniques
   8.6.2 Joule-Thomson process
   8.6.3 Liquid helium-4
   8.6.4 Helium-3
   8.6.5 Adiabatic demagnetisation
Chapter 9 Sanctity of the 2nd Law of Thermodynamics
9.1 MAXWELL’S DEMON
   9.1.1 Statistical nature of the 2nd law
   9.1.2 The Szilard engine
   9.1.3 Measurement, memory, erasure
   9.1.4 Maxwell’s demon, e
ciency, power
9.2 THERMODYNAMICS & COMPUTATION
9.3 MORE ABOUT FLUCTUATIONS
   9.3.1 Smoluchowski’s trapdoor
   9.3.2 Feynman ratchet and pawl
9.4 BROWNIAN RATCHETS
   9.4.1 Fluctuation phenomena
   9.4.2 Asymmetry & flashing Brownian ratchet
   9.4.3 Other Brownian ratchets
   9.4.4 Brownian ratchets & the 2nd law
9.5 ATTEMPTS TO VIOLATE THE 2ND LAW
   9.5.1 Perpetual motion machines
   9.5.2 Challenges to the 2nd law
   9.5.3 Thermal electrons in a magnetic field
   9.5.4 Thermal electrons in a capacitor
   9.5.5 Theory of air column in gravitational field
   9.5.6 Spontaneous pressure di
erences
Chapter 10 Reflections & Extensions
10.1 REFLECTIONS
10.2 EXTENSIONS
   10.2.1 Lieb-Yngvason formulation of thermodynamics
   10.2.2 Quantum mechanics and the second law
Chapter 11 Appendices: Mathematical identities
   11.1 DERIVATIVES & GIBBS-DUHEM EQUATION
 

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