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
History
Ignore the laws
New synthesis of thermodynamics
Intuition, logic, algorithm, data, application
Gas
Experiment to study gas
What is temperature?
Boltzmann constant
Avogadro constant
Gas constant
State
Moist Air
Phase
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
System
A system interacts with its surroundings
Isolated system
An isolated system conserves energy, space, matter, and charge
A classification of systems
Energy
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
Entropy
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
Subsystems
Constraint internal to an isolated system
Internal variable
Equilibrium
Reversibility
Irreversibility
Fluctuation
Kinetics
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
Calorimetry
Thermometry
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)
Metastability
Thermal environment
Temperature as an independent variable
Thermostat
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
Metastability
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
Entropy
Energy
Competition between entropy and energy
Maxwell rule
From ideal gas to real fluid, multicomponent materials, and materials genome
Fossil-fueled civilization
Steam engine
Generator
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
Exergy
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
Compressor
Condenser
Nozzle
Throttle
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
Psychrometrics
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
Work
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
Ferroelectrics
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