Showing papers on "Non-equilibrium thermodynamics published in 1971"

Fluctuations in Nonequilibrium Systems

Abstract: The theory of fluctuations is extended to nonlinear systems far from equilibrium. Systems whose evolution involves two separate time scales, e.g., chemically reacting mixtures near a local equilibrium regime, are studied in detail. It is shown that the usual stochastic description of chemical kinetics based on a “birth and death” model is inadequate and has to be replaced by a more detailed phase-space description. This enables one to develop for such systems a plausible mechanism for the emergence of instabilities, in which the departure from the steady state is governed by large fluctuations of macroscopic size, while small thermal fluctuations are still described by a generalization of Einstein's equilibrium theory. On the other hand, far from a local equilibrium regime, infinitesimal fluctuations may increase and attain macroscopic values. In this case the system evolves to a state of “generalized turbulence”, in which the distinction between macroscopic averages and fluctuations becomes meaningless.

Introduction to Thermodynamics: Classical and Statistical

Abstract: Some Concepts and Definitions. Properties of a Pure Substance. Work and Heat. The First Law of Thermodynamics. First-Law Analysis for a Control Volume. The Second Law of Thermodynamics. Entropy. Second-Law Analysis for a Control Volume. Some Power and Refrigeration Cycles. An Introduction to the Thermodynamics of Mixtures. Thermodynamic Relations. Chemical Reactions. Introduction to Phase and Chemical Equilibrium. Quantum Mechanics. Molecular Distributions and Models. Statistical Mechanics and Thermodynamics. Applications of Statistical Thermodynamics. Appendices. Some Selected References. Answers to Selected Problems. Index.

Thermodynamics of Fermions in One Dimension with a δ-Function Interaction

Abstract: The equilibrium thermodynamics of a one-dimensional fermion system with a repulsive $\ensuremath{\delta}$-function interaction is found to be derivable from the solution of a set of coupled integral equations. The equations for the attractive case are also given.

Kinetics of collisional-radiation recombination and ionization in low-temperature plasma

Abstract: A review is made of the approaches and approximations used by different authors to calculate coefficients of collisional-radiative ionization (β) and recombination (α). In calculating these quantities, consideration is given to a wide range of varying conditions in plasmas, and account is taken of different factors violating thermodynamic equilibrium, such as a possible departure from a Maxwellian distribution of free electrons, radiation escape with allowance for reabsorption, etc. Simple analytical expressions are given for β and α, as well as calculation results for plasmas of different compositions and different parameters. Experimental studies are also discussed in which β and α are measured. Calculation and experiment are compared and found in fair agreement. Special attention is given to major factors of nonequilibrium, affecting the rate of electron density change in different experimental conditions.

Nonequilibrium Thermodynamics and Its Application to Bioenergetics

Abstract: Publisher Summary Nonequilibrium thermodynamics or the thermodynamics of irreversible processes extends and complements the classical method by the explicit introduction of time. It enables one to formulate a description of real processes rather than idealizations that happen in well-defined equilibrium states; the correlations it provides are between kinetic parameters. The most tractable processes are those that occur when the system is in a steady state. However, under stationary conditions, the state parameters of the system give no information about the processes occurring; to study these processes, it is necessary to look at their effects on the surroundings and indeed this is the essence of the approach. The resulting analysis immediately determines the number and nature of the degrees of freedom involved. The thermodynamic considerations lead to criteria that may help to distinguish between models of oxidative phosphorylation. These criteria neither depend on the isolation of an intermediate nor is it necessary to observe a component of hydrogen ion flow used for phosphorylation. It is necessary to determine the electrochemical potential difference of hydrogen and possibly of potassium across the mitochondrial membrane; however, the remaining parameters are evaluated externally. It is possible in principle to envisage conditions in which the flow of hydrogen ion across the membrane may be maintained non-zero and constant for brief periods

Kinetic theory of a two-dimensional magnetized plasma.

Abstract: Several features of the equilibrium and nonequilibrium statistical mechanics of a two-dimensional plasma in a uniform dc magnetic field are investigated. The charges are assumed to interact only through electrostatic potentials. The problem is considered both with and without the guiding-center approximation. With the guiding-center approximation, an appropriate Liouville equation and BBGKY hierarchy predict no approach to thermal equilibrium for the spatially uniform case. For the spatially nonuniform situation, a guiding-center Vlasov equation is discussed and solved in special cases. For the nonequilibrium, nonguiding-center case, a Boltzmann equation, and a Fokker-Planck equation are derived in the appropriate limits. The latter is more tractable than the former, and can be shown to obey conservation laws and an H-theorem, but contains a divergent integral which must be cut off on physical grounds. Several unsolved problems are posed.

Irreversibility and existence of entropy

Abstract: The existence of entropy as a state function is established. This is shown for reversible and irreversible systems and processes, irrespective of the constitutive equations of the systems. In the case of a reversible system, entropy is a function of the deformation gradients (strains) and temperature; in the case of an irreversible system it is also a function of n internal variables necessary to describe the irreversibility of the system. The existence of internal energy and the validity of the first law of thermodynamics are assumed. The existence of entropy then follows as a consequence of the integrability of the differential form of the first law using an extended form of the Caratheodory conjecture, to the effect that in the neighborhood of a thermodynamic state there exist other states which are not accessible by processes which are reversible and adiabatic.

A Gas‐Dynamic Model for Coupled Vibrational and Radiative Nonequilibrium in CO2—with Application to the Spectrophone

Abstract: Macroscopic equations are formulated for the nonequilibrium interaction of vibrational and radiative rate processes in CO2. A model for CO2 is used that assumes that the energy levels of each vibrational mode are evenly spaced and that each mode can be assigned a vibrational temperature. The bending and symmetric‐stretching modes are, however, taken to be in mutual equilibrium so that they have the same vibrational temperature. Collisional rate equations for the V—T and V—V processes are derived on a phenomenological basis. The resulting phenomenological coefficients are interpreted, with the help of basic knowledge of the microscopic physics, in terms of characteristic relaxation times and parameters measuring the relative amounts of energy exchanged by the various modes during V—V transitions. Radiative transfer equations are developed for the three strongest infrared bands, located in the spectrum at 15, 4.3, and 2.7 μ, by appropriately summing a previously derived microscopic transfer equation. It is found that the absorption coefficient is a function of the kinetic and the vibrational temperatures in a manner that depends on the band in question. The source function, which is also different for each band, depends strongly on the temperature of the vibrational modes involved in the transition and weakly on the kinetic temperature. The rate and transfer equations are then incorporated with the conservation equations of gas dynamics for application to linearized nonequilibrium flows of carbon dioxide gas. As a particularly simple example, a solution for the spectrophone is presented, including expressions for the phase lag in the pressure signal that results from radiative excitation via each of the bands individually. One of these expressions can be used in conjunction with experimental results from other sources to draw conclusions about predominant V—V transitions in CO2. The results of doing this using the 4.3‐μ band have been reported previously. The utility of a spectrophone can also be extended by exploiting the possibility of selectively exciting CO2 through the different bands and making use of all the phase‐lag expressions. All equations were derived without restriction to room temperature, allowing for possible use of spectrophones at higher temperatures. The approach used to derive the macroscopic rate equations can equally well be applied to other polyatomic molecules.

Molecular derivation of the hydrodynamic equations for a binary fluid

Abstract: In this paper, the hydrodynamic equations and the associated transport coefficients are derived for a simple binary fluid from molecular considerations. This is a generalization of the methods of Felderhof and Oppenheim and of Selwyn to multicomponent systems. A linear response formalism is used to describe the relaxation of the binary system from an initial nonequilibrium state. Explicit molecular expressions are given for the transport coefficients in terms of time correlation functions of generalized current densities. These densities have the useful property of not containing a conserved part. The correlation functions are then related to a set of phenomenological coefficients in the theory of nonequilibrium thermodynamics. This explicit identification enables one to relate the correlation functions to experimentally measured transport coefficients.

Nonequilibrium Thermodynamics in Chemical Kinetics

Abstract: The description of chemical reaction rates, in terms of the language of nonequilibrium thermodynamics, is compared with the conventional language of chemical kinetics. It is concluded that the formalism of nonequilibrium thermodynamics possesses considerable disadvantages, even in the regime where the rate is a linear function of affinity; this conclusion also holds for cases where chemical rates are coupled to diffusion processes. Some of the difficulties involved are illustrated using the experimental data of Nebeker and Pings (28).

The generalized Langevin equation and the fluctuation- dissipation theorems

Abstract: Two forms of Langevin equation are used to describe the equilibrium and nonequilibrium behaviour of a particle undergoing a Brownian motion. By comparing the results of these two forms it is shown that the fluctuation- dissipation theorems depend on two main assumptions. First, the after-effect functions are the same for the equilibrium and nonequilibrium states and second, the velocity power spectra are identical or the velocity autocorrelation function (V(t)V(t+T)) does not depend on the time t in the nonequilibrium state.

One possible formulation of the thermodynamics of sorption equilibrium

Abstract: 1. To obtain the basic functions of the thermodynamics of Sorption equilibrium there is no need to separate the entire sorbate into gas and sorption phases. 2. The thermodynamics of sorption equilibrium can be represented as the result of replacement of the variables in the thermodynamic functions for a cylinder filled with gas and closed with a piston, within which the sorbent is included. 3. The method of replacement of variables makes the relationship of functions of the type of Clausius-Clapeyron and Kirchhoff formulas, used in the thermodynamics of sorption, to the axioms of thermodynamics more graphic, and also permits a refinement of the thermodynamic meaning of these functions.

Topological representations of thermodynamic systems—II. Some elemental subunits for irreversible thermodynamics

Abstract: Topological representations, using the bond graph rotation developed in Part 1, are presented for several common thermodynamic couplings. Examples of more complex systems are presented, including diffusion with chemical reaction, relaxation oscillations in electrochemical systems and nonlinear phenomena in charged membrane structures.

Sonine Polynomial Solution of the Boltzmann Equation for Relaxation of Initially Nonequilibrium Distribution

Abstract: Using the Sonine polynomial expansion method the nonlinear Boltzmann equation for time‐dependent spatially uniform gases is solved to examine the relaxation of an initially nonequilibrium distribution toward the equilibrium. For an inverse‐fifth power law force, a simple analytical expression is presented for equations for expansion coefficients. As a result the higher‐order expansion coefficients as well as the lower‐order ones are obtained, so that the decay of larger initial departure of the distribution function from the equilibrium is dealt with. The resulting distribution function is compared with the corresponding one obtained on the basis of the Bhatnagar‐Gross‐Krook model. The latter model is shown to be adequate only when the departure of distribution function from the equilibrium becomes small.

Solutions for Reacting and Nonreacting Viscous Shock Layers with Multicomponent Diffusion and Mass Injection

Abstract: Numerical solutions are presented for the viscous shocklayer equations where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium. Also the effects of the diffusion model, surface catalyticity, and mass injection on surface transport and flow parameters are considered. The equilibrium calculations for air species using multicomponent: diffusion provide solutions previously unavailable. The viscous shock-layer equations are solved by using an implicit finite-difference scheme. The flow is treated as a mixture of inert and thermally perfect species. Also the flow is assumed to be in vibrational equilibrium. All calculations are for a 45 deg hyperboloid. The flight conditions are those for various altitudes and velocities in the earth's atmosphere. Data are presented showing the effects of the chemical models; diffusion models; surface catalyticity; and mass injection of air, water, and ablation products on heat transfer; skin friction; shock stand-off distance; wall pressure distribution; and tangential velocity, temperature, and species profiles.

Non-Equilibrium Thermodynamics: Steady State Thermodynamic Relations in the Non-Linear Current-Affinity Region

Abstract: A simple heat conduction example is used to show that the choice of boundary conditions for describing a steady process, although of no consequence in the linear current-affinity region, governs the applicability (or the lack thereof) of various thermodynamic assertions to the non-linear current-affinity region. The need for a whole family of classificatory principles to aid us in organizing our knowledge about steady processes is pointed out.