Concise, detailed, and transparently structured, this upper-level undergraduate textbook is an excellent resource for a one-semester course on thermodynamics for students majoring in physics, chemistry, or materials science. Throughout the seven chapters and three-part appendix, students benefit from numerous practical examples and solved problems ranging in broad scope from cosmic to molecular evolution; cloud formation to rubber elasticity; and Carnot engines to Monte Carlo simulation of phase equilibria.
Lauded in Physics Today as “a valuable resource for students and faculty”, Hentschke’s Thermodynamics presents in this long-anticipated second edition new and extended coverage of a range of topical material, such as thermodynamics of the universe and atmospheric thermodynamics, while also featuring a more application-oriented treatment of surfaces, interfaces, and polymers. Touching on subjects throughout soft-matter physics, superconductors, and complex fluids, this textbook delivers the foundation and breadth of scope necessary to prepare undergraduate students for further study in this timeless yet ever-changing field.
Author(s): Reinhard Hentschke
Series: Undergraduate Lecture Notes in Physics
Edition: 2
Publisher: Springer
Year: 2022
Language: English
Pages: 353
City: Cham
Preface
Contents
1 Two Fundamental Laws of Nature
1.1 Types of Work
1.1.1 Mechanical Work
Mechanical Work Involving Elastic Media
1.1.2 Electric Work
1.1.3 Chemical Work
1.1.4 The First Law
1.2 The Postulates of Kelvin and Clausius
1.2.1 Postulate of Lord Kelvin (K)
1.2.2 Postulate of Clausius (C)
1.3 Carnot’s Engine and Temperature
1.4 Entropy
1.4.1 Theorem of Clausius
1.4.2 Consequences of Clausius’ Theorem
1.4.3 Important Properties of the Entropy
2 Thermodynamic Functions
2.1 Internal Energy and Enthalpy
2.2 Simple Applications
2.2.1 Ideal Gas Law
\partial {\bf E}/\partial {\bf V}{\mid }_T=0 for an Ideal Gas
Kinetic Pressure
Isotherms and Adiabatic Curves
Efficiency of Engines with Ideal Gas as Working Substance
Cycles in the T-S-Plane
Temperature Profile of the Troposphere
Speed of Sound in Gases and Liquids
Joule-Thomson Coefficient
2.3 Free Energy and Free Enthalpy
2.3.1 Relation to the Second Law
2.3.2 Maxwell Relations
2.4 Extensive and Intensive Quantities
2.4.1 Homogeneity
3 Equilibrium and Stability
3.1 Equilibrium and Stability via Maximum Entropy
3.1.1 Equilibrium
3.1.2 Gibbs Phase Rule
3.1.3 Stability
3.2 Chemical Potential and Chemical Equilibrium
3.2.1 Chemical Potential of Ideal Gases and Ideal Gas Mixtures
3.2.2 Chemical Potential in Liquids and Solutions
3.3 Applications Involving Chemical and Mechanical Equilibrium
3.3.1 Osmotic Pressure
3.3.2 Equilibrium Adsorption
3.3.3 Law of Mass Action
3.3.4 Surface Effects in Condensation
3.3.5 Debye-Hückel Theory
3.3.6 Gibbs-Helmholtz Equation
3.3.7 Boiling-Point Elevation
3.3.8 Freezing-Point Depression
3.3.9 The Osmotic Coefficient Revisited
3.3.10 Measuring Surface Tension
4 Simple Phase Diagrams
4.1 Van Der Waals Theory
4.1.1 The Van Der Waals Equation of State
4.1.2 Gas-Liquid Phase Transition
4.1.3 Other Results of the Van Der Waals Theory
Isobaric Thermal Expansion Coefficient
Isothermal Compressibility
Isochoric Heat Capacity
Inversion Temperature
4.2 Beyond Van Der Waals Theory
4.2.1 The Clapeyron Equation
Phase Separation in the RPM
Electric Field Induced Critical Point Shift
4.3 Low Molecular Weight Mixtures
4.3.1 A Simple Phenomenological Model for Liquid-Liquid Coexistence
4.3.2 Gas-Liquid Coexistence in a Binary System
4.3.3 Solid-Liquid Coexistence in a Binary System
Solubility
4.3.4 Ternary Systems
4.4 Phase Equilibria in Macromolecular Systems
4.4.1 A Lattice Model for Binary Polymer Mixtures
A Digression—One-Component Gas-Liquid Phase Behavior
Polymer Mixtures
Polymers in Solution
Osmotic Pressure in Polymer Solutions
5 Microscopic Interactions
5.1 The Canonical Ensemble
5.1.1 Entropy and Information
5.1.2 E and the Hamilton Operator\,{{{\cal H}}}
5.1.3 The Ideal Gas Revisited
5.1.4 Gibbs Paradox
5.1.5 Ideal Gas Mixture
5.1.6 Energy Fluctuations
5.1.7 The Likelihood of Energy Fluctuations
5.1.8 Harmonic Oscillators and Simple Rotors
5.2 Generalized Ensembles
5.2.1 Fluctuation of {{{\varvec X}}}
5.3 Grand-Canonical Ensemble
5.3.1 Pressure
5.3.2 Fluctuating Particle Number and Energy
5.3.3 Bosons and Fermions
5.3.4 High Temperature Limit
5.3.5 Two Special Cases—ϵ∝k2 and ϵ∝k
5.4 The Third Law of Thermodynamics
6 Thermodynamics and Molecular Simulation
6.1 Metropolis Sampling
6.2 Sampling Different Ensembles
6.3 Selected Applications
6.3.1 Simple Thermodynamic Bulk Functions
6.3.2 Phase Equilibria
6.3.3 Osmotic Equilibria
6.3.4 Chemical Potential
7 Non-equilibrium Thermodynamics
7.1 Linear Irreversible Transport
7.1.1 Fluctuations Revisited
7.1.2 Onsager’s Reciprocity Relations
7.2 Entropy Production
7.2.1 Entropy Production—Fluctuation Approach
7.2.2 Theorem of Minimal Entropy Production
7.2.3 A Differential Relation in the Linear Regime
7.2.4 Entropy Production—Balance Equation Approach
7.2.5 General Form of a Balance Equation
7.2.6 A Useful Formula
7.2.7 Mass Balance
7.2.8 Internal Energy Balance
7.2.9 Affinity
7.2.10 Entropy Balance Equation
7.2.11 Evolution Criterion
7.3 Complexity in Chemical Reactions
7.3.1 Bray Reaction
7.3.2 Logistic Map
7.3.3 Chemical Clocks
7.3.4 Linear Stability Analysis
7.4 Remarks on Evolution
Appendix A The Mathematics of Thermodynamics
A.1 Exact Differential and Integrating Factor
A.2 Three Useful Differential Relations
A.3 Legendre Transformation
Appendix B Grand-Canonical Monte Carlo: Methane on Graphite
Appendix C Constants, Units, Tables
References
Index
