Showing papers on "Non-equilibrium thermodynamics published in 1975"

Metric geometry of equilibrium thermodynamics

Abstract: It is shown that the principal empirical laws of equilibrium thermodynamics can be brought into correspondence with the mathematical axioms of an abstract metric space. This formal correspondence permits one to associate with the thermodynamic formalism a geometrical aspect, with intrinsic metric structure, which is distinct from that arising from graphical representations of equilibrium surfaces in phase space.

Thermodynamics, kinetic theory, and statistical thermodynamics

Abstract: 1. Fundamental Concepts. 2. Equations of State. 3. The First Law of Thermodynamics. 4. Some Consequences of the First Law. 5. Entropy and the Second Law of Thermodynamics. 6. Combined First and Second Laws. 7. Thermodynamic Potentials. 8. Applications of Thermodynamics to Simple Systems. 9. Kinetic Theory. 10. Intermolecular Forces: Transport Phenomena. 11. Statistical Thermodynamics. 12. Applications of Statistics to Gases. 13. Applications of Quantum Statistics to Other Systems. Appendices.

Inadequacy of entropy and entropy derivatives in characterizing the steady state

Abstract: In bistable systems the transition kinetics between the two locally stable states can be altered without changing the behavior in the immediate vicinity of the two favored steady states. It follows that quantities which characterize only the vicinity of the favored states cannot determine the most probable state. A second point: Even in monostable linear circuits the steady state need not correspond to minimum entropy production.

Irreversible Thermodynamics of Nonequilibrium Alignment Phenomena in Molecular Liquids and in Liquid Crystals

Abstract: Abstract To treat nonequilibrium alignment phenomena in molecular liquids and in liquids crystals two points of the usual irreversible thermodynamics have to be modified. Firstly, in the specific energy a term quadratic in the alignment tensor is included. Secondly, terms up to 4th order in the alignment are taken into account in the entropy for a nonequilibrium situation. Then the entropy production is calculated. Constitutive laws are set up for the friction pressure tensor and for the tensor which characterizes the decay and the production of the alignment in the balance equation for the alignment tensor. As a first application, the nonlinear relaxation equation for the alignment is considered. For a uni-axial alignment zero and nonzero stable stationary values of the order parameter are found for temperatures above and below the temperature TK at which the transition from the isotropic to the nematic phase takes place. Small deviations from the equilibrium alignment decay exponentially. For temperatures below TK the relaxation time turns out to be anisotropic. In the appendix, the entropy associated with the alignment is calculated for a special case.

Stochastic models of firstorder nonequilibrium phase transitions in chemical reactions

Abstract: The steady states of a simple nonlinear chemical system kept far from equilibrium are analyzed. A standard macroscopic analysis shows that the nonlinearity introduces an instability causing a transition analogous to a thermodynamic first-order phase transition. Near this transition the system exhibits hysteresis between two alternative steady states. Fluctuations are introduced into this model using a stochastic master equation. The solution of this master equation is unique, preventing two alternative exactly stable states. However, a quasi-hysteresis occurs involving transitions between alternative metastable steady states on a time scale that is longer than that of the fluctuations around the mean steady state values by a factor of the formeΔφ, where Δo is the height of a generalized thermodynamic potential barrier between the two states. In the thermodynamic limit this time scale tends to infinity and we have essentially two alternative stable steady states.

Metric geometry of equilibrium thermodynamics. III. Elementary formal structure of a vector-algebraic representation of equilibrium thermodynamics

Abstract: The thermodynamic geometry established in an earlier paper is taken as the basis for an abstract vector‐algebraic representation of equilibrium thermodynamics. In this representation, thermodynamic field variables appear as abstract Euclidean vectors whose lengths and internal angles describe the equilibrium properties. A variety of thermodynamic indentities, stability conditions, and other relationships are derived and shown to have simple and natural geometric significance in the new framework. The geometric viewpoint is also found to suggest certain lines of development—such as the use of self‐conjugate (’’normal’’) field variables—with no obvious counterpart in the traditional differential formalisms. The formal ideas are illustrated throughout with elementary applications to properties of a simple homogeneous fluid.

On the theory of boundary conditions

Abstract: The question which boundary conditions are appropriate for the given differential equations of a continuum theory, is treated by the method of nonequilibrium thermodynamics. In the first part the previous investigation1) which had been confined to ordinary hydro(aero-)dynamics is generalized by taking into account higher derivatives in the continuum constitutive laws. This kind of generalization becomes important when a rarefied gas with boundary is treated phenomenologically (wall influence, slip-flow regime). In the second part an even more general scheme is discussed. The underlying applications now are rarefied polyatomic gases within walls, perhaps in an external field. So, the starting point is a general set of transport-relaxation equations with more variables than the hydrodynamical ones. By considering the corresponding entropy production, especially its part due to the boundary, it is again possible to set up constitutive laws, i.e., matching or boundary conditions, at an interface or a surface.

Entropy and mass flow for energy conversion

Abstract: Energy conversion takes place either in generalized capacitor or generalized resistor networks, that is, C- and R-fields in the sense of Paynterian bondgraphs. Entropy is interpreted as a kind of thermal charge. An electrical example is the difference of conduction and convection associated with mass flow. The generation of entropy in irreversible processes is represented by RS-fields as extension of the simple generalized resistors or R-elements. Thermoelectric power conversion is described by combined RS-fields, and Onsager's symmetry conditions for such fields are derived from the second law of thermodynamics.

A characteristic class of quantities in nonequilibrium thermodynamics and a statistical justification of the local equilibrium approximation

Abstract: Starting from entropy in equilibrium thermodynamics, defined as the mean value of a bit-number, the cumulants of this bit-number are discussed Moreover, relative bit-numbers of two probability distributions, and their cumulants are considered All these cumulants are additive quantities for independent systems, and are invariants with respect to reversible motion The cumulants of lowest order are well known quantities in statistical thermodynamics, which play important roles in nonequilibrium thermodynamics as well Their reversibility invariance gives a justification of the macroscopic approximation by “local equilibrium” for hydrodynamic system on a very general level

Non-equilibrium one-dimensional two-phase flow in variable area channels

Abstract: A one-dimensional nonequilibrium flow analysis has been formulated for a one component two phase flow. The flow is considered homogeneous and essentially isothermal. Phase change is assumed to occur at heterogeneous nucleation sites and the growth of the vapor bubbles is governed by heat conduction from the liquid to the bubble. The analysis adjusted for friction is applied to liquid nitrogen flow in a venturi and comparison is made with the NASA experimental results of Simoneau. Good agreement with the experiments is obtained when one assumes the effective activation energy for nucleus formation to be small but nonzero. The computed pressure distributions deviate from the experimental results in the throat region of the venturi in a manner consistent with centrifugal effects not accounted for in the one-dimensional theory. The results are shown to depend not only on cavitation number but on additional dimensionless parameters governing the nonequilibrium production and subsequent growth of nuclei.

Isotope separation in chemical reactions of vibrationally excited molecules

Abstract: The vibrations] distribution functions are analyzed theoretically for a binary mixture of diatomic gases modeled by anharmonic oscillators. It is assumed that the conditions are far from equilibrium. The results are used to calculate the isotope separation coefficient for chemical reactions involving vibrationally excited molecules. It is shown that far from equilibrium the separation coefficient is no longer an exponential function of the ratio of the activation energy to the gas temperature but depends only on the nonequilibrium store of the vibrational energy of the system.

Evaporation and condensation for general gas–liquid surface scattering

Abstract: The Onsager matrix for the liquid−vapor phase change of a monatomic gas in the presence of a Knudsen layer is calculated for a general gas surface sscattering law. The linearized Boltzmann equation is solved by the variational technique. The driving forces are the macroscopic pressure and temperature jumps. The calculated phenomenological coefficients show the influence of the reflection probability of the molecules on the surface and satisfy Onsager’s symmetry relation and the inequalities which follow from the fact that the entropy production rate in nonequilibrium is positive definite. In particular, the influence of the evaporation coefficient and the thermal accomodation coefficient is given. Simpler expressions are given for a generalized Maxwellian boundary condition.

The kinetics of phase separation in a liquid binary mixture

Abstract: A dynamical theory for the spontaneous formation and growth of spherical drops in a metastable liquid phase is constructed out of hydrodynamics, nonequilibrium thermodynamics, and thermodynamic fluctuation theory and used to predict the nucleation kinetics for phase separation in a liquid binary mixture. The nucleation rate is considerably lower than that predicted by classical nucleation theory and the inhomogeneities which result from forming nuclei in a finite time cause the actual kinetic path to differ considerably from the classical path. A qualitative agreement with experiment is demonstrated.

Entropy extremum of relativistic self-bound systems: A geometric approach

Abstract: Conditions for entropy extremum of self-bound relativistic systems of particles, in stationary axisymmetric motion, are obtained under the following constraints: (i) The system is kept isolated in a geometrical sense, implying that the total mass-energy and total angular momentum, defined by the asymptotic behavior of the metric, are kept constant, (ii) the total number of particles is kept constant, and (iii) Einstein's constraint equations are imposed on a spacelike hypersurface. It is shown that if the system is in mechanical equilibrium, the total entropy is an extremum for all trial nonequilibrium configurations that satisfy the constraints and respect the symmetry, if and only if (i) Einstein's dynamical equations are satisfied, (ii) the temperature and the chemical free energy, as seen from infinity, are constant, and (iii) the system is rigidly rotating. The proof does not depend on a particular functional expression for the mass or for the angular momentum; consequently, no related Lagrange multipliers have been used.

Continuum thermodynamics based on a notion of rate of loss of information

Abstract: It is not known for sure how to formulate the second law so as to describe adequately the behaviour of bodies which deform and remember the past. Following the lead of COLEMAN & NOLL 1 it has become common practice in continuum mechanics to take as the second law the proposition that the Clausius-Duhem inequality holds in every process compatible with the balance of mass, momentum, moment of momentum and energy. Interpreted in that way the law leads to restrictions on constitutive relations, and COLEMAN & NOLL developed a method for determining those res t r i c t ions -a method which has been extended, elaborated and applied by many. 2 To take the second law to be the Clausius-Duhem inequality is to assume, among other things, that temperature and entropy are defined far from equilibrium. Those who do not find the truth of that assumption transparently obvious ask for an alternative approach and my intention is to propose one tentatively. The future behaviour of a body is determined by prescribing initial data, which may well include information about its past history, and also the action of the external world by way of surface traction and body forces and the supply of heat through conduction and radiation. The action of the external world may be such that only certain gross features of the initial data remain relevant to predicting the ultimate behaviour whereas the details become less and less relevant. Thus a homogeneous, rigid, heat conductor, which is thermally isolated and whose initial temperature field is prescribed, approaches equilibrium at a temperature determined solely by the total initial internal energy and the specific heat of the conductor; all features of the initial temperature other than the total energy ultimately become irrelevant. In statistical mechanics the increasing irrelevance of the details of the initial data is called, not strictly accurately, loss of information and I shall use the same terminology here.

Analytical thermodynamics. Part I. Thermostatics—General theory

Abstract: A new axiomatic treatment of equilibrium thermodynamics—thermostatics—is presented. The equilibrium states of a thermal system are assumed to be represented by a differentiable manifold of dimensionn + 1 (n finite). The empirical temperature is defined by the notion of thermal equilibrium. Empirical entropy is shown to exist for all systems with the property that the total work delivered along closed adiabats is zero. Absolute entropy and temperature follow from the additivity of heat and energy for two separate systems in thermal equilibrium considered as a whole. The absolute temperature is defined up to a multiplicative constant. The exterior differentiable calculus of Cartan is introduced and in a subsequent paper its use for the derivation of standard results in thermostatics will be explained.