1 Gases and fluids
1.1 Introduction
1.2 The perfect gas
1.3 The perfect gas law - a thermal equation of state
1.4 Temperature and temperature scales
1.5 Applications of the perfect gas equation
1.6 Description of real gases: Compression factor
1.7 Virial coefficients: empirical approx. of the compression factor
1.8 Condensation of real gases
1.9 Supercritical fluids (SCF) - properties and applications
1.10 Van-der-Waals (vdW) equation
1.11 Maxwell construction and subcritical isotherms
1.11.1 Critical constants and vdW equation
1.11.2 vdW equation and Leiden form
1.12 Corresponding states (cs) and reduced variables
2 First law: internal energy and heat capacity
2.1 Basic Notation: System and state
2.2 Description of systems by state functions
2.3 Internal energy U and First Law
2.4 A comment on internal pressure and Joule’s experiment
2.5 Work
2.6 Reversible vs. irreversible processes
2.6.1 Work of reversible isothermal expansion
2.7 Heat and heat capacity
2.8 Enthalpy and heat capacity at constant pressure
2.9 Experimental data on the heat capacity
2.9.1 Heat capacity for solids: Einstein- and Debye-model
2.9.2 Estimation of heat capacity for gases
2.10 Cp-Cv for perfect gases
2.11 Adiabatic changes - Poisson equations
2.12 Isenthalpic processes
2.13 Joule-Thomson: adiabatic + isenthalpic expansion
2.14 Calculation of Joule-Thomson coefficient for different models
3 Second and third law: work, heat, and entropy
3.1 Spontaneous processes
3.2 Entropy
3.3 Change of entropy
3.4 Calculation of change of S for an irreversible change of state
3.5 Carnot cycle: p-V diagram and T-S diagram
3.6 Efficiency and Carnot cycle
3.7 Third law
3.8 Magnetocaloric cooling: adiabatic demagnetization
3.9 Delta S for first-order phase transitions
3.10 Changes of entropy with T
3.11 Combining the first and second law
3.12 The inverse temperature as an integrating factor
3.13 What is a potential
3.14 Thermodynamic Contacts: The isolated system
3.15 Thermodynamic Contacts: A system in thermal equilibrium
3.16 Thermodynamic Contacts: Temperature and pressure are defined by the surrounding area
3.17 Thermodynamic Contacts: Examples for other contacts
3.18 The free energy as an example for a thermodynamic potential
3.19 The transformation of thermodynamic potentials
3.20 The Legendre transformation in 1D
3.21 From the free energy to the inner energy
3.22 Calculation of the free energy of an ideal gas
3.23 Overview of thermodynamic potentials
3.24 Guggenheim scheme
3.25 Fundamental equations and exact differentials
3.26 Maxwell relations
3.27 Maxwell relations, example for vdW gas
3.28 Maxwell relations, calculation of residual functions
3.29 Residual functions of enthalpy and Gibbs potential
3.30 Cp-Cv: general relation
3.31 Fugacity: Definition and relation to residual function
3.32 Fundamental equations for open systems
3.33 Principle dependence of G on T and p
4 Gibbs phase rule and pure substances
4.1 Gibbs phase rule - general discussion
4.2 Gibbs phase rule including chemical reactions and other restraints
4.2.1 Examples: Errors in binary phase diagrams
4.3 Equilibrium conditions for pure substances and second law
4.4 p,V,T surface for pure substance
4.5 Clapeyron’s equation and application to melting
4.6 Clapeyron’s equation and application to vaporization
4.7 Clapeyron’s equation and application to sublimation
4.7.1 Examples for solid-solid equilibria
4.8 Ehrenfest classification of phase transitions
5 Mixtures: Simple, Ideal, Real
5.1 Classification
5.2 Caloric properties of ideal-gas mixtures
5.3 Thought experiment: Gibbs paradox
5.4 What is the most entropic ideal-gas binary mixture?
5.5 Extensive properties of mixtures: Volume of mixtures and partial molar volume
5.6 Example for negative partial molar volume: salt + water
5.7 Gibbs-Duhem equation
5.7.1 Application of Gibbs-Duhem: rationalization of phi/x-curves
5.8 Excess functions
5.9 Phase separation
5.10 Activity of solutions of condensed systems (liquid, solid)
5.11 Raoult and Henry law for activity and fugacity
5.12 Activities of regular solutions
5.13 Colligative properties of ideal systems
5.14 Colligative properties - osmosis
5.15 Quantification of osmosis (ideal systems): Van’t Hoff equation
5.16 Stability and infinitesimal fluctuations
6 Transport and Kinetics
6.1 Basics using some examples
6.2 Kinetics of chemical reactions
6.3 Kinetics of a bottle with sparkling water
6.4 Mathematical solutions for limiting cases
6.5 Advanced analysis of kinetic reactions
6.6 Parallel reactions