Use of Gibbs equation in irreversible thermodynamics. I. Gibbs and Gibbs-Duhem equations and definition of partial quantities in specific variables

AbstractFirst, the special-relativistic Theory of Irreversible Processes for a multi-component fluid is formulated. It is based on (i) the balance equations of the particle number and the energy-momentum for the total system (i. e., the mixture of the components) as well as the sub-systems (i. e., the components) and (ii) the dissipation inequality and the Gibbs equation for the mixture. In order to allow for reactions between the single components, in contrast to the total system, the sub-systems are assumed to be open, which means that their particle number and energy-momentum are not constrained by conservation laws. Without making any assumptions on the thermodynamic behavior of the interacting components, one arrives at a thermodynamic description of the mixture showing now heat conduction and viscosity. In particular, this makes it possible to calculate the entropy production and, thus, to identify thermodynamic currents and forces. In a second part, the post-Newtonian limit of this theory is calculated to show that for the mixture there result relations known from classical Extended Thermodynamics that partly are corrected by entrainment terms. The mathematical origin and physical consequences of these terms are discussed.

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A Derivation of the Gibbs Equation and the Determination of Change in Gibbs Entropy from Calorimetry

Australian Journal of Chemistry ◽

10.1071/ch16447 ◽

2016 ◽

Vol 69 (12) ◽

pp. 1413 ◽

Cited By ~ 1

Author(s):

Denis J. Evans ◽

Debra J. Searles ◽

Stephen R. Williams

Keyword(s):

Fundamental Equation ◽

Space Distribution ◽

Irreversible Processes ◽

Gibbs Equation ◽

Gibbs Entropy ◽

Relaxation Theorem ◽

Definition Of ◽

Physical Quantities ◽

Specific Definition

In this paper, we give a succinct derivation of the fundamental equation of classical equilibrium thermodynamics, namely the Gibbs equation. This derivation builds on our equilibrium relaxation theorem for systems in contact with a heat reservoir. We reinforce the comments made over a century ago, pointing out that Clausius’ strict inequality for a system of interest is within Clausius’ set of definitions, logically undefined. Using a specific definition of temperature that we have recently introduced and which is valid for both reversible and irreversible processes, we can define a property that we call the change in calorimetric entropy for these processes. We then demonstrate the instantaneous equivalence of the change in calorimetric entropy, which is defined using heat transfer and our definition of temperature, and the change in Gibbs entropy, which is defined in terms of the full N-particle phase space distribution function. The result shows that the change in Gibbs entropy can be expressed in terms of physical quantities.

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Neoclassical Navier–Stokes Equations Considering the Gyftopoulos–Beretta Exposition of Thermodynamics

Energies ◽

10.3390/en13071656 ◽

2020 ◽

Vol 13 (7) ◽

pp. 1656 ◽

Cited By ~ 1

Author(s):

Janusz Badur ◽

Michel Feidt ◽

Paweł Ziółkowski

Keyword(s):

Internal Energy ◽

Stokes Equations ◽

Irreversible Thermodynamics ◽

Navier Stokes ◽

Working Fluid ◽

Navier Stokes Equations ◽

Available Energy ◽

Radiation Fluxes ◽

Total Energy Flux ◽

Definition Of

The seminal Navier–Stokes equations were stated even before the creation of the foundations of thermodynamics and its first and second laws. There is a widespread opinion in the literature on thermodynamic cycles that the Navier–Stokes equations cannot be taken as a thermodynamically correct model of a local “working fluid”, which would be able to describe the conversion of “heating” into “working” (Carnot’s type cycles) and vice versa (Afanasjeva’s type cycles). Also, it is overall doubtful that “cycle work is converted into cycle heat” or vice versa. The underlying reason for this situation is that the Navier–Stokes equations come from a time when thermodynamic concepts such as “internal energy” were still poorly understood. Therefore, this paper presents a new exposition of thermodynamically consistent Navier–Stokes equations. Following that line of reasoning—and following Gyftopoulos and Beretta’s exposition of thermodynamics—we introduce the basic concepts of thermodynamics such as “heating” and “working” fluxes. We also develop the Gyftopoulos and Beretta approach from 0D into 3D continuum thermodynamics. The central role within our approach is played by “internal energy” and “energy conversion by fluxes.” Therefore, the main problem of exposition relates to the internal energy treated here as a form of “energy storage.” Within that context, different forms of energy are discussed. In the end, the balance of energy is presented as a sum of internal, kinetic, potential, chemical, electrical, magnetic, and radiation energies in the system. These are compensated by total energy flux composed of working, heating, chemical, electrical, magnetic, and radiation fluxes at the system boundaries. Therefore, the law of energy conservation can be considered to be the most important and superior to any other law of nature. This article develops and presents in detail the neoclassical set of Navier–Stokes equations forming a thermodynamically consistent model. This is followed by a comparison with the definition of entropy (for equilibrium and non-equilibrium states) within the context of available energy as proposed in the Gyftopoulos and Beretta monograph. The article also discusses new possibilities emerging from this “continual” Gyftopoulos–Beretta exposition with special emphasis on those relating to extended irreversible thermodynamics or Van’s “universal second law”.

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Definition of Heat in Open Systems

Australian Journal of Physics ◽

10.1071/ph800095 ◽

1980 ◽

Vol 33 (1) ◽

pp. 95 ◽

Cited By ~ 3

Author(s):

DA Smith

Keyword(s):

Heat Flux ◽

Heat Flow ◽

Open Systems ◽

Irreversible Thermodynamics ◽

Equilibrium Thermodynamics ◽

Domain Of Applicability ◽

Usual Concept ◽

Closed Systems ◽

Adiabatic Processes ◽

Definition Of

Existing definitions of heat in open systems are considered with the aim of providing acceptable physical motivation in restricted circumstances. The extent to which these definitions are independent of the usual concept of heat in closed systems is clarified: they all have the feature that internal energy may be transferred by convection in workless adiabatic processes. The global definitions are compared with various definitions of heat flux in irreversible thermodynamics. As the domain of applicability of these definitions is wider than that of equilibrium thermodynamics, it is suggested that a minimal check for any definition of heat flux be that it agree with the global definition of heat flow between equilibrium states in as wide a range of circumstances as possible.

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Introductory paper

Symposium - International Astronomical Union ◽

10.1017/s0074180900053031 ◽

1966 ◽

Vol 24 ◽

pp. 3-5

Author(s):

W. W. Morgan

Keyword(s):

Line Intensity ◽

Classification Scheme ◽

Two Dimensional ◽

Spectral Classification ◽

Dimensional Array ◽

Rr Lyrae ◽

Metallic Line ◽

Introductory Paper ◽

Parameter Varying ◽

Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

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2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

International Astronomical Union Colloquium ◽

10.1017/s0252921100050867 ◽

1975 ◽

Vol 26 ◽

pp. 21-26

Keyword(s):

Coordinate System ◽

Working Group ◽

General Character ◽

Coordinate Systems ◽

Reference Coordinate System ◽

Group 2 ◽

Definition Of ◽

Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

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Symbiotic Stars at Optical, Infrared and Radio Wavelengths

International Astronomical Union Colloquium ◽

10.1017/s025292110007336x ◽

1979 ◽

Vol 46 ◽

pp. 125-149 ◽

Cited By ~ 3

Author(s):

David A. Allen

Keyword(s):

Temperature Regime ◽

Type Star ◽

Stellar Systems ◽

Symbiotic Stars ◽

Lower Excitation ◽

Definition Of ◽

Original Type

No paper of this nature should begin without a definition of symbiotic stars. It was Paul Merrill who, borrowing on his botanical background, coined the termsymbioticto describe apparently single stellar systems which combine the TiO absorption of M giants (temperature regime ≲ 3500 K) with He II emission (temperature regime ≳ 100,000 K). He and Milton Humason had in 1932 first drawn attention to three such stars: AX Per, CI Cyg and RW Hya. At the conclusion of the Mount Wilson Ha emission survey nearly a dozen had been identified, and Z And had become their type star. The numbers slowly grew, as much because the definition widened to include lower-excitation specimens as because new examples of the original type were found. In 1970 Wackerling listed 30; this was the last compendium of symbiotic stars published.

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Immunoferritin localization of intracellular antigens in positively stained frozen sections

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010008170x ◽

1978 ◽

Vol 36 (2) ◽

pp. 168-169

Author(s):

K. T. Tokuyasu

Keyword(s):

Surface Tension ◽

Water Surface ◽

Thin Layers ◽

The Other ◽

Positive Staining ◽

Frozen Sections ◽

The Past ◽

Ultrathin Frozen Sections ◽

Definition Of

During the past investigations of immunoferritin localization of intracellular antigens in ultrathin frozen sections, we found that the degree of negative staining required to delineate u1trastructural details was often too dense for the recognition of ferritin particles. The quality of positive staining of ultrathin frozen sections, on the other hand, has generally been far inferior to that attainable in conventional plastic embedded sections, particularly in the definition of membranes. As we discussed before, a main cause of this difficulty seemed to be the vulnerability of frozen sections to the damaging effects of air-water surface tension at the time of drying of the sections.Indeed, we found that the quality of positive staining is greatly improved when positively stained frozen sections are protected against the effects of surface tension by embedding them in thin layers of mechanically stable materials at the time of drying (unpublished).

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Initial Polymerization Sites Indicated During Mitochondrial Oxidation of Diaminobenzidine after Toluene Treatment

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100079498 ◽

1977 ◽

Vol 35 ◽

pp. 408-409

Author(s):

W. A. Shannon ◽

M. A. Matlib

Keyword(s):

Membrane Permeability ◽

Cytochrome Oxidase ◽

Rat Liver ◽

Precise Definition ◽

Cytochemical Localization ◽

Oxidative Reaction ◽

Mitochondrial Oxidation ◽

Definition Of ◽

Exogenous Substrates

Numerous studies have dealt with the cytochemical localization of cytochrome oxidase via cytochrome c. More recent studies have dealt with indicating initial foci of this reaction by altering incubation pH (1) or postosmication procedure (2,3). The following study is an attempt to locate such foci by altering membrane permeability. It is thought that such alterations within the limits of maintaining morphological integrity of the membranes will ease the entry of exogenous substrates resulting in a much quicker oxidation and subsequently a more precise definition of the oxidative reaction.The diaminobenzidine (DAB) method of Seligman et al. (4) was used. Minced pieces of rat liver were incubated for 1 hr following toluene treatment (5,6). Experimental variations consisted of incubating fixed or unfixed tissues treated with toluene and unfixed tissues treated with toluene and subsequently fixed.

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