Showing papers on "Non-equilibrium thermodynamics published in 1972"
Book•
01 Nov 1972
TL;DR: In this paper, the First Law of Thermodynamics and the Second Law of Entropy Irreversibility and Availability of a Pure Substance Work and Heat properties of a pure substance were discussed.
Abstract: Concepts and Definitions Properties of a Pure Substance Work and Heat The First Law of Thermodynamics The Second Law of Thermodynamics Entropy Irreversibility and Availability Some Power and Refrigeration Cycles Thermodynamic Relations Mixtures and Solutions Chemical Reactions Introduction to Phase and Chemical Equilibrium Flow Through Nozzles and Blade Passages.
851 citations
Book•
01 Jan 1972
TL;DR: In this article, the authors present a mathematical preparation for thermodynamics, including the application of the Gibbs Free Energy Function to chemical changes and the ideal solution of nonelectrolyte activities.
Abstract: Partial table of contents: Mathematical Preparation for Thermodynamics. Enthalpy, Enthalpy of Reaction, and Heat Capacity. Application of the First Law to Gases. The Second Law of Thermodynamics. Equilibrium and Spontaneity for Systems at Constant Temperature: The Free Energy Functions. Application of the Gibbs Free Energy Function to Some Phase Changes. The Third Law of Thermodynamics. Application of the Gibbs Free Energy Function to Chemical Changes. Thermodynamics of Systems of Variable Composition. Mixtures of Gases. The Ideal Solution. Dilute Solutions of Nonelectrolytes. Activities and Standard States for Nonelectrolytes. Calculation of Partial Molar Quantities from Experimental Data: Volume and Enthalpy. Determination of Nonelectrolyte Activities. Activity, Activity Coefficients, and Osmotic Coefficients of Strong Electrolytes. Index.
142 citations
TL;DR: In this paper, the theory of nonequilibrium fluctuations in open systems is extended to nonlinear situations, and it is shown that the usual birth-and-death type of stochastic formulation of chemical kinetics is in general inadequate and has to be replaced by a more detailed phase-space description.
Abstract: The theory of nonequilibrium fluctuations in open systems is extended to nonlinear situations. It is shown that the usual birth-and-death type of stochastic formulation of chemical kinetics is in general inadequate and has to be replaced by a more detailed phase-space description. As a consequence, for large classes of nonlinear systems arbitrarily far from equilibrium, the classical Einstein fluctuation formula can be extended, provided the steady reference state is asymptotically stable. The case of oscillatory or unstable systems is also discussed. It is conjectured that in such systems, the departure from the steady state is governed by large fluctuations of “macroscopic” size, while small fluctuations are still described by the extended Einstein formula. Nonequilibrium macroscopic instabilities such as chemical or hydrodynamic instabilities seem therefore to bear strong similarities to first-ordei phase transitions.
106 citations
TL;DR: Caratheodory's formulation of classical thermodynamics is cast into a mathematically rigorous form, in which such well-known results as the existence of entropy and of (positive) absolute temperature, the principle of increase of entropy, and the positivity of isometric specific heats are shown to follow logically from a set of postulates closely related to the traditional laws of thermodynamics and more economical than those of the original formulation as discussed by the authors.
Abstract: Caratheodory’s formulation of classical thermodynamics is cast into a mathematically rigorous form, in which such well-known results as the existence of entropy and of (positive) absolute temperature, the principle of increase of entropy and the positivity of isometric specific heats are shown to follow logically from a set of postulates closely related to the traditional laws of thermodynamics and more economical than those of the original formulation. The basic tools are differential geometry and topology, the latter being needed in order to eliminate those flaws in the old arguments that arise from the erroneous application of local results in a global context.
65 citations
TL;DR: In this article, the number dependence of the vibrational entropy for two-and three-dimensional crystallites was calculated by direct integration of the canonical partition function, showing that small-crystal entropies lie within 10k of the predictions of macroscopic thermodynamics.
Abstract: The approach of small‐crystal thermodynamic properties to the large‐crystal limit of thermodynamics is studied numerically. We calculate the number dependence of the vibrational entropy for two‐ and three‐dimensional crystallites by direct integration of the canonical partition function. A simple functional representation of the data shows that small‐crystal entropies lie within 10k of the predictions of macroscopic thermodynamics.
58 citations
TL;DR: Gurtin et al. as discussed by the authors studied the notion of invariance under time-reversal and established conditions that are both necessary and sufficient for the infinitesmal entropy production to display such invariance.
Abstract: TIME-REVERSAL AND SYMMETRY IN THE THERMODYNAMICS OF MATERIALS WITH MEMORY by Morton E. Gurtin We here study, within the framework of the thermodynamics of materials with memory, the notion of invariance under timereversal. In particular, we establish conditions that are both necessary and sufficient for the infinitesmal entropy production to display such invariance.
45 citations
33 citations
Book•
01 Jan 1972
33 citations
01 Jan 1972
TL;DR: This Chapter and the next two describe a theory of thermodynamics for simple materials with memory in which entropy enters as a derived concept.
Abstract: This Chapter and the next two describe a theory of thermodynamics for simple materials with memory in which entropy enters as a derived concept.
23 citations
TL;DR: In this article, the quantum theory of the one-phonon inelastic scattering of gas atoms in three dimensions by a solid surface, presented recently by F. O. Goodman [Surface Sci. 30, 1 (1972), is used to calculate energy accommodation coefficients for the system He•W. The approximations used are the same as those in the above paper, except that the gas surface interaction is represented by the exponential repulsive potential with zero well depth.
Abstract: The quantum‐mechanical theory of the one‐phonon inelastic scattering of gas atoms in three dimensions by a solid surface, presented recently by F. O. Goodman [Surface Sci. 30, 1 (1972)] is used to calculate energy accommodation coefficients for the system He‐W. The approximations used are the same as those in the above paper, except that the gas‐surface interaction is represented by the exponential repulsive potential with zero well‐depth. The theory is compared with experimental data on both equilibrium and nonequilibrium energy accommodation coefficients for He‐W. With a gas‐surface interaction potential inverse‐length parameter corresponding to a Morse parameter for He‐W in the range 1.3–1.6 A−1, and with a (bulk) Debye temperature for W in the range 320–380°K quantitative agreement is found between theory and experiment in regimes in which the theory may be expected to be applicable. These regimes are those in which effects of bound states of gas atoms at the surface, which are neglected in the theory, are relatively unimportant.
23 citations
TL;DR: In this paper, the retarded and advanced forms of the nonequilibrium statistical operator are derived from the extremum of the information entropy of a system taking into account the additional condition that the values of the generalized thermodynamic coordinates are fixed at the infinitely remote past or infinitely remote future.
TL;DR: The boundary between two phases of a one-component system contains two scalar force-flux pairs as discussed by the authors, i.e., the jumps of the temperature and of (essentially) the chemical potential at the interface; these jumps vanish if the four coefficients vanish.
Abstract: Abstract The entropy production - (3.8.) - in the boundary between two phases of a one-component system contains two scalar force-flux pairs. The \"forces\" are the jumps of the temperature and of (essentially) the chemical potential at the interface; the \"fluxes\" are the heat and mass fluxes nor-mal to the interface. So, four phenomenological coefficients appear in the pertaining local linear constitutive laws - (4.14 and 15) - for the boundary conditions. They can in principle be de-termined by a stationary heat conduction and phase transition experiment. Only measurements of temperature jumps - (5.14 and 15) - are involved. These jumps vanish if the four coefficients vanish
01 Mar 1972
TL;DR: In this paper, the authors explore the domain of validity of linear phenomenological relations and show that onsagers relations have been shown to be valid in the case of non-equilibrium thermodynamics.
Abstract: Experiments for the measurement of electroosmotic pressure, electro-osmotic velocity and streaming potential in the case of kaolinite-water system, have been described and the data analysed in the light of non-equilibrium thermodynamics.Onsagers relations have been shown to be valid. Attempt has been made to explore the domain of validity of linear phenomenological relations.
TL;DR: In this article, a new foundation of equilibrium thermodynamics based on certain ideas of T. Ehrenfest is presented, and the main result is the proof for the existence of entropy as a consequence of the conservation of energy for conservative thermal systems.
Abstract: This paper presents a new foundation of equilibrium thermodynamics based on certain ideas of T. Ehrenfest. The main result is the proof for the existence of entropy as a consequence of the conservation of energy for conservative thermal systems.
01 Jan 1972
TL;DR: In this paper, structural relaxation is defined as the process by which the molecules of a system “flow” from a nonequilibrium configuration to a new equilibrium configuration, and the method by which equilibrium is restored is known as a relaxation process.
Abstract: In general, liquids differ from solids primarily in their ability to flow. While in the process of flowing, however, a liquid is not in thermodynamic equilibrium. On a miscoscopic basis, for flow to occur, the molecules must rearrange relative to each other. In thermodynamic equilibrium, a liquid is completely characterized by a small number of state variables (e.g., the internal energy, volume, number of moles, total magnetic and electric moments, etc.). When a system initially in equilibrium is perturbed into a nonequilibrium state, the method by which equilibrium is restored is known as a relaxation process. Any such nonequilibrium state requires that parameters in addition to the state variables be specified for a complete characterization. In the present chapter, we will be concerned with structural relaxation. This is the process by which the molecules of a system “flow” from a nonequilibrium configuration to a new equilibrium configuration.
TL;DR: Countertransport and competitive acceleration were studied experimentally in the glucose system of the red cell membrane and theoretically by analysis of kinetics and the cross-coefficients are found to be equal in accordance with Onsager's law.
Abstract: Countertransport and competitive acceleration were studied experimentally in the glucose system of the red cell membrane and theoretically by analysis of kinetics. It is shown that, although the conditions for demonstration of the two phenomena differ, they are related by a symmetric interdependence of the simultaneous movements of two substrates. The symmetry can be shown by different types of kinetic treatment. Using the phenomenological equations of nonequilibrium thermodynamics for the description, the cross-coefficients are found to be equal in accordance with Onsager's law.
TL;DR: In this paper, electric field intensity and wall heat transfer measurements have been made for the inlet and asymptotic regions of Ar, He and N2 laminar, atmospheric arcs Comparisons between the data and available equilibrium and nonequilibrium theories were made in an attempt to determine the relative accuracy of single and multifluid arc models.
TL;DR: In this paper, the Kirkwood-buff theory of solutions is applied to solutions of interacting multicomponent charged aggregates and exact expressions which account for aggregation explicitly are derived and compared with the corresponding equations for small systems in a solvent given by T L Hill.
Abstract: The general results obtained previously when methods similar to those of surface thermodynamics were used to provide an alternative derivation of part of the Kirkwood—Buff theory of solutions are applied to solutions of interacting multicomponent charged aggregates General and exact expressions which account for aggregation explicitly are derived and are compared with the corresponding equations for small systems in a solvent given by T L Hill It is shown how the theory can be used to discuss conformation changes in macromolecules A general interpretation in molecular terms of the behaviour of the micelle point in multi-component solutions is also given Finally, expressions are presented for the interpretation of light scattering data
TL;DR: In this article, the results of numerical calculations of a nonequilibrium laminar boundary layer on axisymmetric bodies whose surface has arbitrary catalytic activity using a proposed technique are presented.
Abstract: Results are presented of numerical calculations of a nonequilibrium laminar boundary layer on axisymmetric bodies whose surface has arbitrary catalytic activity using a proposed technique. In the published studies devoted to the exact numerical methods for calculating the boundary layer with chemical reactions, it is assumed that the surface of the body is either noncatalytic or has infinite catalytic activity [1], that thermochemical equilibrium exists at the surface [2], or that the temperature and composition of the gas at the surface are given [3, 4]. This problem has been examined in the approximate formulation in several papers, specifically [5].
TL;DR: In this paper, it was shown that the stability criterion derived by Schlogl from statistical theory leads in the case of hydrodynamical transport states to a global stability criterion for a steady nonequilibrium state which leads under assumption of locality and for infinitesimal deviations from the steady state to the stability criteria of Glansdorff and Prigogine.
Abstract: It is shown that the stability criterion derived by Schlogl from statistical theory leads in the case of hydrodynamical transport states to a global stability criterion for a steady nonequilibrium state which leads under assumption of locality and for infinitesimal deviations from the steady state to the stability criterion of Glansdorff and Prigogine.
TL;DR: In this paper, the time-dependent statistics of binary linear lattices are investigated on the basis of a master equation at the microscopic level, where the kinetics may be formulated as transformations of specified sequences of clusters of units and units into other specified sequences.
Abstract: The time-dependent statistics of binary linear lattices is investigated on the basis of a master equation at the microscopic level. It is assumed that the kinetics may be formulated as transformations of specified sequences of clusters ofA units andB units into other specified sequences. On the basis of aStosszahlansatz, a master equation at the macroscopic level is derived. In the limit of a large system, the densities of clusters of all types satisfy rate equations similar to the equations of chemical kinetics. AnH-theorem is proven and the nonequilibrium thermodynamics of the system is studied. The theory has application to the kinetics of the helix-coil phase transition in biopolymers.
TL;DR: In this paper, the principal transport coefficient sigma was found to be approximately 0.9, which was higher than that measured previously in condensation-of-mercury experiments, and the experimental value of the coupling coefficient K did not agree with the value predicted from Schrage's kinetic analysis of the phase change.
Abstract: The object of this work is to determine the transport coefficients which appear in linear irreversible-thermodynamic rate equations of a phase change. An experiment which involves the steady-state evaporation of mercury was performed to measure the principal transport coefficient appearing in the mass-rate equation and the coupling transport coefficient appearing in both the mass-rate equation and the energy-rate equation. The principal transport coefficient sigma, usually termed the 'condensation' or 'evaporation' coefficient, is found to be approximately 0.9, which is higher than that measured previously in condensation-of-mercury experiments. The experimental value of the coupling coefficient K does not agree with the value predicted from Schrage's kinetic analysis of the phase change. A modified kinetic analysis in which the Onsager reciprocal law and the conservation laws are invoked is presented which removes this discrepancy but which shows that the use of Schrage's equation for predicting mass rates of phase change is a good approximation.
01 Aug 1972
TL;DR: In this article, the authors show that both the incident-and reflected-shock chemical relaxation times are important in governing the time to attain steady state thermodynamic properties, and adjacent to the end wall, an excess-entropy layer develops wherein the steady state values of all the thermodynamic variables except pressure differ significantly from their corresponding Rankine-Hugoniot equilibrium values.
Abstract: The method of characteristics for a chemically reacting gas is used in the construction of the time-dependent, one-dimensional flow field resulting from the normal reflection of an incident shock wave at the end wall of a shock tube. Nonequilibrium chemical reactions are allowed behind both the incident and reflected shock waves. All the solutions are evaluated for oxygen, but the results are generally representative of any inviscid, nonconducting, and nonradiating diatomic gas. The solutions clearly show that: (1) both the incident- and reflected-shock chemical relaxation times are important in governing the time to attain steady state thermodynamic properties; and (2) adjacent to the end wall, an excess-entropy layer develops wherein the steady state values of all the thermodynamic variables except pressure differ significantly from their corresponding Rankine-Hugoniot equilibrium values.
TL;DR: The theory of fluid mechanics can be profitably applied to chemistry by simply noting that many fluids are substances as discussed by the authors, and some of the most valuable parts of this theory may, for some purposes, also be regarded as a part of elementary physics completely independent of thermodynamics.
Abstract: The theory of fluid mechanics can be profitably applied to chemistry by simply noting that many fluids are substances. Certain equations of fluid mechanics then become the counterparts of equations in the theory of the chemical thermodynamics of systems at constant temperature. Consequently, some of the most valuable parts of this theory may, for some purposes, also be regarded as a part of elementary physics completely independent of thermodynamics.
TL;DR: In this article, the existence or absence of higher order symmetry relations among the phenomenological coefficients can depend on the choice of boundary conditions, and the over-all utility of the thermokinetic potential concept is discussed.
Abstract: Two examples, heat conduction in wires and the Poiseuille flow of a gas through a capillary tube, are used to show that the presence or absence of higher order symmetry relations among the phenomenological coefficients can depend on the choice of boundary conditions. A family of thermokinetic potentials is developed for each example, and the over‐all utility of the thermokinetic potential concept is discussed.