Showing papers on "Non-equilibrium thermodynamics published in 1976"

Nonequilibrium thermodynamics and rheology of viscoelastic polymer media

Abstract: Nonlinear constitutive equations for viscoelastic polymer media have been derived with the help of irreversible thermodynamical methods. These equations contain a small number of constants which have obvious physical meaning. The work is based on the hypothesis that the high-elasticity state characterized by large elastic strains is the local equilibrium thermodynamical state of these media. A theoretical description is given to explain the kinetic transition of fluid polymer media into high-elasticity state at temperatures above the flow temperature.

Boundary conditions and non-equilibrium thermodynamics

Abstract: The theory of non-equilibrium thermodynamics is applied to a system of two immiscible fluids and their interface. A singular energy density at the interface, which is related to the phenomenon of surface tension, is taken into account. Furthermore the momentum and the heat currents are allowed to be singular at the interface. Using the conservation laws and the Gibbs' relation for the surface, an expression for the singular entropy production density at the interface is obtained. The linear phenomenological laws between fluxes and thermodynamic forces occurring in this singular entropy production density are given. Some of these linear laws are boundary conditions for the solution of the differential equations governing the evolution of the state variables in the bulk.

Metric geometry of equilibrium thermodynamics. V. Aspects of heterogeneous equilibrium

Abstract: The general analysis of phase equilibrium in heterogeneous systems is considered from an abstract geometric point of view. Particular attention is drawn to the thermodynamic ’’invariants’’ (or ’’symmetries’’), which arise as null eigenvectors of the thermodynamic metric matrix and can be associated with variations which leave the thermodynamic state unchanged. The analysis of these invariants leads to conditions connecting the thermodynamic field vectors, including Gibbs–Duhem relations, Clausius–Clapeyron equations, Gibbs–Konowalow laws, and systematic generalizations thereof.

A Unified Quantum Theory of Mechanics and Thermodynamics. Part I. Postulates

Abstract: A unified axiomatic theory that embraces both mechanics and thermodynamics is presented in three parts. It is based on four postulates; three are taken from quantum mechanics, and the fourth is the new disclosure of the existence of quantum states that are stable (Part I). For nonequilibrium and equilibrium states, the theory provides general original results, such as the relation between irreducible density operators and the maximum work that can be extracted adiabatically (Part IIa). For stable equilibrium states, it shows for the first time that the canonical and grand canonical distributions are the only stable distributions (Part IIb). The theory discloses the incompleteness of the equation of motion of quantum mechanics not only for irreversible processes but, more significantly, for reversible processes (Part IIb). It establishes the operational meaning of an irreducible density operator and irreducible dispersions associated with any state, and reveals the relationship between such dispersions and the second law (Part III).

Dissipation and fluctuations in nonequilibrium thermodynamics

Abstract: A relationship between dissipation and fluctuations is described which leads to a unified theory of irreversible processes far from equilibrium. The development is based on the principle that dissipation and fluctuations are caused by elementary molecular processes. This permits the formulation of a canonical form for the rate of dissipation of the extensive variables. The canonical form depends on the thermodymanic quantities which are conjugate to the extensive variables, and it is shown that the canonical form leads to the customary transport equations for a variety of linear and nonlinear relaxation processes. Because fluctuations are also caused by molecular events, this formulation of dissipation can be used to examine deviations from the average. The theory associates a nonstationary, Markov stochastic process with fluctuations away from the conditionally averaged extensive variables. This description of nonequilibrium thermodynamics does not require the entropy to be introduced, and for rate proce...

Fluctuations, stability, and generalized state functions at nonequilibrium steady states

Abstract: Fluctuation–dissipation postulates, which describe the kinetic effects of molecular processes, are used to characterize nonequilibrium steady states. Attention is restricted to stable, noncritical states which develop in systems with inputs that are time independent. For these systems it is shown that the steady state distribution is Gaussian, which provides a generalization of the well‐known Einstein formula for equilibrium states. For certain systems it is shown that the time dependence of the covariance matrix of the extensive variables gives a necessary and sufficient condition for the stability of a noncritical state. These considerations are illustrated for the steady states accompanying diffusion, heat transport, chemical reactions with linear coupling, and certain nonlinear chemical reactions. These examples show that the covariance matrix is not necessarily related to the local equilibrium entropy. When the covariance matrix is invertible, it can be used to construct generalized state functions w...

A unified quantum theory of mechanics and thermodynamics. Part IIa. Available energy

Abstract: Part II of this three-part paper presents some of the most important theorems that can be deduced from the four postulates of the unified theory discussed in Part I. In Part IIa, it is shown that the maximum energy that can be extracted adiabatically from any system in any state is solely a function of the density operator\(\hat \rho\) associated with the state. Moreover, it is shown that for any state of a system, nonequilibrium, equilibrium or stable equilibrium, a unique propertyS exists which is proportional to the total energy of the system minus the maximum energy that can be extracted adiabatically from the system in combination with a reservoir. For statistically independent systems, propertyS is extensive, it is invariant during all reversible processes, and it increases during all irreversible processes.

Entropy and macroscopic disequilibrium. II. The information theoretic characterization of Markovian relaxation processes

Abstract: This paper considers the characterization of disequilibrium in uniform systems in terms of the time evolution of the macroscopic observables. Using these as the independent variables the procedure of maximal entropy is employed to generate a new, complementary set of independent variables, the thermodynamic forces. An equation for the time rate of change of the macroscopic observables (i.e., for the thermodynamic fluxes) which is valid also for a finite displacement from equilibrium is derived. The kinetic coefficients satisfy reciprocity relations and reduce to the Onsager coefficients in the linear regime. An equation of motion which is linear in the thermodynamic forces throughout the relaxation process is then obtained using the Legendre transform technique. The two possible equations of motion are strictly equivalent and provide (complementary) generating functions for the thermodynamic forces and fluxes. Among all possible population distributions consistent with the magnitude of the macroscopic observables, the ’’most probable’’ distribution is shown to be characterized by having the lowest rate of entropy production throughout the relaxtion process. The Rayleigh–Onsager principle of least dissipation of energy is extended to the nonlinear regime. It is then employed as a variational principle to derive the equations of motion, which inherently satisfy the reciprocity relations and which are valid throughout the relaxation process. An evolution criterion for the system is thereby provided.

Graphite Sublimation Chemistry Nonequilibrium Effects

Abstract: The implications of the assumption of local solid-gas phase equilibrium for subliming carbon species for graphite ablation calculations in an air environment is investigated. The equilibrium assumption is eliminated by considering the Knudsen-Langmuir equation at the interface for each carbon species. Calculated equilibrium and nonequilibrium results are compared for a very wide range of flight and ground-test environments. The nonequilibrium mass addition parameter is always less than the equilibrium value, and the nonequilibrium wall temperature is always larger for a given environment. Calculations made to determine the convective heat flux required to reach an incipient melt temperature of 3800 K indicate that the required flux determined from an equilibrium calculation can be too high by as much as 200-300% for stagnation enthalpies less than 5000 Btu/lb. Calculations for superorbital re-entry conditions show large differences in the mass addition parameter B' when the convective heating rate is low and the external radiation heating level is relatively high. Similar large differences in R' could be simulated in an existing ground-test facility if the reported external radiation heating level could be increased. Such an experiment would provide data to test the validity of present convectiveheating-rate blowing correlations in a combined heating environment.

Statistical thermodynamics of configurational properties

Abstract: The question a student of glass structure asks is of the form: What is the structure of a glass of a particular composition, e.g., SiO, or a Au-Pd-Si alloy? H e is usually aware that the properties of a glass, for example, its density, is somewhat dependent on its thermal history-how rapidly it was cooled through the glass transition range or whether it was annealed or not. But as a practical matter, the radial distribution function (the usual means of specifying structure) is not particularly sensitive to the thermal history, and the latter is therefore regarded as of only peripheral relevance to the problem of structure. For the student of the statistical thermodynamics of the glass transition, however, the notion of the structure is too simplistic. His focus of interest is on all the structures possible. If there were only one structure of a glass, the thermodynamics would be a lot easier than it is, though it wouldn't be easy. I t would presumably be a problem in the vibrational spectrum of a nonperiodic arrangement of atoms-an extremely difficult and as yet unsolved problem. As a glass is warmed up above its transition temperature Tg and becomes a liquid, there are fairly rapid though not discontinuous changes in the second derivative properties specific heat C,, thermal expansion coefficient a, and isothermal compressibility p. The values of these properties in the liquid are higher than in the glass. Accounting for their changes at Tg in molecular terms is the problem the statistical thermodynamicist is concerned with. Now the fact that there are such changes near Tg is not itself a mystery. Their occurrence can be well accounted for without invoking a thermodynamic phase transition, although the behavior can be partly described using some of the mathematics of a second-order transition of the Ehrenfest type.' It is assumed that below Tg the substance is kinetically frozen into a single structure, with only vibrational degrees of freedom active, while above Tg, in the metastable supercooled liquid state, the kinetic restriction is removed by the higher temperature, and the substance is able to explore many structures over the time scale of an observation. And further, as temperature is raised, structures of higher energy and volume become accessible. Hence increases of AC,, A a , and AP in Cp, a, and P are observed at Tg. Molecular models of the glass transition based on these concepts have been constructed, from which predictions of the thermodynamic changes at Tg have been made. The models permit the calculation of the number of structures of a given energy and volume, and hence of the thermodynamic properties.

On the kinetic meaning of the second law of thermodynamics

Abstract: A kinetic‐molecular theory which connects dissipation and fluctuations is used to examine the second law of thermodynamics. Considerations are restricted to systems with stable equilibrium states and are based on a conservation condition satisfied by transport processes which obey microscopic reversibility. The conservation condition leads to a statement about the accessibility of equilibrium states which is comparable to the Caratheodory statement of the second law. Insofar as the transport of heat into a system is the only process which violates microscopic reversibility, this statement is equivalent to the second law. The present treatment also gives a simple kinetic proof of the Clausius inequalities TRdS/dt?dQ/dt and dS/dt?0 for the entropy. Using the statistical aspects of the fluctuation–dissipation postulates, a class of state functions related to the equilibrium statistical distribution are defined, and it is verified that the entropy is one of these functions. A brief discussion is given of how ...

On the nonequilibrium distribution of adatoms resulting from dissociative adsorption of a diatomic gas

Abstract: Kinetic equations governing the distribution of adatoms resulting from irreversible, dissociative adsorption of homonuclear diatoms onto a two‐dimensional lattice are derived. Desorption and atomic skating are ignored, which allows the problem to be conveniently formulated from a molecular viewpoint. The rate constant for adsorption is assumed to be of an Arrhenius form with an activation energy which consists of an additive contribution from the interaction of the adsorbing molecule with each adatom on the surface. Special attention is paid to the relationship between the molecular distribution resulting from irreversible adsorption and the equilibrium molecular distribution. The kinetic equations are solved as a power series in the covering fraction; the coefficients involve molecular cluster diagrams similar to those in equilibrium, virial expansions. Comparison of the nonequilibrium and equilibrium covering fraction expansions of the molecular pair distribution functions is made, and an illustrated ex...

Non-equilibrium thermodynamics of electro-osmosis of liquid mixtures. Studies on acetone + water mixtures

Abstract: Electro-osmosis of acetone + water mixtures through a Pyrex sintered glass membrane (porosity G-4) has been studied, and the data analysed using non-equilibrium thermodynamics. The validity of the linear phenomenological equations and Onsager's reciprocal relations, for all the compositions of the mixture, has been demonstrated. The concentration dependence of the phenomenological coefficients has been shown to be in conformity with Spiegler's frictional model. The data have also been utilised to calculate the efficiencies of electrokinetic energy conversion for both electro-osmosis and streaming potential, and the results obtained shown to be in accordance with the thermodynamic theories.

The onset of instabilities in nonequilibrium systems

Abstract: The nonlinear master equation previously proposed by Malek-Mansour and Nicolis is applied to the analysis of unstable transitions leading to temporally or spatially organized patterns. Thecorrelation length of the destabilizing fluctuations is determined, and a number of striking analogies with equilibrium phase transitions are pointed out.

Linear response theory of a turbulent plasma

Abstract: The linear response theory of a turbulent plasma is presented. The procedure of obtaining the dielectric constant of a turbulent plasma is presented using quasi‐linear techniques. The principal result of the theory is the electron orbit modification due to the steady Langmuir turbulence fields. The collisional dissipative parametric destabilizing effect of the Langmuir turbulence fields on the ion sound waves appears. A steady turbulent state is maintained by the competing processes between the linear Landau damping effect and the collisional dissipative parametric destabilizing effect of the Langmuir turbulences. It is suggested that the generalized parametric resonance effect is effective for ion heating through linear Landau resonance. The critical Langmuir wave fluctuation level is given in terms of the ion‐to‐electron temperature ratio and wavelength. The steady plasma turbulence theory is applicable to plasma far from the thermal equilibrium state.

Thermal Physics: An Introduction to Thermodynamics, Statistical Mechanics and Kinetic Theory

Abstract: Part 1 Thermodynamics: first law of thermodynamics - Zeroth law and scale of temperature, equation of state, the reversible quasi-static process, work, specific heat or heat capacity, heat engines, conclusions based on the first law second law of thermodynamics - an integrating factor for dQR entropy as a function of state, the calculation of entropy changes in principle, principle of increase of entropy, the entropy of a perfect gas, adiabatic equation for a perfect gas, the Carnot theorems for heat engines, history of thermodynamics, the traditional approach to the second law further concepts of thermodynamics - the fundamental equations, the Maxwell relations, thermodynamic equilibrium, third law of thermodynamics, thermodynamic systems with a variable number of particles further applications of thermodynamics - reduction of measurements to constant volume, the principal specific heats, cooling and liquefaction of gases, phase transitions. Part 2 Equilibrium statistical mechanics: weakly coupled systems - systems of identical particles, two model systems, the general weakly coupled localized system, a gas of weakly coupled particles, conclusion equilibrium statistical mechanics - ensemble averages, the canonical partition function, the connection with thermodynamics, localized systems, classical perfect gas, the equipartition of energy, fluctuations about equilibrium, negative temperature, conclusion, systems with a variable numbers of particles. Part 3 Kinetic theory: kinetic theory of gases I - distribution functions, mean values, Doppler broadening of spectral lines, the passage of molecules across a plane surface, effusion kinetic theory of gasses II - the mean free path, atomic beams, the verification of the Maxwell velocity distribution, transport properties of a perfect gas, the Boltzmann transport equation, conclusion. Part 4 Applications of thermodynamics and statistical mechanics: further applications - quantum gases, black-body radiation, heat capacity of solids, magnetism conclusion - functions of two or more variables, useful mathematics, Lagrange undetermined multipliers, density of single-particle states, systems with a variable number of particules, approximate values of fundamental constants, properties of the elements (required for exercises), properties of gases at NTP.

Nonequilibrium velocity distribution and reaction rate in hot-atom reactions

Abstract: The nonequilibrium velocity distribution and reaction rate in the hot‐atom reactions are studied by solving the time‐dependent Boltzmann equation with the Monte Carlo simulation. The explicit time‐dependent velocity distribution, temperature, and rate constant of hot atoms from initial to steady states are obtained for a simple model system, where hot atoms are dispersed in the heat bath of surrounding molecules without internal degrees of freedom and the cross sections are chosen as a simple hard sphere model. The low‐ or high‐temperature steady state exists in consistence with the prediction of Keizer with the Maxwell distribution approximation. The hot‐atom velocity distribution for the high‐temperature steady state is, however, different from the Maxwell distribution. The nonequilibrium velocity distribution yields a much smaller value of the lower limit of the ratio of reactive to elastic cross sections for the existence of the high‐temperature steady state and a smaller rate constant than those of the Maxwell distribution approximation by Keizer.

An approach to thermodynamics of polymer flow based on internal state variables

Abstract: Two kinds of thermodynamic theories, which seem to be applicable to polymer deformation and flow, have been developed in the recent literature. One of these approaches utilizes entropy far from equilibrium as a primitive undefined concept. The alternate kind of theory involves the idea of a quasi-static process as a primitive concept. In this work, an approach based on internal state variables (specifically, the micro structure of the polymeric material) is used to argue that both primitive concepts are in some sense legitimate on physical grounds. In particular, the legitimacy of the quasi-static process concept is related to the smoothness of the function delivering the rate of change of the microstructure.