Thermodynamics and Statistical Mechanics deals with the method of thermodynamic potentials, the four Gibbsian potentials, and Boltzmann's statistics. The book reviews the general considerations of thermodynamics, such as the first and second laws of thermodynamics, the van der Waals equation, and Nernst's third law of thermodynamics. The text also discusses the application of thermodynamics to special systems, the theory of phase equilibria, the electromotive force of galvanic cells, and the thermodynamics of near-equilibrium processes. The book explains the equation of state of a perfect gas, the Maxwellian velocity distribution, and the statistical significance of the constants in van der Waal's equation. The text notes that the states of equilibrium can be treated in a simple manner compared to complex methods used in problems connected with irreversible processes. The book explains that the atoms in a molecule are capable of performing small vibrations about their position of equilibrium as they possess both kinetic and potential energy. The text also discusses the quantization of vibrational energy and rotational energy. The book can be helpful for students of physics, thermodynamics, and related subjects. It can also be used by instructors in advanced physics.

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Author's Preface

Editor's Preface

Translator's Preface

Chapter I. Thermodynamics. General Considerations

Temperature as a Property of a System
Work and Heat
The Perfect Gas
A. Boyle's Law (The Law of Boyle and Mariotte)
B. Charles' Law (The Law of Gay-Lussac)
C. Avogadro's Law and the Universal Gas Constant
The First Law. Energy and Enthalpy as Properties
A. Equivalence of Heat and Work
B. The Enthalpy as a Property
C. Digression on the Ratio of Specific Heats cp and cv
The Reversible and the Irreversible Adiabatic Process
A. The Reversible Adiabatic Process
B. The Irreversible Adiabatic Process
C. The Joule-Kelvin Porous Plug Experiment
D. A Conclusion of Great Consequence
The Second Law
A. The Carnot Cycle and Its Efficiency
B. The First Part of the Second Law
C. The Second Part of the Second Law
D. Simplest Numerical Examples
E. Remarks on the Literature of the Second Law
F. On the Relative Rank of Energy and Entropy
The Thermodynamic Potentials and the Reciprocity Relations
Thermodynamic Equilibria
A. Unconstrained Thermodynamic Equilibrium and Maximum of Entropy
B. An Isothermal and Isobaric System in Unconstrained Thermodynamic Equilibrium
C. Additional Degrees of Freedom in Retarded Equilibrium
D. Extremum Properties of the Thermodynamic Potentials
E. The Theorem on Maximum Work
The van der Waals Equation
A. Course of Isotherms
B. Entropy and the Caloric Behavior of the van der Waals Gas
Remarks on the Liquefaction of Gases According to van der Waals
A. The Integral and the Differential Joule-Thomson Effect
B. The Inversion Curve and Its Practical Utilization
C. The Boundary of the Region of Co-existing Liquid-Vapor Phases in the p, v Plane
The Kelvin Temperature Scale
Nernst's Third Law of Thermodynamics

Chapter II. The Application of Thermodynamics to Special Systems

Gaseous Mixtures. Gibbs' Paradox. The Law Due to Guldberg and Waage
A. Reversible Separation of Gases
B. The Increase in Entropy During Diffusion and Gibbs' Paradox
C. The Law of Mass Action Due to Guldberg and Waage
Chemical Potentials and Chemical Constants
A. The Chemical Potentials µi
B. Relation Between the µi's and the gi's for Ideal Mixtures
C. The Chemical Constant of a Perfect Gas
Dilute Solutions
A. General and Historical Remarks
B. Van 't Hoff's Equation of State for Dilute Solutions
The Different Phases of Water. Remarks on the Theory of the Steam Engine
A. The Vapor-Pressure Curve and Clapeyron's Equation
B. Phase Equilibrium Between Ice and Water
C. The Specific Heat of Saturated Steam
General Remarks on the Theory of Phase Equilibria
A. The Triple Point of Water
B. Gibbs' Phase Rule
C. Raoult's Laws for Dilute Solutions
D. Henry's Law of Absorption (1803)
The Electromotive Force of Galvanic Cells
A. Electrochemical Potentials
B. The Daniell Cell, 1836
C. Contraction of Individual Reactions into a Simplified Overall Reaction
D. The Gibbs-Helmholtz Fundamental Equation
E. Numerical Example
F. Remarks on the Integration of the Fundamental Equation
Ferro- and Paramagnetism
A. Work of Magnetization and Magnetic Equation of State
B. Langevin's Equation for Paramagnetic Substances
C. The Theory of Ferromagnetic Phenomena Due to Weiss
D. The Specific Heats cH and cM
E. The Magneto-Caloric Effect
Black Body Radiation
A. Kirchhoff's Law
B. The Stefan-Boltzmann Law
C. Wien's Law
D. Planck's Law of Radiation
Irreversible Processes. Thermodynamics of Near-Equilibrium Processes
A. Conduction of Heat and Local Entropy Generation
B. The Conduction of Heat in an Anisotropic Body and Onsager's Reciprocal Relations
C. Thermoelectric Phenomena
D. Internal Transformations
E. General Relations
F. Limitations of the Thermodynamic Theory of Irreversible Processes

Chapter III. The Elementary Kinetic Theory of Gases

The Equation of State of a Perfect Gas
The Maxwellian Velocity Distribution
A. The Maxwellian Distribution for a Monatomic Gas. Proof of 1860
B. Numerical Values and Experimental Results
C. General Remarks on the Energy Distribution. The Boltzmann Factor
Brownian Motion
Statistical Considerations on Paramagnetic Substances
A. The Classical Langevin Function
B. Modification of Langevin's Function with the Aid of Quantum Mechanics
The Statistical Significance of the Constants in van der Waals' Equation
A. The Volume of a Molecule and the Constant b
B. The van der Waals Cohesion Forces and the Constant a
The Problem of the Mean Free Path
A. Calculation of the Mean Free Path in One Special Case
B. Viscosity
C. Thermal Conductivity
D. Some General Remarks on the Problems Associated with the Concept

Chapter IV. General Statistical Mechanics: Combinatorial Method

Liouville's Theorem, T-space and µ- space
A. The Multidimensional T-space (Phase Space)
B. Liouville's Theorem
C. Equality of Probability for the Perfect Gas
Boltzmann's Principle
A. Permutability as a Measure of the Probability of a State
B. The Maximum of Probability as a Measure of Entropy
C. The Combining of Elementary Cells
Comparison with Thermodynamics
A. Constant Volume Process
B. General Process Performed by a Gas in the Absence of External Forces
C. A Gas in a Field of Forces; the Boltzmann Factor
D. The Maxwell-Boltzmann Velocity Distribution Law
E. Gaseous Mixtures
Specific Heat and Energy of Rigid Molecules
A. The Monatomic Gas
B. Gas Composed of Diatomic Molecules
C. The Polyatomic Gas and Kelvin's Clouds
The Specific Heat of Vibrating Molecules and of Solid Bodies
A. The Diatomic Molecule
B. Polyatomic Gases
C. The Solid Body and the Dulong-Petit Rule
The Quantization of Vibrational Energy
A. The Linear Oscillator
B. The Solid Body
C. Generalization to Arbitrary Quantum States
The Quantization of Rotational Energy
Supplement to the Theory of Radiation and to that of Solid Bodies
A. Method of Natural Vibration…