This brief provides a modern pedagogical exposition of the mechanical approach to statistical mechanics initiated by Boltzmann with his early works (1866-1871). Despite the later contribution by Helmholtz, Boltzmann himself (1884-1887), Gibbs, P. Hertz, and Einstein, the mechanical approach remained almost unknown to the modern reader, in favour of the celebrated combinatorial approach, developed by Boltzmann himself during his probabilistic turn (1876-1884). The brief constitutes an ideal continuation of a graduate course of classical mechanics and requires knowledge of basic calculus in many dimension (including differential forms), thermodynamics, probability theory, besides Hamiltonian mechanics. The cornerstone of the whole presentation is the ergodic hypothesis. Special attention is devoted to Massieu potentials (the Legendre transforms of the entropy) which are most natural in statistical mechanics, and also allow for a more direct treatment of the topic of ensemble equivalence.
This brief provides a modern pedagogical exposition of the mechanical approach to statistical mechanics initiated by Boltzmann with his early works (1866-1871). Despite the later contribution by Helmholtz, Boltzmann himself (1884-1887), Gibbs, P. Hertz, and Einstein, the mechanical approach remained almost unknown to the modern reader, in favour of the celebrated combinatorial approach, developed by Boltzmann himself during his probabilistic turn (1876-1884). The brief constitutes an ideal continuation of a graduate course of classical mechanics and requires knowledge of basic calculus in many dimension (including differential forms), thermodynamics, probability theory, besides Hamiltonian mechanics. The cornerstone of the whole presentation is the ergodic hypothesis. Special attention is devoted to Massieu potentials (the Legendre transforms of the entropy) which are most natural in statistical mechanics, and also allow for a more direct treatment of the topic of ensemble equivalence.
German scholars, against odds now not only forgotten but also hard to imagine, were striving to revivify the life of the mind which the mental and physical barbarity preached and practised by the -isms and -acies of 1933-1946 had all but eradicated. Thinking that among the disciples of these elders, restorers rather than progressives, I might find a student or two who would wish to master new mathematics but grasp it and use it with the wholeness of earlier times, in 1952 I wrote to Mr. HAMEL, one of the few then remaining mathematicians from the classical mould, to ask him to name some young men fit to study for the doc torate in The Graduate Institute for Applied Mathematics at Indiana University, flourishing at that time though soon to be destroyed by the jealous ambition of the local, stereotyped pure. Having just retired from the Technische Universitat in Charlottenburg, he passed my inquiry on to Mr. SZABO, in whose institute there NOLL was then an assistant. Although Mr.
Designed by two MIT professors, this authoritative text discusses basic concepts and applications in detail, emphasizing generality, definitions, and logical consistency. More than 300 solved problems cover realistic energy systems and processes.
Twenty Lectures on Thermodynamics is a course of lectures, parts of which the author has given various times over the last few years. The book gives the readers a bird's eye view of phenomenological and statistical thermodynamics. The book covers many areas in thermodynamics such as states and transition; adiabatic isolation; irreversibility; the first, second, third and Zeroth laws of thermodynamics; entropy and entropy law; the idea of the application of thermodynamics; pseudo-states; the quantum-static al canonical and grand canonical ensembles; and semi-classical gaseous systems. The text is recommended for physics students who are in need of a basic yet effective knowledge in the foundations of thermodynamics, as the book explains its many concepts in such an elementary and pedagogic manner, giving the readers a greater understanding of the core of the subject.
Classic 1912 article reformulated the foundations of the statistical approach in mechanics. Largely still valid, the treatment covers older formulation of statistico-mechanical investigations, modern formulation of kineto-statistics of the gas model, and more. 1959 edition.
Mathematical Foundations of Thermodynamics details the core concepts of the mathematical principles employed in thermodynamics. The book discusses the topics in a way that physical meanings are assigned to the theoretical terms. The coverage of the text includes the mechanical systems and adiabatic processes; topological considerations; and equilibrium states and potentials. The book also covers Galilean thermodynamics; symmetry in thermodynamics; and special relativistic thermodynamics. The book will be of great interest to practitioners and researchers of disciplines that deal with thermodynamics, such as physics, engineering, and chemistry.
Clear treatment of systems and first and second laws of thermodynamics features informal language, vivid and lively examples, and fresh perspectives. Excellent supplement for undergraduate science or engineering class.
The present book covers material in intermediate thermodynamics. It is aimed at those students who desire a deep fundamental understanding of the subject of thermodynamics. It is assumed that the student is familiar with differential equations and has completed a first course in thermodynamics. The material covered in the book is in four parts. In Part I, consisting of Lectures 1 and 2, we cover fundamental concepts of thermodynamics. These lectures provide a brief overview of the subject of thermodynamics, the generality, the applicability, how it's related to the composition of matter, and the laws of thermodynamics. Dimensions and units of various quantities, the definitions of a system, the boundary, the surroundings, constraints, and processes, as well as thermodynamic postulates which lead to the definition of entropy, the fundamental relation, and the energy minimum principle are also introduced in these lectures.Part II, consisting of Lectures 3 through 9, covers the theoretical basis of thermodynamics. Lecture 3 discusses the fundamental relation, the Euler equation, the equations of state, as well as the equilibrium state. Lecture 4 discusses the Gibbs-Duhem relation, molar coordinates, the ideal gas, generalized compressibility, and the virial equations of state. Lecture 5 provides an application of basic concepts to obtain the fundamental relation of the van der Waals fluid. Additional forms of the fundamental relation which are more useful in applications (the Helmholtz free energy, the enthalpy, and the Gibbs free energy), obtained via Legendre transformations, and a discussion on the chemical potential are given in Lectures 6 and 7. Lecture 8 discusses the number of properties necessary to fully describe a system, and the relationship between Maxwell relations and the restrictions on such properties. Lastly, Lecture 9 discusses the concept of thermodynamic stability and the Le Chatelier and Le Chatelier-Braun principles. Part III consists of Lectures 10 through 14 and deals with phase transitions, mixtures, solutions, and excess functions. Phases, phase transitions, latent heat, the Clapeyron equation, and the Gibbs phase rule are covered in Lectures 10 and 11. Lectures 12 and 13 deal with ideal and non-ideal gas mixtures and solutions. Lecture 14 provides a discussion of the concept of mixing and excess functions. Part IV, consisting of Lectures 15 through 17, covers chemical reactions and combustion. Lecture 15 deals with chemical reactions of ideal gases, the equilibrium constant, the law of mass action, the energy of formation, and the heat release from reactions. Lectures 16 and 17 cover fundamental concepts of combustion including the mass and energy balances in open and closed systems.Two appendices are included to aid the understanding of some fundamental concepts. Appendix A discusses the relationship between the macroscopic view of thermodynamics and the microscopic mechanical view and how the two are connected through statistics. Appendix B provides a clear explanation of Legendre transformations which are necessary to obtain alternate forms of the fundamental relation.Offering a concise overview of the most critical concepts of thermodynamics, the volume is ideal for those desiring a deeper understanding of the subject.
