Elementary and Advanced Thermodynamics

The first part is an undergraduate course with many worked exercises, covering the vocabulary, formalism, and fundamental principles of thermodynamics, the study of gases and phase transitions, and heat engines and thermal cycles. The following parts explore more advanced topics: differential geometry in thermodynamics, Maxwell's demon, endoreversibility, climate physics, thermoelectricity, near-equilibrium thermodynamics (Onsager relations, etc.), and quantum thermodynamics.

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Elementary and Advanced Thermodynamics
2026

Contents

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Lesson 01

General Introduction

The nature of thermodynamics.

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Lesson 02

A History of Thermodynamics and Calorimetry

From the caloric theory to Clausius's entropy.

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Lesson 03

Fundamental Concepts

Equilibrium, walls, state variables and functions, and thermodynamic transformations.

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Lesson 04

The First Law of Thermodynamics

Work, heat, internal energy, and the first law.

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Lesson 05

Application to the Ideal Gas

Application of the first law to ideal-gas transformations.

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Lesson 06

Reversibility and Irreversibility: The Second Law

Entropy, reversibility, and the second law.

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Lesson 07

Mathematical Structure: The Fundamental Relations

Fundamental relations and thermodynamic potentials.

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Lesson 08

Formal Structure: Changes of Variables

Differential calculus, the Legendre transform, and thermodynamic potentials.

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Lesson 09

Calorimetric and Thermoelastic Coefficients

Calorimetric and thermoelastic coefficients, and equations of state.

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Lesson 10

Phase Transitions

Phase diagrams, instabilities, and the Van der Waals gas.

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Lesson 11

Heat Engines

Two-reservoir cycles, the Carnot cycle, efficiencies, and statements of the second law.

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