Block by Block: The Historical and Theoretical Foundations of Thermodynamics

Cover
Block by Block: The Historical and Theoretical Foundations of Thermodynamics
Copyright
Dedication
Acknowledgements
Contents
List of Figures
Introduction
Prologue
My Motivation – Too Many Unanswered Questions
General Approach
The Four Parts
Part I – The Big Bang and the Synthesis of the Elements in the Stars
Part II – The Atom: Hard Spheres that Attract and Repel
Part III – Energy and the Conservation Laws
Part IV – Entropy and the Laws of Thermodynamics
History
The Silent Evidence
This Book is for the Curious Mind
PART I: The Big Bang
Chapter 1: The Big Bang: science
The Inflation Theory of How the Universe Began and the Atoms Arrived
After the First Three Minutes – One Billion °C and the Formation of Heavier Nuclei
After the First 300 000 Years – 3000 °C and Recombination
The Formation of the Elements
Chapter 2: The Big Bang: discovery
Copernicus – the Return to a Sun-centered Universe and the Onset of the Scientific Revolution
Brahe and Kepler – the Elliptical Orbit
Galileo – One Data Point is Worth One Thousand Opinions
Newton and Gravity
The Twentieth Century
Einstein and the Static Universe
Friedmann, Lemaître, and the Expanding Universe
Deciphering Starlight
Henrietta Leavitt’s Cepheid Variables
Einstein credits Lemaître
The Meeting of Two Worlds: Cosmology and Particle Physics
Gamow, Alpher, and Herman Calculate Conditions of the Early Universe
The 5- and 8-Particle Gaps
Hoyle Shows the Bridge across the 8-Particle Gap
Up Until Now, Only Theory. Then Serendipity Arrived.
Epilogue: The Validating Imperfection
On to the Atom
PART II: The Atom
Chapter 3: The Atom: science
Forming the Elements – Review
Some Staggering Numbers
Strange Behavior at Small Scales
The Atomic Building Blocks and the Interactions Between Them
Quarks – Source of the Strong Interaction
Nuclear Decay – Alpha, Beta and Gamma
The Electromagnetic Interaction
Why the Atom has Volume – the Quantized Orbit
Why a Minimum Radius?
Heisenberg Uncertainty
Pauli Exclusion
The Behavior of Orbiting Electrons Enables Modeling the Atoms as Hard Spheres
The Incomplete Outer Shell
Chapter 4: The Atom: discovery
The Rise of Chemistry from Alchemy
The False Clarity of History
The Rise of Modern Physics
Brownian Motion – Manifestation of Atoms in Motion
Discovering What’s Inside the Atom
Crookes ➔ Thomson ➔ Röntgen ➔ Becquerel ➔ Curie ➔ Rutherford ➔ Planck ➔ Einstein ➔ Bohr ➔ Schrödinger ➔ Heisenberg ➔ Born
Crookes ➔ Thomson ➔ Röntgen ➔ Becquerel ➔ Curie ➔ Rutherford ➔ Planck ➔ Einstein ➔ Bohr ➔ Schrödinger ➔ Heisenberg ➔ Born
Crookes ➔ Thomson ➔ Röntgen ➔ Becquerel ➔ Curie ➔ Rutherford ➔ Planck ➔ Einstein ➔ Bohr ➔ Schrödinger ➔ Heisenberg ➔ Born
Crookes ➔ Thomson ➔ Röntgen ➔ Becquerel ➔ Curie ➔ Rutherford ➔ Planck ➔ Einstein ➔ Bohr ➔ Schrödinger ➔ Heisenberg ➔ Born
Crookes ➔ Thomson ➔ Röntgen ➔ Becquerel ➔ Curie ➔ Rutherford ➔ Planck ➔ Einstein ➔ Bohr ➔ Schrödinger ➔ Heisenberg ➔ Born
Crookes ➔ Thomson ➔ Röntgen ➔ Becquerel ➔ Curie ➔ Rutherford ➔ Planck ➔ Einstein ➔ Bohr ➔ Schrödinger ➔ Heisenberg ➔ Born
Plum Pudding
Blackbody Radiation
Crookes ➔ Thomson ➔ Röntgen ➔ Becquerel ➔ Curie ➔ Rutherford ➔ Planck ➔ Einstein ➔ Bohr ➔ Schrödinger ➔ Heisenberg ➔ Born
Crookes ➔ Thomson ➔ Röntgen ➔ Becquerel ➔ Curie ➔ Rutherford ➔ Planck ➔ Einstein ➔ Bohr ➔ Schrödinger ➔ Heisenberg ➔ Born
Just When it Seemed that Physics was Ending
Crookes ➔ Thomson ➔ Röntgen ➔ Becquerel ➔ Curie ➔ Rutherford ➔ Planck ➔ Einstein ➔ Bohr ➔ Schrödinger ➔Heisenberg ➔ Born
The Balmer Series
Crookes ➔ Thomson ➔ Röntgen ➔ Becquerel ➔ Curie ➔ Rutherford ➔ Planck ➔ Einstein ➔ Bohr ➔ Schrödinger ➔ Heisenberg ➔ Born
Particles Behave Like Waves
Crookes ➔ Thomson ➔ Röntgen ➔ Becquerel ➔ Curie ➔ Rutherford ➔ Planck ➔ Einstein ➔ Bohr ➔ Schrödinger ➔ Heisenberg ➔ Born
Crookes ➔ Thomson ➔ Röntgen ➔ Becquerel ➔ Curie ➔ Rutherford ➔ Planck ➔ Einstein ➔ Bohr ➔ Schrödinger ➔ Heisenberg ➔ Born
The Historic Solvay Conference of 1927
Pauli Exclusion, the Zeeman Effect, and Electron Spin
Spectroscopy
Paul Dirac
The Neutron
The Weak Interaction
The Splitting of the Atom
The Strong Interaction
The Quark
The Standard Model
Conclusion
PART III: Energy and theConservation Laws
Chapter 5: Energy: science (and some history)
Energy Invented to Quantify Change
Events Happen but Total Energy Remains the Same
It’s the Change in Energy that Matters
Force, Energy, Terminology, History, and Theory – All Intertwined
The Deep Dive into the Four Fundamental Interactions
Force Results from the Change in Potential Energy with Distance
It’s the Change in Potential Energy with Distance that Causes Acceleration
What is Force?
Empirically Derived Force Equations as a Reasonable Assumption
Force and Conservation of Energy
Energy Lies at the Core of Thermodynamics
Energy of Motion of a Single Body
Temperature Quantifies the Average Kinetic Energy of Many Bodies
Radiant Energy of Photons
Free Fall Theory – the Fundamental Connection between Δ h and v2
The Lever – It’s All About wΔh
Free Fall History – Galileo Discovers the Relationship between h and v2
The Mechanical Theory of Heat – Weight Falls, Paddle Spins, Water Heats
The Kinetic Theory of Gases
The 1st Law of Thermodynamics
Chapter 6: Motion prior to Galileo
History is Only Clear in Hindsight
How to Reconcile the Varieties of Motion
Classical Mechanics – the Lever and Free Fall
Aristotle Turned Man’s Mind toward the Natural World
Chapter 7: Galileo and the Law of Fall
Galileo’s Break from Aristotle
Discovery of the Parabolic Shape of a Projectile’s Trajectory
Galileo’s “Radical Re-orientation” from Pure to Applied Science
The Pull toward Experimentation
The Law of Fall
The Law of Fall Determined by an Ingenious Experiment
How Did Galileo Measure a Time-varying Speed?
The Dawn of a New Variable to Science – Time
What is Speed?
Galileo’s Use of Mathematics to Quantify the Physical World
Galileo Chose to Ignore Cause
The Scientific Method
Galileo and the Launch of the Scientific Revolution
One Data Point is Worth One Thousand Opinions
Chapter 8: Newton and the Laws of Motion
Sir Isaac Newton
Annus Mirabilis – Newton’s Miraculous Year
Gravity and Action at a Distance
The Rise of Calculus
The Privacy of His Thoughts
The Dispute with Leibniz
The Path to the Principia
Robert Hooke and the Challenge of Circular Motion
1679 – Newton Conquers Circular Motion
Why not Hooke?
Newton’s 1st Law of Motion
The Inadequacy of Language
Newton’s Early Insights into Universal Gravitation
Mass – a New Concept
Newton’s 2nd Law of Motion – “Soul of Classical Mechanics”
Newton Turns to Experimentation
Newton’s 3rd Law of Motion
Force – a New Concept
Newton’s Law of Universal Gravitation
“A prudent question is one-half of wisdom” – Francis Bacon
“The Principia was a Tour-de-Force Demonstration of the Intelligibility of the Universe”
The Principia Broke Physics Away from Philosophy
Epilogue – Completion of the Scientific Revolution
Newton’s Relevance to Energy
Chapter 9: The lever
Analysis of the Lever led to the Creation of Potential Energy
Aristotle and Archimedes—Two Different Views of the Lever
Aristotle—Equate the Effects at the Opposite Ends of the Lever
Hero and his Five Simple Machines
Jordanus and Vertical Displacement
The Inclined Plane
You Can’t Prove a Law
Perpetual Motion and the March of Analysis
Chapter 10: The rise of mv2
Galileo Connected h with v2
Descartes – the First to Attempt a Conservation Law based on Motion and . . .
Descartes –. . . the First to Propose a Mathematical Characterization of Said Motion
The Evolution of Kinetic Energy
Huygens – Galileo’s Successor
Collision Theory – the First Recorded Usage of mv2
Center of Gravity Calculations Provided a Means to Connect Weight (Mass) with Speed
Leibniz and the Birth of Modern Physics
Leibniz’s Famed Thought Experiment Provided a Different Means to Connect Weight with Speed
1686 – the Birth of dynamics
Chapter 11: Bernoulli and Euler unite Newton and Leibniz
The Bernoulli Family and Johann the Father
First Use of the Word “Energy” in Physics
Daniel Bernoulli
The Bernoulli Equation for Fluid Flow
The Bernoulli Family Drama
Leonhard Euler
Bernoulli and Euler
Chapter 12: Rudimentary version of the conservation of mechanical energy (1750)
Simple Machines Revealed Potential Energy in the Form of mg∆h (Mechanical Work)
Free Fall and Ascent Revealed the Interplay between v2 and ∆h
Leibniz Revealed the Logical Connection between mg∆h and mv2
Newton and Leibniz Revealed the Fundamental Connection between Force, mg∆h, and ½mv2
From the Single Body to Many Particles
Chapter 13: Heat: the missing piece to the puzzle
The Historians’ Perspectives
The 1st Law of Thermodynamics – Revisited
The Thermometer
Interlude – the Various Theories of Heat
The Material Theory of Heat: Caloric
The Mechanical Theory of Heat: Work–Heat Equivalence
The Kinetic Theory of Gases
Chapter 14: Joseph Black and the rise of heat capacity
Joseph Black – Separated Temperature from Heat
Evaporative Cooling Does Not Make Sense in the Caloric World
The Science of Calorimetry and the Doctrines of Sensible and Latent Heats
The Dulong–Petit Law
Understanding Heat Capacity at the Atomic Scale
Conclusion: The Heat Capacity per Atom is the Same for Monatomic Gases = 1.5 R
Cvof Crystalline Solid = 3 R
Chapter 15: Lavoisier and the birth of modern chemistry
Joseph Priestley and Oxygen
Cavendish Resolves the Water Controversy – 2 Parts Hydrogen, 1 Part Oxygen
Lavoisier – Making Sense of the Data
The Death of Phlogiston
Conservation of Mass
Lavoisier Lays the Foundation for Modern Chemistry
A Real Guinea Pig Experiment – Respiration as a Form of Combustion
The Two Competing Theories of Heat – Material (Caloric) vs. Motion
Lavoisier (Unfortunately) Gave Significance to Caloric
Chapter 16: Rise of the steam engine
It Started with the Newcomen Engine
Lazare Carnot and the Reversible Process
“The Great Carnot” – Referring to Father, not Son
Sadi Carnot
Saved by a Thread
Chapter 17: Caloric theory: beginning of its end
Early 1800s Provides New Evidence Challenging the Caloric Theory
Rumford Bores a Cannon and so Boils Water
Davy Melts Ice by Using Friction
Young and the Connection between Light and Radiant Heat
The Challenge of Invalidating Caloric – There was no Competing Hypothesis
Mayer and Joule – Succeeded in Killing Caloric by Ignoring It
Work ⇔ Heat
Chapter 18: The ideal gas
Theorists Attempt to Explain Heat Capacity
Chapter 19: The final steps to energy and its conservation
But the Science of Heat was Already Complete, Right?
Chapter 20: Julius Robert Mayer
The Java
The Meaning of Bright Red Blood
Return to Heilbronn
Mayer’s Technical Journey
The Challenge of Building a Conservation Law that includes Heat
The Piston
Mayer’s Logic
The Math
The Mechanical Equivalent of Heat (MEH)
The Community’s Response
Returning to Kuhn’s “Inner Belief” Trigger
Mayer’s 1845 Publication
Mayer’s Fall and Rise
Chapter 21: James Joule
It Began with the Electric Motor
The Impossibility of Perpetual Motion
Turning Away from the Electro-Magnetic Motor toward the Magneto-Electric Generator
Hand Crank Turns ➞ Magneto-Electric Motor Spins ➞ Current Flows ➞ Water Warms
Weight Falls ➞ Magneto-Electric Motor Spins ➞ Current Flows ➞ Water Warms
Direct Friction ➞ Water Warms
Weight Falls ➞ Paddle Spins ➞ Water Warms
Thomson meets Joule
Mayer and Joule – Conclusion
Chapter 22: The1st Law of Thermodynamics
Returning to Kuhn – the Triggers that led to Completion of Boyer’s Three Steps
Interpreting Nature without Prejudice
Reflections on Work–Heat Equivalence
Energy – a New Hypothesis
Energy Moves into Academia and the 1st Law of Thermodynamics is Born
The Kinetic Theory of Gases: Matter-in-Motion
Conclusion
Chapter 23: Epilogue: The mystery of beta decay
What’s next?
PART IV: Entropy and the Laws of Thermodynamics
Chapter 24: Entropy: science (and some history)
Entropy as a Consequence of Our Discrete World
Atoms in a Box
The Appearance of Structure in Large Systems of Colliding Atoms
Why Uniform-Location and Gaussian-Velocity Distributions Make Sense
The Microstate and Statistical Mechanics
Mathematical Approach to Analyzing the Microstates – Balls in Buckets
Finally, the Relevance of the Number of Microstates
The Discovery of Entropy – Clausius and the Steam Engine
Entropy Enabled Completion of Thermodynamics
Die Entropie der Welt strebt einem Maximum zu10 – Clausius’Version of the 2nd Law
Toward a Deeper Understanding of Clausius’ 2nd Law
The Historical Path toward Entropy
Chapter 25: It started with the piston
Heat and Work Met for the First Time Inside the Steam Engine
Discovering that We Live at the Bottom of a Sea of Air
The Power of a Vacuum
The Persistence of Denis Papin
Chapter 26: Britain and the steam engine
To Summarize
Selecting the Path from the Steam Engine to Sadi Carnot
Chapter 27: The Newcomen engine
Before Newcomen came Savery’s patent
The Hornblowers – a Short Overview
The Newcomen and Savery Partnership
The Increasing Relevance of Engine Efficiency
Chapter 28: James Watt
Engine Efficiency – Moving the Condenser out of Newcomen’s One-Cylinder Operation
Continuous Improvement
Watt’s Early Steps toward the Founding of Thermodynamics
The Boulton–Watt partnership
Jonathan (#2) Hornblower
Chapter 29: Trevithick, Woolf, and high-pressure steam
Cornwall – “the Cradle of the Steam Engine”
“Trevithick Created the Engine that was Destined to Drive the Industrial and Transport Revolutions”
Arthur Woolf – Failure in London led to Success in Cornwall
The Cornish Engine
Thermal Efficiency
Measurement Drives Improvement
The Role of the Water Wheel in This Story
The Origin of Reversibility
Sadi Carnot
Conclusion
Chapter 30: Sadi Carnot
Historical Context
Thermodynamic Context
The Stage Was Set for Carnot’s Inquiry
Revisiting the Caloric Theory
Carnot’s Hypothesis: Thermal Efficiency = f (TH – TC)
What Does the Thermal Efficiency of a Heat Engine Really Mean?
Carnot Did the Best He Could with What He Had
Carnot’s Logic for Why His Engine Was the Best
The Refrigeration Cycle
Nature of Working Substance is Irrelevant
The Clapeyron and Clausius–Clapeyron Equations
Reflections Wrap-up
Chapter 31: Rudolf Clausius
The Challenge of Creating a New Paradigm
The Critical Question Confronting Clausius: What is Heat?
Clausius’ Two Principles
Heat–work Equivalence Provides New Approach to Analyzing the Heat Engine
More Consequences of Heat–Work Equivalence – Again Asking, Where Does the Heat Go?
The Arrival of Internal Energy (U) and the 1st Law of Thermodynamics
Using the 1 st Law to Study the Properties of Saturated Steam
Clausius Took the First Major Step toward Thermodynamics
Chapter 32: William Thomson (Lord Kelvin)
Thomson’s Early Education was Influenced by French Thought – Heat is Conserved
The Thomson Brothers Discover Carnot
Challenge #1 – the Ice Engine
Prelude to Challenge #2 – Switching Paradigms
Challenge #2 – Conduction
The Science of Conduction – There is No Such Thing as “Heat Flow”
The 1st Law Revisited – a Closer Look at Heat and Work
The 2nd Law Struggles to Emerge
A Final Note on Thomson’s Consequence Branch of the Entropy Tree
William Rankine
What Role did Clausius Play in Thomson’s Eventual Paradigm Shift?
The Value of Learning History
The Two Laws
The 2nd Law from Different Perspectives – Down in the Branches of the Entropy Tree
A Brief Return to Conduction
Thomson’s Paradigm Shift
Energy Dissipation and Heat Death
Age of Earth Calculations
Concluding Thoughts on Thomson
Helmholtz’s Rational Approach to a Science based on Cause–Effect
Chapter 33: The creation of thermodynamics
Temperature
The History of Temperature
Thomson and the First Glimpse of δQ/T
Capturing the New Science of Thermodynamics in the Written Word
P. G. Tait
Revisionist History
John Tyndall
The New Thermodynamics Still Lacking a Definitive 2nd Law
Chapter 34: Clausius and the road to entropy
The Power of Isolation
A Brief Recap of How We Got Here
Why Two Laws are Needed to Govern the Maximum Performance of Carnot’s Engine
What to Do with δ Q/T?
Revisiting Carnot’s Engine
To Summarize: What Heat is and is not
As Discussed Previously, the Properties of Matter
The Logic behind Clausius’ Discovery of Entropy
More Discussions about Clausius’ Logic
Carnot’s Cycle was Unknowingly Designed to Reveal Entropy
The Concept of “Equivalent Transformations”
From Carnot to Cosmos
It Wasn’t Just Entropy that was Important, but the Declaration of an Increasing Entropy
The Rise of Irreversibility in Thermodynamics
And So We Return Again to Conduction
Completing Clausius’ Equivalent Transformation Table
Applying his Concepts to Analysis of an Irreversible Heat Engine
The Entropy of the Universe Increases
But What Happens to the Entropy of an Isolated Body?
Gibbs’ Famed Obituary on Clausius
Chapter 35: J. Willard Gibbs
He Found Problems to Solve in the Papers He Read
Gibbs Built on Clausius
Gibbs’ First Two Papers
Moving Beyond the PV Indicator Diagram: U(S,V)
3D Graphics
Early Steps toward Phase Equilibrium of a Single Compound
Entropy Maximum leads to Energy Minimum
Thought Experiments Involving Isolated Systems: (dG)T,P ≤ 0 for Spontaneous Change
Discussion of Select Results from Gibbs’ First Two Papers
Chapter 36: Gibbs’ third paper
Chemical Potential (µ) Created to Enable Analysis of Equilibrium
Development One: Chemical Potential (Continued)
Development Two: Gibbs’ Phase Rule
Development Three: The Rise of Composite Properties
Pure Mathematics
Pure Science
Combining Math and Science
One More Demonstration of the Power of Calculus in Thermodynamics
Deduction and the Scientific Method
Gibbs Revealed the Central Theories of Classical Thermodynamics
Chapter 37: Practical applications and Gibbs energy (G)
Maximum Work, Free Energy, Available Energy
The Use of Gibbs Energy (G) to Quantify Maximum Work for Constant Temperature and Pressure
Interpreting (∆G)T,P as regards Chemical Reaction Spontaneity
Summary
Chapter 38: Dissemination of Gibbs’ work
Path 1: Gibbs ➔ Maxwell ➔ Pupin ➔ Helmholtz ➔ van’t Hoff ➔ community
Path 2: Gibbs ➔ van der Waals ➔ Roozeboom ➔ Community
Francis Arthur Freeth – Gibbs’ Phase Rule in Practice
Translating Gibbs
Chapter 39: The 2nd Law, entropy, and the chemist
A Most Challenging Chapter
The Thomsen–Berthelot Principle
Many Wondered, Why Do We Need Entropy?
The Meaning of T∆Srxn
∆Grxn Alone Determines Reaction Spontaneity
The Electrochemical Cell Directly Measures dGrxn
The Inadvertent Contribution of the Electrochemical Cell to Thermodynamics
History of Gibbs’ Influence on Electrochemistry Theory
The Gibbs–Helmholtz Equation — the Impact of Temperature on ∆G and thus on Equilibrium
Chapter 40: Clausius: the kinetic theory of gases
Rudolf Clausius
The Math behind the Kinetic Theory of Gases
Heat Capacity and the Monatomic Gas
Mean Free Path
Interesting Consequences of the Kinetic Theory of Gases
Chapter 41: Maxwell: the rise of statistical mechanic
Early Life and Saturn’s Rings
From Micro to Macro
Testing for Absurdity
Maxwell’s Two Publications on the Kinetic Theory of Gases
Colliding Balls – Physical Model
Maxwell’s Path to the Gaussian Distribution
A Beautiful Confirmation Experiment of the Maxwell Distribution
The Physical Meaning of γ
Gas Viscosity – Theory Followed by Experimental Validation
Does the Meaning of Entropy Lay inside the Mechanical Models?
Chapter 42: Boltzmann: the probabilistic interpretation of entropy
A Mathematical Tour de Force
Boltzmann’s Shift into the World of Probability
A Challenge Presented to Boltzmann: the Reversibility Paradox
Boltzmann’s Response to the Challenge
Boltzmann’s Shift to an Even Deeper World of Probability
How Many Different Ways to Put Balls in Buckets?
One Approach to Understanding Statistical Mechanics
Cutting up a High-Speed Film – Each Frame Equals a Unique “Complexion”
How Many Ways Can You Place 7 Balls in 8 Buckets?
The Meaning of Entropy from Different Perspectives
Constraints decrease entropy
Intermolecular interactions decrease entropy
Energy gradients decrease entropy
Thoughts on the mechanical meaning of entropy
Sackur–Tetrode Validation
Boltzmann – Standing Alone on the Battlefield
Boltzmann’s Influence on Those who Followed
Gibbs and the Completion of Statistical Mechanics
Before Leaving Boltzmann – a Final Comment Regarding His Famed Distribution
Statistical Mechanics Provides the “Why”
Gibbs – a Great Capstone to His Life
Chapter 43: Shannon: entropy and information theory
Samuel F. B. Morse
Shannon Embraces Statistical Mechanics Terminology to Describe Information Theory
Afterword
The Science
Revisiting the 1st Law of Thermodynamics
Revisiting the 2nd Law of Thermodynamics
The History
The Nature of Scientific Discovery – Thrills, Hard Work, Emotional Hardship
Creative Thinking – Solitude Versus Group
Creative Thinking – Power of Working at an Interface
The Impact of Paradigms
The Scientific Method
The Human Drama of Science
Final Thoughts
Bibliography
Index