Showing papers on "Non-equilibrium thermodynamics published in 1969"
01 Jan 1969
TL;DR: De Groot and Mazur as mentioned in this paper provided full release of this book in ePub, DjVu, txt, doc, PDF formats, in order to load instructions and diverse artistic eBooks online, either load theirs or download.
Abstract: If looking for a ebook by S. R. de Groot and P. Mazur Non-Equilibrium Thermodynamics in pdf form, in that case you come on to the correct site. We furnish full release of this book in ePub, DjVu, txt, doc, PDF formats. You may read by S. R. de Groot and P. Mazur online Non-Equilibrium Thermodynamics or download. In addition, on our website you may reading instructions and diverse artistic eBooks online, either load theirs. We like attract consideration what our site does not store the eBook itself, but we grant ref to website whereat you may load either reading online. So if have necessity to download pdf Non-Equilibrium Thermodynamics by S. R. de Groot and P. Mazur, then you have come on to faithful website. We have Non-Equilibrium Thermodynamics ePub, txt, PDF, DjVu, doc formats. We will be glad if you will be back to us anew.
403 citations
••
TL;DR: In this article, it was shown that a system made up of nuclei and electrons, the constituents of ordinary matter, has a well-defined statistical-mechanically computed free energy per unit volume in the thermodynamic (bulk) limit.
Abstract: It is shown that a system made up of nuclei and electrons, the constituents of ordinary matter, has a well-defined statistical-mechanically computed free energy per unit volume in the thermodynamic (bulk) limit This proves that statistical mechanics, as developed by Gibbs, really leads to a proper thermodynamics for macroscopic systems
137 citations
••
TL;DR: In this article, a combination of the Gibbs equation of thermostatics, with appropriate conservation equations, is shown to yield an expression, (10), for the local production of entropy accompanying the flow of heat and mass.
70 citations
••
63 citations
••
TL;DR: In this paper, it is shown that a modification which differentiates between a dynamic and a thermostatic temperature is necessary in order to make classical thermodynamics of irreversible processes consistent.
Abstract: Thermodynamics of processes in continuous matter has found several treatments: (1) classical thermodynamics of irreversible processes, (2) the nonlinear field theory of mechanics with the incorporation of thermodynamic aspects, (3) the new entropyfree thermodynamics of processes. An important feature of the last theory is the fundamental inequality. It provides a basis for the formulation of constitutive equations, which are discussed for simple thermodynamic fluid materials. Classical thermodynamics of irreversible processes results as a well defined special case with a modification that has been overlooked previously. It is shown by an example that this modification which differentiates between a dynamic and a thermostatic temperature is necessary in order to make classical thermodynamics of irreversible processes consistent.
63 citations
••
TL;DR: In this paper, it is shown that in a large class of far-from-equilibrium systems, described by a discrete set of variables, it is possible to extend the classical Einstein fluctuation formula, provided one uses suitable steadystate parameters rather than equilibrium quantities.
Abstract: The probability of occurrence of fluctuations around nonequilibrium steady states or states slowly varying in time is discussed from a kinetic viewpoint. The limitations of the thermodynamic theory of fluctuations are investigated. It is shown that in a large class of far‐from‐equilibrium systems, described by a discrete set of variables, it is possible to extend the classical Einstein fluctuation formula, provided one uses suitable steady‐state parameters rather than equilibrium quantities. This conclusion is shown to be in agreement with the results of recent work by Prigogine and Glansdorff.
54 citations
••
34 citations
••
TL;DR: Boltzmann's decisive association of the second law with probability in 18772 was just such a problem as mentioned in this paper, but it was not a mechanical idea, for it was a purely mechanical explanation of entropy encountered insoluble problems.
Abstract: THE REDUCTION of the second law of thermodynamics to mechanics in the latter half of the nineteenth century poses an interesting question: how did probability, a concept foreign to traditional mechanics, enter the theoretical model? Changes in mechanical theories were always natural extensions of mechanical ideas. For example, Rudolf Clausius, when challenged by C. H. Buijs-Ballot with the apparent contradiction between the slow diffusion of gases and the supposedly rapid movement of molecules which the kinetic theory assumed, added collision spheres to his analysis.1 No such natural line of thought could lead to introducing probability, however, for it was not a mechanical idea. Probability entered only when purely mechanical explanations of entropy encountered insoluble problems. The occasion for Ludwig Boltzmann's decisive association of the second law with probability in 18772 was just such a problem. He had discovered in 18723 a function for colliding particles which apparently mirrored the behavior of entropy; that is, its value always decreased to a minimum and never increased. Thermodynamic equilibrium, therefore, characterized by entropy becoming a maximum, would seem to correspond to the collision function reaching a minimum. In 1877, however, Boltzmann
28 citations
••
TL;DR: Ion momentum transfer through charge exchange in mixture of ion gases and parent neutral gases under thermal nonequilibrium, noting role of Boltzmann equation as mentioned in this paper, was shown to be possible.
19 citations
••
TL;DR: In this paper, the authors present an analysis of the origin and calculation of the replacement free energy in the thermodynamics of small systems and obtain an exact expression for the replacement energy of a one-dimensional "crystal" with free ends.
Abstract: The object of this study is to present an analysis of the origin and calculation of the replacement free energy in the thermodynamics of small systems. An exact expression is obtained for the replacement free energy of a one‐dimensional “crystal” with free ends.
16 citations
••
TL;DR: In this paper, it was shown how the mathematical theory of stability of motion can be applied to kinetic equations, describing irreversible processes in an isolated, homogeneous system, and that functions having all the properties of entropy exist throughout the domain of definition of the kinetic equations.
Abstract: In this paper it is demonstrated how the mathematical theory of stability of motion can be applied to kinetic equations, describing irreversible processes in an isolated, homogeneous system. It turns out that functions having all the properties of entropy exist throughout the domain of definition of the kinetic equations. Since the kinetic equations depend only on variables defined outside equilibrium thermodynamics, it is possible to define entropy far beyond the range of validity of the thermodynamics of irreversible processes. It is shown that the commonly assumed properties of entropy are not sufficient, however, to single out just one entropy function.
01 May 1969
TL;DR: In this paper, an integral method is presented for the adiabatic compressible turbulent boundary layer which extends recent concepts of turbulent equilibrium boundary layers to the study of nonequilibrium flows.
Abstract: : An integral method is presented for the adiabatic compressible turbulent boundary layer which extends recent concepts of turbulent equilibrium boundary layers to the study of nonequilibrium flows. Coles' law of the wall and wake is extended to the case of compressible adiabatic flows with pressure gradient by employing Van Driest's generalized velocities. An analytical expression for the compressible turbulent equilibrium dissipation integral is then derived from the integral momentum, mean energy and local skin friction equations. For the general case of nonequilibrium flows with arbitrary pressure gradients, the dissipation integral is 'unhooked' from the equilibrium pressure gradient parameter through the use of a single empirical curve of existing incompressible flow data. Numerical solutions are then presented for a variety of compressible flows. As a first step in developing an integral method for nonadiabatic flows, the family of incompressible equilibrium enthalpy profiles are solved for from the thermal energy equation. (Author)
••
TL;DR: In this paper, the Liouville operator formalism is used to convert the fluxes into a general fluctuation form and an extension of the results to interference effects is given.
Abstract: Einstein‐type expressions for transport coefficients are obtained by introducing Onsager's regression hypothesis for fluctuations into the statistical‐mechanical expressions for the fluxes. Liouville operator formalism is used to convert the fluxes into a general fluctuation form. Introduction of a local equilibrium distribution function and linearization in the macroscopic gradients yield the Einstein‐type equations. An extension of the results to interference effects is given. The fluctuation form of the fluxes is converted into one in which the nonequilibrium distribution function is used. The latter expressions form the basis for the theories of Kirkwood, Rice and Allnatt, and others. An application is made to particles interacting via a square‐well potential.
••
••
TL;DR: Sanfeld as mentioned in this paper showed that the entropy change in an incremental process which takes place in a macroscopic volume element of a system is written as dcS + d1S.
Abstract: A. Sanfeld Sussex: John Wiley. 1968 Pp. xxiv + 258. Price £4 10s. In irreversible thermodynamics the entropy change in an incremental process which takes place in a macroscopic volume element of a system is written as dcS + d1S. The first term is the entropy flow from the outside due to interactions with the surroundings, the second term arises from internal changes and the second law is introduced in the form d1S≥0.
••
01 Aug 1969••
TL;DR: In this paper, the authors use statistical mechanics to extend the above evolution criterion and the principle of minimum entropy production to partially ionized, collision-dominated plasmas interacting with radiation.
Abstract: One of the basic problems in the theory of irreversible thermodynamics is the formulation of general evolution criteria. A universal criterion of this kind for macroscopic systems with time independent boundary conditions has been derived by Glansdorff and Prigogine. The derivation refers to transport processes in matter like diffusion, heat conduction and chemical reactions. Radiative transfer has not been included. In this investigation, we use statistical mechanics to extend the above evolution criterion and the principle of minimum entropy production to partially ionized, collision-dominated plasmas interacting with radiation. We consider a plasma with collisional—and radiative excitation—and ionization phenomena not restricted to local equilibrium. The entropy production, which is defined as the entropy change per unit time due to emission, absorption and scattering of radiation, is formulated with the use of statistical analogues to the fluxes and forces or irreversible thermodynamics. The time change of the entropy production is investigated for a homogeneous plasma and an isotropic radiation field.
••
TL;DR: In this article, it was shown that the thermodynamic Laplace and Young equations, even in conjunction with a knowledge of temperature, partial potentials, phase mass, and solid surface configuration, do not provide a complete characterization of equilibrium.
••
••
••
TL;DR: In this article, the existence of local thermodynamic equilibrium for the ground state of He I in a time-independent and homogeneous plasma is discussed, and the validity criteria for the existence is discussed.
••
TL;DR: In this article, the probability of occurrence of fluctuations around nonequilibrium steady states is discussed from a kinetic viewpoint, and it is shown that in a large class of continuous media it is possible to extend the thermodynamic theory of fluctuations, provided one uses suitable steady-state parameters rather than equilibrium quantities.
Abstract: The probability of occurrence of fluctuations around nonequilibrium steady states is discussed from a kinetic viewpoint. It is shown that in a large class of continuous media it is possible to extend the thermodynamic theory of fluctuations, provided one uses suitable steady-state parameters rather than equilibrium quantities.
••
••
TL;DR: In this article, it is shown that those molecular collisions which tend toward equalization of molecular energies also tend to maximize the phase space available to a closed system, which helps to motivate the hypothesis that a functional relationship exists between the thermodynamic entropy and the available phase space.
Abstract: It is shown that those molecular collisions which tend toward equalization of molecular energies also tend to maximize the phase space available to a closed system. This helps to motivate the hypothesis that a functional relationship exists between the thermodynamic entropy and the available phase space for a closed system. The calculation, simple enough for an introductory course, is also illuminating in itself as an insight into the statistical nature of the second law of thermodynamics.
••
••
TL;DR: In this paper, a simple mixture in an approximation for highly diluted binary phases is used to develop the primitive model for the dyeing of hydrophobic textile substrates with nonionic dyes.
Abstract: A model of a simple mixture in an approximation for highly diluted binary phases is used to develop the primitive model for the dyeing of hydrophobic textile substrates with nonionic dyes. The form...