Showing papers on "Non-equilibrium thermodynamics published in 1968"

Relativistic Thermodynamics of Moving Systems

Abstract: The rmodynamics is extended to systems moving with relativistic velocities. It is shown that one is led naturally, although not necessarily, to the thermodynamics of Ott, if one maintains the first and second law in their original form. The classical theory of Planck et al. can also be obtained in the case of a homogeneous fluid; the difference with Ott's theory is that the fluid alone is regarded as the thermodynamic system, rather than the fluid together with the box in which it is enclosed. Subsequently, a third form of relativistic thermodynamics is obtained by replacing the first law with a covariant equation expressing conservation of both energy and momentum. This leads to a formulation in which not only $S$ but also $T$ and $\dj{}Q$ are scalars. The discussion of heat transfer between systems with different velocities is thereby simplified. It is shown that such processes are irreversible even for equal temperatures, unless the velocities are equal too.

Axiomatic Thermodynamics and Extensive Measurement.

Abstract: : The paper applies set theory to various phases of thermodynamics and measurement systems.

Attainment of Statistical Equilibrium in Excited Nuclei

Abstract: The usual interpretation of high-energy nuclear reactions entails a two-step mechanism: (1) a first step, which includes the emission of knock-on particles in an intranuclear cascade generated by the incident particle, followed by (2) the "evaporation" of particles from the residual excited nucleus, which is assumed to be at statistical equilibrium. If the independent-particle model with residual two-body interaction is taken as a description of the residual excited nucleus, the assumption in the second step requires that the nonequilibrium distribution of nucleons and holes that are produced in the fast step approach the equilibrium distribution before more particles leave the nucleus. This requirement has been investigated and shown to be valid by numerically solving a Boltzmann-like master equation for a Fermi-gas system.

Carathéodory's principle and the existence of global integrating factors

Abstract: A proof is given of a theorem on the integrability of Pfaffian forms which is used in Caratheodory's approach to thermodynamics. It is pointed out that Caratheodory's original proof of the existence of entropy and of absolute temperature is incomplete, since it fails to take into account the local nature of this theorem. By combining the theorem with the results ofBuchdahl andGreve on the existence of continuous empirical entropy functions, it is shown that the First and Second Laws of Thermodynamics imply the existence of a globally defined differentiable empirical entropy function for every simple thermodynamic system. This result supplies the missing step in Caratheodory's argument and makes a separate proof of the principle of increase of entropy unnecessary.

Theory of Nonequilibrium Distribution Coefficients during Crystallization

Abstract: A phase transformation in a multicomponent system is described in terms of a set of coupled reactions of the transformation type and the redistribution type. The interface region is considered as an open thermodynamic system undergoing irreversible changes. The nonequilibrium partitioning of impurities is calculated for nonionic systems and the nonequilibrium partition coefficient is found to depend on the interface temperature Ti and the growth velocity V of the new phase. Whether the equilibrium partition coefficient ke is greater than, less than, or equal to 1, for an ideal solution the actual partition coefficient k is greater than, less than, or equal to 1 dependening on Ti and V. Using a “large departure from equilibrium” approximation, it is shown that k → 1 as V → ∞ independent of whether ke is less than or greater than 1, and a mathematical relationship is derived to give k as a function of V.

An analysis of the coupled chemically reacting boundary layer and charring ablator. Part 5 - A general approach to the thermochemical solution of mixed equilibrium-nonequilibrium, homogeneous or heterogeneous systems

Abstract: Computer program for solutions to equilibrium and nonequilibrium chemical state relations for open and closed thermodynamic systems

Fundamental Thermodynamics Since Carathéodory

Abstract: The uneasiness prevailing in thermodynamics is the inevitable result of the absence of clearly understood basic concepts. Since thermodynamics, the doctrine of equilibrium, encompasses parts of all branches of the physical sciences, its basic concepts must be explained in ordinary language, free from all references to a specific branch. Moreover, the general applicability of the concepts must be demonstrated.Carath\'eodory has introduced new ideas of fundamental importance. But his shortcomings concerning basic concepts have been repeated and intensified by his successors in axiomatics.A properly constructed basis of thermodynamics elucidates the fundamental distinction of generalized coordinates and generalized forces from each other and from other properties. As an accessorial result one notices a unique quality of the generalized forces (and the temperature): They can be measured only if equilibrium has been established.The so-called "zeroth law" is neither a law nor a generalized observation. The clarification of its significance contributes to the epistemological understanding of thermodynamics.

Nonequilibrium Effects in Free‐Radical Recombination and Ion‐Molecule Reaction Kinetics

Abstract: Distortion of the molecular velocity distribution functions from the Maxwellian form and the resulting deviation of the reaction‐rate coefficients from the values calculated with the equilibrium assumption of conventional chemical kinetics are considered for two types of reactions in dilute, isothermal, spatially uniform gas mixtures: free‐radical recombination reactions and ion‐molecule reactions, both proceeding without an activation energy. The reactive collision cross sections used are those derived from the attractive potentials of the reacting pairs, which are inversely proportional to the sixth and the fourth powers of interparticle distances, respectively. The treatment is based on generalized Boltzmann equations which take into account the effects of reactive collisions, as well as elastic collisions, on the change of the velocity distributions with time. For free‐radical recombination reactions, a first‐order perturbation approximation analogous to that of Chapman and Enskog is used to derive the composition dependence of nonequilibrium effects. This differs from Mahan's earlier calculation; and, contrary to Mahan's result, the present calculation shows that the deviation of the rate coefficient from the equilibrium value remains small for any mole fraction of free radicals and typical values for various molecular parameters. The possible origin of the difference between the two calculations is analyzed. For the ion‐molecule reactions, it is first shown that there is no distortion of the Maxwellian distribution by first‐order perturbation theory irrespective of the choice of the series expansion. Next it is proved, without using a perturbation scheme, that nonequilibrium effects in the reaction rates vanish exactly for the ion‐molecular reactions. The last conclusion is reached without an explicit assumption about the form of the velocity distribution, just as in the case of the transport properties of Maxwellian molecules which interact according to an inverse fourth‐power repulsion potential. The reason for small or vanishing nonequilibrium effects in these reactions without activation energy is discussed.

Microwave Breakdown in High‐Temperature Air

Abstract: A review of investigations of microwave breakdown in high‐temperature air reveals significant discrepancies between theoretical expectations and experimental observations. Experimental measurements obtained in shock‐heated air are presented to confirm the temperature dependence of ionization frequency previously observed. The data are examined with regard to the nonequilibrium thermodynamic state of the gas behind the shock wave. An explanation is offered that attributes the temperature effect to the temperature dependence of the electron‐molecule energy‐transfer rate, and a method for modifying the conventional theory to take account of this is indicated. The relevance of these results to antenna breakdown on reentry vehicles is discussed.

Thermodynamics of adsorption from solution. Part 3.—The parallel-layer model

Abstract: This paper gives representative numerical solutions of the equilibrium equations for adsorption at a solid surface from non-athermal polymer solutions according to the parallel monolayer model. The underlying assumptions of the model are discussed.

Thermodynamics of the mechanico-chemical effect

Abstract: Phenomenological equations describing the mechanico-chemical effect in the range of operation of nonlinear laws were derived, and the validity of these equations was qualitatively proved by experiment.

Compatibility property of steady systems

Abstract: The concept of compatibility of steady nonequilibrium systems, analogous to the equilibrium property in thermostatics, is examined. Compatibility parameters, which play the part of generalized intensive parameters for nonequilibrium steady systems, are introduced.

Vibrational Energy Transfer in a System of Radiating Oscillators

Abstract: The distribution function and the total band intensity for a system of excited oscillators that can both exchange vibrational energy among themselves through collisions and emit their energy through radiative transitions has been obtained for several pressure conditions The nonequilibrium solution for an initial Boltzmann distribution is not a time‐dependent Boltzmann distribution as has been obtained for non‐radiating models This solution is investigated for (1) very low pressures in which there are no interactions between the oscillators and (2) pressures high enough that collisional exchanges are much more rapid than the radiative transitions but not so high as to involve collisional deactivation or reabsorption Both of these cases yield identical solutions, namely, a Boltzmann distribution with a time‐dependent temperature The solution for the second condition is also obtained by assuming a Boltzmann distribution is maintained at all times and solving for the temperature as a function of time Although the non‐equilibrium solution is not Boltzmann, it is very close, deviating at most 2% for CO The solution for an initial delta‐function distribution is also non‐Boltzmann under nonequilibrium conditions, being given by a hypergeometric function The total band intensity which is proportional to the first moment is exponential with respect to time and is independent of the initial distribution and the pressure Also, the effect of first overtone transitions on both the distribution function and the total band intensity is bound to be negligible, the deviation for CO being less than 1%

Flow of a Dissociating Gas past a Convex Corner

Abstract: The nonequilibrium flow of an ideal dissociating gas past a convex corner is studied. Linearized theory based on the undisturbed flow is reexamined, and it is shown that it does not give a good quantitative description of the variation of flow quantities along the wall, even for relatively small corner angles. The apparent agreement between the results of linear theory and characteristics solutions reported in earlier work is shown to be due to an ambiguous definition of the characteristic relaxation time. It is only when a characteristic relaxation time based on downstream conditions, rather than upstream conditions, is used in the linearized theory that the results agree reasonably with the numerical calculations. The modified linear theory is used to calculate the increase in entropy along the wall, and it is shown that normal gradients in entropy exist even far downstream of the corner. The calculated increase in entropy along the wall is related explicitly to the asymptotic wall values of the other flow variables, and these values are shown to be different from the infinite‐reaction‐rate equilibrium values. The calculated asymptotic values are in good agreement with those obtained from numerical calculations.

Self-similar motion of a gas heated by a nonequilibrium continuous radiation spectrum

Abstract: In this paper we discuss the motion of the vapor formed during the evaporation of a solid by a continuous radiation spectrum. The vapor is assumed to be heated by this radiation to a temperature T much higher than the phase-transition temperature Tv and much higher than the temperature Ti at which significant ionization of the vapor begins.