Problems after each chapter

Physicists firmly believe that the differential equations of nature should be hyperbolic so as to exclude action at a distance; yet the equations of irreversible thermodynamics - those of Navier-Stokes and Fourier - are parabolic. This incompatibility between the expectation of physicists and the classical laws of thermodynamics has prompted the formulation of extended thermodynamics. After describing the motifs and early evolution of this new branch of irreversible thermodynamics, the authors apply the theory to mon-atomic gases, mixtures of gases, relativistic gases, and "gases" of phonons and photons. The discussion brings into perspective the various phenomena called second sound, such as heat propagation, propagation of shear stress and concentration, and the second sound in liquid helium. The formal mathematical structure of extended thermodynamics is exposed and the theory is shown to be fully compatible with the kinetic theory of gases. The study closes with the testing of extended thermodynamics through the exploitation of its predictions for measurements of light scattering and sound propagation.

Classical irreversible thermodynamics, as developed by Onsager, Prigogine and many other authors, is based on the local-equilibrium hypothesis. Out of equilibrium, any system is assumed to depend locally on the same set of variables as when it is in eqUilibrium. This leads to a formal thermody namic structure identical to that of eqUilibrium: intensive parameters such as temperature, pressure and chemical potentials are well-defined quantities keeping their usual meaning, thermodynamic potentials are derived as Leg endre transformations and all equilibrium thermodynamic relations retain their validity. The theory based on this hypothesis has turned out to be very useful and has achieved a number of successes in many practical situations. of interest in going However, the recent decade has witnessed a surge beyond the classical formulation. There are several reasons for this. One of them is the development of experimental methods able to deal with the response of systems to high-frequency and short-wavelength perturbations, such as ultrasound propagation and light and neutron scattering. The ob served results have led to generalizations of the classical hydrodynamical theories, by including memory functions or generalized transport coefficients depending on the frequency and the wavevector. This field has generated impressive progress in non-equilibrium statistical mechanics, but for the moment it has not brought about a parallel development in non-equilibrium thermodynamics. An extension of thermodynamics compatible with gener alized hydrodynamics therefore appears to be a natural subject of research.

Discover the many facets of non-equilibrium thermodynamics. The first part of this book describes the current thermodynamic formalism recognized as the classical theory. The second part focuses on different approaches. Throughout the presentation, the emphasis is on problem-solving applications. To help build your understanding, some problems have been analyzed using several formalisms to underscore their differences and their similarities.

This monograph presents, from the viewpoint of continuum mechanics, a newly emerging field of irreversible thermodynamics, in which linear irreversible thermodynamics are extended to the nonlinear regime and macroscopic phenomena far removed from equilibrium are studied in a manner consistent with the laws of thermodynamics. The tool to develop this thermodynamic theory of irreversible processes are the generalized thermodynamics, which also extends the classical hydrodynamics of Navier, Stokes and Fourier to nonlinear irreversible processes. On the basis of mathematically rigorous representations of the first and the second law of thermodynamics, phenomenological theory (continuum mechanics) deductions are made from the thermodynamic laws of R. Clausius and Lord Kelvin and by this continuum mechanics theories are formulated for macroscopic irreversible processes occurring far removed from equilibrium. Non-equilibrium thermodynamics are developed for thermodynamic functions. The macroscopic irreversible processes studied include global irreversible processes as well as local hydrodynamic processes at an arbitrary degree of removal from equilibrium. Applications of the theories cover global irreversible processes, simple flows of non-Newtonian and non-Fourier fluids, shock waves of monatomic and diatomic gases, rarefied gas dynamics, ultrasonic wave absorption and dispersion of monatomic and diatomic gases, electrochemical processes, neural networks of chemical reactors, microflows, etc. Variational principles in irreversible thermodynamics and contact manifolds in thermodynamics are also discussed.' This monograph, will be of interest to condensed matter physicists, chemical physicists, biophysicists, mechanical and aerospace engineers, and specialists and graduate students in the fields of irreversible thermodynamics and non-equilibrium statistical mechanics.

Covers a wide spectrum of applications and contains a wide discussion of the foundations and the scope of the most current theories of non-equilibrium thermodynamics. The new edition reflects new developments and contains a new chapter on the interplay between hydrodynamics and thermodynamics.

Thermodynamic Approaches in Engineering Systems responds to the need for a synthesizing volume that throws light upon the extensive field of thermodynamics from a chemical engineering perspective that applies basic ideas and key results from the field to chemical engineering problems. This book outlines and interprets the most valuable achievements in applied non-equilibrium thermodynamics obtained within the recent fifty years. It synthesizes nontrivial achievements of thermodynamics in important branches of chemical and biochemical engineering. Readers will gain an update on what has been achieved, what new research problems could be stated, and what kind of further studies should be developed within specialized research. - Presents clearly structured chapters beginning with an introduction, elaboration of the process, and results summarized in a conclusion - Written by a first-class expert in the field of advanced methods in thermodynamics - Provides a synthesis of recent thermodynamic developments in practical systems - Presents very elaborate literature discussions from the past fifty years

Although the basic theories of thermodynamics are adequately covered by a number of existing texts, there is little literature that addresses more advanced topics. In this comprehensive work the author redresses this balance, drawing on his twenty-five years of experience of teaching thermodynamics at undergraduate and postgraduate level, to produce a definitive text to cover thoroughly, advanced syllabuses. The book introduces the basic concepts which apply over the whole range of new technologies, considering: a new approach to cycles, enabling their irreversibility to be taken into account; a detailed study of combustion to show how the chemical energy in a fuel is converted into thermal energy and emissions; an analysis of fuel cells to give an understanding of the direct conversion of chemical energy to electrical power; a detailed study of property relationships to enable more sophisticated analyses to be made of both high and low temperature plant and irreversible thermodynamics, whose principles might hold a key to new ways of efficiently covering energy to power (e.g. solar energy, fuel cells). Worked examples are included in most of the chapters, followed by exercises with solutions. By developing thermodynamics from an explicitly equilibrium perspective, showing how all systems attempt to reach a state of equilibrium, and the effects of these systems when they cannot, the result is an unparalleled insight into the more advanced considerations when converting any form of energy into power, that will prove invaluable to students and professional engineers of all disciplines.

Introduction to Non-equilibrium Physical Chemistry presents a critical and comprehensive account of Non-equilibrium Physical Chemistry from theoretical and experimental angle. It covers a wide spectrum of non-equilibrium phenomena from steady state close to equilibrium to non-linear region involving transition to bistability, temporal oscillations, spatio-temporal oscillations and finally to far from equilibrium phenomena such as complex pattern formation, dynamic instability at interfaces, Chaos and complex growth phenomena (fractals) in Physico-chemical systems. Part I of the book deals with theory and experimental studies concerning transport phenomena in membranes (Thermo-osmosis,Electroosmotic ) and in continuous systems (Thermal diffusion,Soret effect) close to equilibrium Experimental tests provide insight into the domain of validity of Non-equilibrium Thermodynamics ,which is the major theoretical tool for this region. Later developments in Extended Irreversible Thermodynamics and Non-equilibrium Molecular dynamics have been discussed in the Appendix. Part II deals with non-linear steady states and bifurcation to multistability, temporal and spatio- temporal oscillations (Chemical waves). Similarly Part II deals with more complex phenomena such as Chaos and fractal growth occurring in very far from equilibrium region. Newer mathematical techniques for investigating such phenomena along with available experimental studies. Part IV deals with analogous non-equilibrium phenomena occurring in the real systems (Socio-political, Finance and Living systems etc.) for which physico-chemical systems discussed in earlier chapters provide a useful model for development of theories based on non-linear science and science of complexity. - The book provides a critical account of theoretical studies on non-equilibrium phenomenon from region close to equilibrium to far equilibrium - Experimental studies have been reported which provide test of the theories and their limitations - Impacts of the concepts developed in non-equilibrium Physical Chemistry in sociology, economics and other social science and living systems has been discussed

Ordinary thermodynamics provides reliable results when the thermodynamic fields are smooth, in the sense that there are no steep gradients and no rapid changes. In fluids and gases this is the domain of the equations of Navier-Stokes and Fourier. Extended thermodynamics becomes relevant for rapidly varying and strongly inhomogeneous processes. Thus the propagation of high frequency waves, and the shape of shock waves, and the regression of small-scale fluctuation are governed by extended thermodynamics. The field equations of ordinary thermodynamics are parabolic while extended thermodynamics is governed by hyperbolic systems. The main ingredients of extended thermodynamics are • field equations of balance type, • constitutive quantities depending on the present local state and • entropy as a concave function of the state variables. This set of assumptions leads to first order quasi-linear symmetric hyperbolic systems of field equations; it guarantees the well-posedness of initial value problems and finite speeds of propaga tion. Several tenets of irreversible thermodynamics had to be changed in subtle ways to make extended thermodynamics work. Thus, the entropy is allowed to depend on nonequilibrium vari ables, the entropy flux is a general constitutive quantity, and the equations for stress and heat flux contain inertial terms. New insight is therefore provided into the principle of material frame indifference. With these modifications an elegant formal structure can be set up in which, just as in classical thermostatics, all restrictive conditions--derived from the entropy principle-take the form of integrability conditions.