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Showing papers on "Non-equilibrium thermodynamics published in 1974"


Journal ArticleDOI
TL;DR: In this paper, the thermodynamics of a solid-liquid-vapor system both under chemical equilibrium and nonequilibrium conditions, based on the model of Gibbs, are discussed, and the degree of wetting or nonwetting of a flat and nondeformable solid by the liquid is defined by Young's equation in terms of the static interfacial tensions.
Abstract: The thermodynamics of a solid-liquid-vapor system both under chemical equilibrium and nonequilibrium conditions, based on the model of Gibbs, is discussed. Under chemical equilibrium conditions, the degree of wetting or nonwetting of a flat and nondeformable solid by the liquid is defined by Young's equation in terms of the static interfacial tensions. Under chemical nonequilibrium conditions, mass transfer across an interface results in a transient decrease in the corresponding specific interfacial free energy and the interfacial tension by an amount equal to the free energy of the effective chemical reaction per area at that interface. When the reaction is between the solid and the liquid, this transient lowering of the interfacial tension can cause the liquid drop to spread on the solid substrate if the interfacial energy reduction is large enough and also if the diffusion rates of the reacting components in the solid phase are slow enough relative to the flow rate of the liquid to cause the liquid at the periphery of the drop to be in dynamic contact with unreacted solid.

313 citations


Journal ArticleDOI
TL;DR: In this article, the macroscopic temperature and pressure jumps that occur at a condensate surface during a nonequilibrium phase change are calculated using a variational principle on the linearized Boltzmann equation.
Abstract: The macroscopic temperature and pressure jumps that occur at a condensate surface during a nonequilibrium phase change are calculated using a variational principle on the linearized Boltzmann equation. When evaluated for the BGK collisional model, the macroscopic jumps have values within 1% of a recent numerical calculation. Furthermore, the microscopic density and temperature jumps are estimated using an ansatz for the distribution function of molecules impinging on the surface. The jumps obtained in this way are correct to within 5% of the numerical values when evaluated for the BGK model. Also a simple procedure is described by which the jumps occuring at a surface for which the mass accommodation (condensation) coefficient σ≠1 may be calculated from those for which σ=1. In addition the connection of this kinetic theory with the thermodynamics of irreversible processes is made and the elements of the appropriate Onsager matrix are expressed in terms of the macroscopic jumps for arbitrary values of σ.

130 citations


Journal ArticleDOI
TL;DR: In this paper, a mathematical theory of chemical reaction systems is proposed, which separate equilibrium, nonequilibrium and stoichiometric aspects of a chemical reaction system, and the role of various constitutive assumptions is investigated.
Abstract: A mathematical theory of chemical reaction systems is proposed. Generic equations of motion are developed which separate equilibrium, nonequilibrium and stoichiometric aspects. The role of various constitutive assumptions is investigated.

123 citations


01 Jun 1974
TL;DR: In this paper, numerical solutions of the viscous-shock-layer equation where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium are presented, and the effects of the diffusion model, surface catalysis, and mass injection on surface transport and flow parameters are considered.
Abstract: Numerical solutions of the viscous-shock-layer equation where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium are presented. Also the effects of the diffusion model, surface catalysis, and mass injection on surface transport and flow parameters are considered. The flow is treated as a mixture of five inert and thermally perfect species. The viscous-shock-layer equations are solved by using an implicit-difference scheme. All calculations are for hyperboloids with included angles of 20 and 45. The flight conditions are those for various altitudes and velocities in the earth's atmosphere. Data are presented to show the effects of the chemical models; diffusion models; surface catalysis; and mass injection of air on heat transfer; skin friction; shock standoff distance; wall pressure distribution; and tangential velocity, temperature, and species profiles. The results show that an equilibrium analysis can substantially overpredict the heat-transfer rates for flow conditions experienced by earth-orbital entry vehicles. Moreover, at such conditions surface catalysis significantly influences heat-transfer and flow-field properties. If a binary rather than a multicomponent diffusion model is assumed, negligible errors in most flow properties result. Quantitative results are presented that show the effect of mass injection on flow properties within and downstream of the injection region.

83 citations


Journal ArticleDOI
TL;DR: In this article, the authors analyzed the far from equilibrium steady states of a simple nonlinear chemical system and showed that the nonlinearity introduces an instability which causes a transition analogous to a thermodynamic second-order phase transition.
Abstract: The far from equilibrium steady states of a simple nonlinear chemical system are analyzed. A standard macroscopic analysis shows that the nonlinearity introduces an instability which causes a transition analogous to a thermodynamic second-order phase transition. Fluctuations are introduced into this model through a stochastic master equation approach. The solution of this master equation in the steady state reveals that the system goes into a more ordered state above the transition point. An analogy is drawn with the nonequilibrium phase transition occurring in the laser at threshold.

71 citations


Journal ArticleDOI
TL;DR: In this article, the authors construct a thermodynamics which is surprisingly simple and yet capable of modeling viscous fluids, viscoelastic bodies, elastic bodies, and heat conduction.

51 citations


Journal ArticleDOI
TL;DR: In this paper, the linear Onsager theory of irreversible thermodynamics is extended to include nonlinear phenomenological relations by means of onsager fluxes, which satisfy a full system of reciprocity relations, vanish in thermodynamic equilibrium, and give a nonnegative production of entropy.

39 citations


Journal ArticleDOI
TL;DR: In this article, the thermodynamics of simple multicomponent hard-sphere polar mixtures are examined for the case of equal hardsphere radii, based on the exact solution of this model by Adelman and Deutch.
Abstract: The thermodynamics of two recent models of hard-sphere polar fluids is investigated. The two models are the Onsager model developed by Nienhuis and Deutch and the mean spherical approximation results obtained by Wertheim. The equation of state, vapour pressure curve, and other pertinent thermodynamic properties are determined. These results for the pure hard-sphere polar fluid complement the results recently reported by Rushbrooke, Stell and Hoye. The thermodynamics of simple multicomponent hard-sphere polar mixtures is examined for the case of equal hard-sphere radii. Results for the multicomponent MSM are based on the exact solution of this model by Adelman and Deutch. The Onsager model is generalized to the case of many components. For both multicomponent models it is demonstrated that a variety of regions of instability exist for the one-phase fluid. Finally a discussion is included of how well these models agree with experiment.

30 citations


Journal ArticleDOI
TL;DR: A new interpretation of thermodynamics is presented in this article, which is the study of those properties of macroscopic matter that follow from the symmetry properties of physical laws mediated through the statistics of large systems.
Abstract: A new interpretation of thermodynamics is advanced; thermodynamics is the study of those properties of macroscopic matter that follow from the symmetry properties of physical laws, mediated through the statistics of large systems.

28 citations


Journal ArticleDOI
TL;DR: In this paper, a nonlinear master equation describing the nucleation of critical fluctuations leading to an instability and subsequently to a dissipative structure is derived, and it is suggested that the formation of these structures bears strong analogies with first order phase transitions.

22 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the mean square fluctuation computed from a master equation in the space of internal states of the reacting species is identical to that calculated from Einstein's fluctuation formula.
Abstract: We study fluctuations around nonequilibrium steady states of some model nonlinear chemical systems. A previous result of Nicolis and Prigogine states that the mean square fluctuation computed from a master equation in the space of internal states of the reacting species is identical to that calculated from Einstein's fluctuation formula. Our analysis of fluctuations based on that master equation leads with the assumption of local equilibrium to a result identical to that obtained from a master equation for the total concentration of the reacting species, which is different from the equilibrium (Einstein relation) result. Nicolis and Prigogine approximated one term in their master equation, and a discussion of this approximation is presented. The master equation without this approximation yields at equilibrium the result expected on the basis of Einstein's formula.


Journal ArticleDOI
TL;DR: In this paper, the elements of the entropy matrix are determined from the derived total entropy density, which contains all possible interactions, and the element of the conductivity matrix characterizing the vortex motion is also evaluated.
Abstract: The different magnetic states of superconductors are characterized by extensive and intensive parameters. The elements of the entropy matrix are determined from the derived total entropy density, which contains all possible interactions. The element of the conductivity matrix characterizing the vortex motion is also evaluated. Stability criteria for the Meissner, flux creep, and flux flow states and the value of the needed external generation are given, as are the nonequilibrium deviations, thermodynamical forces, currents and entropy productions for the different cases. The nature of the unstable flux jump state is discussed.


Journal ArticleDOI
B. H. Lavenda1
TL;DR: In this paper, a theory for the space-time structure of nonequilibrium processes is developed, based on the validity of the kinetic form of the Gibbs equation and the generalized thermodynamic potentials.
Abstract: A theory treating the space-time structure of nonequilibrium processes is developed. The basis of the theory is founded upon the validity of: (i) the kinetic form of the Gibbs equation and consequently, the generalized thermodynamic potentials, and (ii) the balance equation of entropy, the continuity equation, and the conservation of energy. The dissipation function is derived from the kinetic form of the Gibbs equation. The only additive invariant remaining in nonequilibrium thermodynamics is the energy; within the entropy representation, it can be used to establish a local energy conservation or power equation. The first and second variations of the power equation determine the stationary-state conditions and the stability of the stationary state, respectively. It is impossible to characterize nonequilibrium stationary states in terms of only one generalized thermodynamic potential; a free extremum of the potential does not exist since the stationary-state values of the forces enter in the first variation of the potential. A constrained variational principle of least dissipation of energy is applicable to certain classes of nonequilibrium stationary-states, which may or may not be spatially homogeneous. Distinction is made between variational principles (e.g., least dissipation of energy) and extremum principles (e.g., minimum production of entropy). A kinetic criterion of mechanical equilibrium is derived from the direction of the entropy flux.

Journal ArticleDOI
TL;DR: It is shown that the exchange of thermal energy with the surrounding medium, acting as a reservoir, does not violate the second law of thermodynamics within broad limits.
Abstract: Bioenergetic processes are viewed as processes of free energy transduction. The free energies of both local equilibrium and fluctuation states are being considered. It is shown that the exchange of thermal energy with the surrounding medium, acting as a reservoir, does not violate the second law of thermodynamics within broad limits. There is sufficient latitude for proteins to carry out their function of transduction utilizing thermal energy in the process.


Proceedings ArticleDOI
01 Jul 1974
TL;DR: In this paper, a simple method of predicting aerodynamic heating and corresponding radiation equilibrium surface temperature-time histories for critical locations on space shuttle orbiter-type vehicles is presented, based on a generalization of correlation equations developed earlier by Rosner for predicting the energy transfer and radiation equilibrium temperatures of surfaces with arbitrary catalytic activity and total hemispheric emittance.
Abstract: A simple method of predicting aerodynamic heating and corresponding radiation equilibrium surface temperature-time histories for critical locations on space shuttle orbiter-type vehicles is presented. The method is based on a generalization of correlation equations developed earlier by Rosner for predicting the energy transfer and radiation equilibrium temperatures of surfaces with arbitrary catalytic activity and total hemispheric emittance. Recently obtained experimental data for O and N atom recombination probabilities on candidate material surfaces above 1000 K are used to assess nonequilibrium effects for a range of nose radii and a specific space shuttle re-entry trajectory. It is concluded that low catalytic activity will be especially important in locations of large effective nose radii by both increasing oxidation-resistant coating lifetime and reducing energy transfer into the vehicle.

Journal ArticleDOI
TL;DR: In this article, it was shown that a large class of approximations in statistical thermodynamics that are based on the free-energy variational principle for the density operator yield expressions for the macroscopic quantities of the system that are consistent from both the statisticalmechanical and thermodynamic points of view.
Abstract: It is shown that a large class of approximations in statistical thermodynamics that are based on the free-energy variational principle for the density operator yield expressions for the macroscopic quantities of the system that are consistent from both the statisticalmechanical and thermodynamical points of view. This corrects some erroneous statements in the literature. In an exact treatment of the statistical mechanics of a system in thermal equilibrium there is complete consistency between the definitions of the macroscopic quantities from the statisticalmechanical point of view and the corresponding ones from the standpoint of phenomenological thermodynamics. This great achievement of statistical mechanics can easily be established within the formulation of statistical therraodynamics„because the exact Hamiltonian of the system is a purely mechanical quantity independent of any thermodynamic parameters, such as temperature, etc. In various unavoidable approximation procedures for the thermal-equilibrium properties of systems, ho~ever, the Hamiltonian is approximated by an effective one that depends on such thermodynamic parameters. In such a case the statistical-thermodynamic consistency mentioned above is brought into question. In fact, it has been stated' that in the weil-known thermal Hartree-Fock approximation" for a system of interacting fermions this consistency is sacrificed. An approximation scheme in statistical thermodynamics that yields results that violate the consistency between the statistical and thermodynamical definitions of various observable quantities is clearly undesirable (at the very least one would have to give a reason for choosing one rather than the other definition}. In the following we shall show that there is a large class of approximations in statistical thermodynamics that are free from this serious drawback. According to the laws of thermodynamics' the complete macroscopic description of a system in thermodynamic equilibrium under certain constraints is provided by the fundamental relation appropriate to the constraints on the system, i.e., by a function of the appropriate independent variables. For example, for a simple, singlecomponent system of volume V in contact with a heat reservoir at temperature T and a particle reservoir at chemical potential p, , the fundamental relation is

Journal ArticleDOI
TL;DR: In this paper, the authors developed these relations using the terminology of non-equilibrium thermodynamics to show how the appropriate transport coefficients can be estimated from readily available transport coefficients, and developed the relation between the transport coefficients and the transport functions.
Abstract: It is the purpose of this article to develop these relations using the terminology of non equilibrium thermodynamics to show how the appropriate transport coefficients can be estimated from readily...


Journal ArticleDOI
TL;DR: In this article, the role of finite fluctuations in transitions between nonequilibrium steady states in nonlinear systems is investigated, focusing on a model biochemical system for which the usual deterministic chemical kinetics predicts a far-from-equilibrium region of multiple steady states.

Journal ArticleDOI
TL;DR: In this paper, the velocity correlation functions describe a source with time-dependent or independent Oseen propagators, and the correlation of pressure fluctuations, which exists even in the absence of dissipation, agrees with the result derived from the relaxation function of the mechanical fluctuation-dissipation theorem, as well as with the thermodynamic equilibrium correlation.
Abstract: Hydrodynamic propagators of forces are formulated and studied in the following cases: for uniform temperature, neglecting convection or using Oseen's linearization, with or without compressibility, and also for nonuniform temperature. Discussions and comparisons are given wherever possible. Such a propagator formalism is useful in cases of hydrodynamic interactions among solid bodies, as well as thermodynamic fluctuation forces. It is found that the velocity correlation functions describe a source with time‐dependent or ‐independent Oseen propagators. The correlation of pressure fluctuations, which exists even in the absence of dissipation, agrees with the result derived from the relaxation function of the mechanical fluctuation‐dissipation theorem, as well as with the thermodynamic equilibrium correlation. The correlation of temperature fluctuations describes a diffusion process of the variance κ/ρ0cp when cp = cν. In accordance with Curie's principle of nonequilibrium thermodynamics, it is found that th...

Journal ArticleDOI
TL;DR: In this paper, the nonequilibrium axisymmetric stagnation point boundary layer over an ablating graphite surface is considered and the external stream is a high temperature mixture of hydrogen and helium.

Journal ArticleDOI
TL;DR: In this article, the consequences of the second law of thermodynamics (Clausius-Duhem inequality) on the constitutive relations for the heat flux and the dectric current in isotropic solids are examined.
Abstract: In this work the Authors examine the consequences of the second law of thermodynamics (Clausius-Duhem inequality) on the constitutive relations for the heat fluxqand the dectric currentjin isotropic solids.


Journal ArticleDOI
TL;DR: In this article, the entropy of a general Ising chain with free ends has been found and the zero-temperature limit of the entropy reveals several cases, including some previously known, when the third law of thermodynamics is violated.


Journal ArticleDOI
TL;DR: In this article, it was shown that the ambiguity in the transformation laws of some thermodynamic quantities is not a consequence of special relativity, and that it is not due to any special relativity.

Journal ArticleDOI
TL;DR: In this paper, ideal gas models for equilibrium osmotic pressure and for nonequilibrium flow of solvent through an ideal semi-permeable membrane are presented, which can easily be introduced in general physics courses for students of the life sciences.
Abstract: Ideal gas models for equilibrium osmotic pressure and for nonequilibrium flow of solvent through an ideal semi-permeable membrane are presented. These models can easily be introduced in general physics courses for students of the life sciences. The models are justified in Appendices, which include a summary of the irreversible thermodynamics of flow through membranes. Some physiological examples are presented, including the Nernst equation and Gibbs-Donnan equilibrium.