I just completed Section 4 – The Physical Meaning of Thermodynamic Properties of my continually evolving book, The Machinery Underneath, and wanted to share the new material here. As this is a work-in-progress, I embrace the theme of continuous improvement and so welcome your feedback.

Here is the table of contents. The new (linked) chapters are 8 – 17. On to Section 5 – Gases, ideal and non-ideal.

Table of Contents

Preface

Introduction

Section 1 – Atomic Theory

Thermodynamics describes the macroscopic behavior of matter at the scale we can measure. But that behavior originates at a scale we cannot see — the scale of atoms. This section introduces the cast of characters: what atoms are, what forces act between them, and how their constant motion and interaction give rise to the macroscopic world thermodynamics describes. Everything that follows builds on this foundation.

Chapter 1 – Atoms and forces

Chapter 2 – The movement of atoms

Section 2 – Conservation of Mass and Energy

Atoms move and interact, but they don’t disappear — and neither does the energy they carry. This section establishes the two great conservation laws that govern all of thermodynamics: mass is conserved and energy is conserved. Together they produce the most powerful everyday tool in engineering and science — the mass and energy balance. It is these laws that tell you when a process doesn’t add up.

Chapter 3 – Energy, mass, and the First Law of Thermodynamics

Chapter 4 – The mass and energy balance (w/ stories from the field)

Section 3 – Law of Large Numbers

Conservation tells us what is possible. It does not tell us what actually happens. A gas could, in principle, spontaneously crowd into one corner of its container — energy would still be conserved. But it never does. This section explains why: nature moves toward its most probable state. When atoms are present in vast numbers, probability becomes a law, and that law is the Second Law of Thermodynamics. This section introduces entropy, the Boltzmann distribution, and the statistical foundation on which all of classical thermodynamics rests.

Chapter 5 – Entropy and the Second Law of Thermodynamics

Chapter 6 – The Boltzmann energy distribution – illustrated

Chapter 7 – Micro-to-Macro: setting the stage

Section 4 – The Physical Meaning of Thermodynamic Properties

Classical thermodynamics is built on a set of properties — temperature, pressure, energy, entropy, enthalpy, Gibbs energy, chemical potential — each defined mathematically and connected to the others by exact equations. But what do these properties actually mean at the atomic level? What is entropy, physically? What does Gibbs energy represent? Why does enthalpy exist at all? This section answers those questions, one property at a time, using the atomic foundation built in Sections 1 through 3. It is the core of this book.

Chapter 8 – T, P, V, m

Chapter 9 – Heat capacity (C)

Chapter 10 – Internal energy (U)

Chapter 11 – Enthalpy (H)

Chapter 12 – Entropy (S)

Chapter 13 – Calorimetry: Heat of reaction (ΔH_rxn)

Chapter 14 – Gibbs energy (G) and Helmholtz energy (A)

Chapter 15 – The physical meaning of TΔS

Chapter 16 – Chemical potential (µ)

Chapter 17 – Thermodynamic properties summary