An introduction to thermodynamics

This doc aims to help you master thermodynamics. It gives you an overview of the subject and is useful for beginners and experts.

higher education
laws of thermodynamics
teaching materials
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An introduction to thermodynamics

This doc aims to help you master thermodynamics. It gives you an overview of the subject and is useful for beginners and experts.

By Zhigang Suo, Professor of Mechanics and Materials, Harvard University

higher education, education, teaching, physics, laws of thermodynamics, teaching materials

An introduction to thermodynamics

Basic algorithm of thermodynamics

Zhigang Suo @zhigangsuo

This book aims to help you master thermodynamics. The book does not center on the laws of thermodynamics, but on the basic algorithm of thermodynamics. For teachers, I outline this approach in the first chapter, The Play of Thermodynamics.

Feel free to share this book with anyone and use it in any way. I will keep updating the book as a Google Doc. If you have the Google Doc app on your phone, pad, and computer, your copy of the book is synced with mine.

Throughout the book, I have linked many parts of the notes to tweets. If you add a comment on any tweet, you and I can start a conversation on thermodynamics.

Table of contents

The play of thermodynamics

The cast

Thermodynamics for everyone


Ignore the laws

New synthesis of thermodynamics

Intuition, logic, algorithm, data, application


Experiment to study gas

What is temperature?

Boltzmann constant

Avogadro constant

Gas constant


Moist Air


Ideal gas mixture

Saturated vapor pressure

Relative humidity

Dew point

Ice and water

Pure substance

Experiment to study ice and water

Temperature-energy plane

Water and steam

Experiment to study water and steam

Temperature-volume plane

Many functions of two variables

Steam tables and steam apps

Pressure-volume plane

Temperature-pressure plane

Ice, water, and steam

Three-phase equilibrium

Experimental observations of three-phase equilibrium

Rule of three-phase mixture

Water expands on freezing

Temperature-volume plane

Pressure-volume-temperature surface

Pressure-volume plane

Temperature-pressure plane

Energy-volume plane

Three types of thermodynamic planes

Three phases of carbon dioxide

Isolated system

Energy, space, matter, and charge


A system interacts with its surroundings

Isolated system

An isolated system conserves energy, space, matter, and charge

A classification of systems


Definition of energy

Measurement of thermal energy and energy transfer

Work and heat

Transfer energy by work

Transfer energy by heat

Sign convention

Misuse of the word heat

Work and heat are superfluous ideas in thermodynamics

The first law of thermodynamics

Thermal energy of an ideal gas

Thermal capacity of an ideal gas

Energy transfer by work and by heat

Constant-volume process

Constant-pressure process

Isothermal process

Adiabatic process


Sample space

Sample space of an isolated system

Definition of entropy

Entropy is a thermodynamic property

Entropy is extensive

Entropy is dimensionless

Entropy is absolute

Absolute, dimensionless entropies per molecule of H2O at various thermodynamic states

Numbers of quantum states per molecule in ice, water, and steam

Basic algorithm of thermodynamics

Fundamental postulate of the statistics of an isolated system

Random variable

Ignorance is bliss

Dispersion of ink

Separation of phases


Constraint internal to an isolated system

Internal variable






Basic algorithm of thermodynamics

The second law of thermodynamics

Thermal system

Entropy and energy

A family of isolated systems of a single independent property

Energy-entropy plane

Common features of the function S(U)

Phrases associated with a family of isolated systems

Dissipation of energy

BAT on thermal contact

Definition of temperature

The zeroth law of thermodynamics

Degradation of energy

Features of the function T(U) common to all thermal systems

Thermal capacity



Count the number of quantum states of an isolated system experimentally

Debye model

Theory of melting

Model melting using a thermal system

Primitive curves

A mixture of two homogeneous states

A mixture of any number of homogeneous states

Convex hull

Derived curve

Equilibrium of a single homogeneous state

Equilibrium of two homogeneous states

Equilibrium of three homogenous states does not exist in a thermal system

Temperature-entropy curve

Thermal system of a nonconvex characteristic function s(u)


Thermal environment

Temperature as an independent variable


Thermal reservoir

A thermal system in a thermal environment

Partial equilibrium

Massieu function

Helmholtz function

Melting analyzed using the Helmholtz function

Closed system

A family of isolated systems of two independent variables

Energy-volume plane

Energy-volume-entropy space

Constant-volume process

Adiabatic process

Experimental determination of the function S(U,V) of a closed system

BAT on two closed systems in contact

Features of the function S(U,V) common to all closed systems

Thermal capacity

Theory of ideal gas

Ideal gas law derived

Energy of an ideal gas

Enthalpy of an ideal gas

Entropy of an ideal gas

Summary of equations of ideal gas

Entropic elasticity

Theory of osmosis

Theory of pure substance

Primitive surfaces

Rule of mixture

Derived surface

Equilibrium of a single homogeneous state

Equilibrium of two homogeneous states

Equilibrium of three homogeneous states

Equilibrium of four homogeneous states is impossible for a pure substance

Critical state


Energy-volume plane

Temperature and pressure

Alternative independent properties

Entropy S(U,V)

Energy U(S,V)

Enthalpy H(S,P)

A closed system and a weight together constitute a thermal system

Enthalpy of a closed system

H(S,P) is a characteristic function of a closed system

Thermal capacity of a closed system in a constant-pressure process

Helmholtz function F(T,V)

Helmholtz function F(T,V) is a characteristic function of a closed system

Maxwell relation

Increment of the function U(T,V)

Increment of the function S(T,V)

A closed system in a thermal environment

Massieu function

Gibbs function G(T,P)

Gibbs function G(T,P) is a characteristic function of a closed system

Other mathematical relations

A closed system in a thermomechanical environment

Planck function vs Gibbs function

Equilibrium of two homogeneous states by equating the Gibbs function

Clapeyron equation

Breed thermodynamic relations like rabbits

Van der Waals model of liquid-gas phase transition

Equation of state, P(T,V)

Critical state

Helmholtz function



Competition between entropy and energy

Maxwell rule

From ideal gas to real fluid, multicomponent materials, and materials genome

Fossil-fueled civilization

Steam engine


From sunlight to electricity—an indirect route

From sunlight to electricity—a direct route

Energy flow chart

Rejected energy

Carnot cycle

Carnot question

Carnot engine

BAT on an engine

Reversible work

Energy efficiency

Carnot efficiency

Entropy efficiency

Entropy generation

Entropic price


Carnot refrigerator

Produce athermal energy using a thermal system and an environment

Produce mechanical energy using a closed system and environment

Steady flow devices

Motion of a fluid

Control volume

Energy transfer at inlet and exit

Adiabatic turbine

Diabatic turbine





Heat exchanger

Slides: engine and refrigerator

Ideal gas mixture

Thermodynamic states of an ideal gas mixture

Volume of an ideal gas mixture

Sliding semipermeable boxes

Energy of an ideal gas mixture

Enthalpy of an ideal gas mixture

Entropy of an ideal gas mixture

Gibbs function of an ideal gas mixture

Entropy of mixing


Psychrometric state

Psychrometric chart

Psychrometric property

Psychrometric process

Open system

A family of isolated systems of many independent variables

Definition of chemical potentials

Temperature vs. chemical potential

BAT on two open systems in contact

Experimental determination of the chemical potential of a species of molecules in an open system

No litter

Gibbs function

Binary system

Unfinished business of collecting big data

Homogeneous function

Chemical potentials of molecules in simple systems

Pure substance

Incompressible pure substance

Pure ideal gas

Ideal gas mixture

Electronic nose

Relative humidity

The ascent of sap

The cost of an invasion

Transpiration pulls liquid water up

The tensile stress in xylem at the top of a tree

BAT on a tree

Mechanical, thermal, and chemical environment

Thermochemical environment

An open system in mechanical, thermal, and chemical environment

Partial equilibrium


Chemical reaction

Chemical reaction conserves atoms

Properties of compounds

Use chemical reaction to produce thermal energy

Direction of chemical reaction

Use chemical reaction to produce athermal energy

Fuel cell

The heaviest weight that can be raised to a height by coal

Hydrogen peroxide powers soft robots

Theoretical air

Dew point

Energy transfer by heat

Adiabatic flame temperature

Chemical equilibrium

Degree of reaction

Condition of chemical equilibrium

Chemical equilibrium in an ideal gas mixture

Simultaneous reactions

Linear algebra of chemical reaction

Summary of this play of thermodynamics

Our accomplishments

Isolated system

Thermal system

Closed system

Open system

Pure substance

Incompressible pure substance

Ideal gas

Ideal gas mixture

Notes not used in ES 181

Dilute solution


Dimensionless chemical potential

Flexibility in defining chemical potentials

Dimensionless chemical potential

Pure substance

Ideal gas

The Boltzmann distribution

Freely jointed chain

Electric potential

The play of thermodynamics

This chapter outlines the play, and is mostly written for teachers. If you are new to thermodynamics, please start with an example: gas.

In class, I do not cover this chapter in one go. I pick a bit at a time, throughout the semester. If at any point the reading gets hard, just skip ahead. Unlike watching a play, reading a script can be nonlinear. Return to this chapter for perspective.

The cast

I start the class by introducing the cast o

An introduction to thermodynamics
Tags Higher education, Education, Teaching, Physics, Laws of thermodynamics, Teaching materials
Type Google Doc
Published 14/03/2023, 20:08:05


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