Tensorielle chemische Potentiale — eine notwendige Erweiterung der Gibbs'schen Thermodynamik / Tensorial Chemical Potentials — a Necessary Extension of Gibbs' Thermodynamics

1975 ◽  
Vol 30 (11) ◽  
pp. 1433-1440 ◽  
Author(s):  
B. Stuke
Keyword(s):  
Chemical Potential ◽  
Spherically Symmetric ◽  
Relaxation Phenomena ◽  
Pressure Tensor ◽  
Equilibrium Thermodynamics ◽  
Equilibrium Conditions ◽  
Chemical Potentials ◽  
Thermodynamic Pressure ◽  
Fundamental Equations ◽  
Non Equilibrium

In a system with a non spherically symmetric pressure tensor, the chemical potential of at least one substance in the system has to be a tensor of the same character as the pressure. The necessary generalization of Gibbs' fundamental equations of thermodynamics is presented. Being already of consequence for equilibrium, this extension is more important for non-equilibrium thermodynamics, in particular for the proper thermodynamic formulation of general relaxation phenomena. Reasons are given why the distinction between dynamic and thermodynamic pressure, originating from the incomplete formulation of customary thermodynamics, is erroneous. Finally a tensorial temperature is introduced which can exist under extreme non-equilibrium conditions, e.g. shock waves

scholarly journals Covariant Relativistic Non-Equilibrium Thermodynamics of Multi-Component Systems

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1034
Author(s):  
Wolfgang Muschik
Keyword(s):  
Momentum Flux ◽  
Equilibrium Thermodynamics ◽  
Equilibrium Conditions ◽  
Component Mixture ◽  
Component Systems ◽  
General Relativistic ◽  
Entropy Flux ◽  
Special Case ◽  
Multi Component System ◽  
Non Equilibrium

Non-equilibrium and equilibrium thermodynamics of an interacting component in a relativistic multi-component system is discussed covariantly by exploiting an entropy identity. The special case of the corresponding free component is considered. Equilibrium conditions and especially the multi-component Killing relation of the 4-temperature are discussed. Two axioms characterize the mixture: additivity of the energy momentum tensors and additivity of the 4-entropies of the components generating those of the mixture. The resulting quantities of a single component and of the mixture as a whole, energy, energy flux, momentum flux, stress tensor, entropy, entropy flux, supply and production are derived. Finally, a general relativistic 2-component mixture is discussed with respect to their gravitation generating energy–momentum tensors.

scholarly journals A Non-Equilibrium Thermodynamics-Based View of the Kinetics of Autocatalytic Reactions – a Simple Illustrative Example

2020 ◽  
Author(s):  
Miloslav Pekař
Keyword(s):  
Second Law Of Thermodynamics ◽  
Rate Equations ◽  
Second Law ◽  
Equilibrium Thermodynamics ◽  
Autocatalytic Reactions ◽  
Chemical Potentials ◽  
Entropic Inequality ◽  
Reaction Stoichiometry ◽  
Kinetics Of ◽  
Non Equilibrium

Autocatalytic reactions are in a certain contrast with the linear algebra of reaction stoichiometry, on whose basis rate equations respecting the permanence of atoms are constructed. These mathematical models of chemical reactions are termed conservative.Using a non-equilibrium thermodynamics-based theory of chemical kinetics, this paper demonstrates how to properly introduce an autocatalytic step into a (conservative) rate equation. Further, rate equations based on chemical potentials or affinities are derived, and conditions for the consistency of rate equations with entropic inequality (the second law of thermodynamics) are illustrated.<br><div><br></div>

scholarly journals A Non-Equilibrium Thermodynamics-Based View of the Kinetics of Autocatalytic Reactions – a Simple Illustrative Example

2020 ◽  
Author(s):  
Miloslav Pekař
Keyword(s):  
Second Law Of Thermodynamics ◽  
Rate Equations ◽  
Second Law ◽  
Equilibrium Thermodynamics ◽  
Autocatalytic Reactions ◽  
Chemical Potentials ◽  
Entropic Inequality ◽  
Reaction Stoichiometry ◽  
Kinetics Of ◽  
Non Equilibrium

Autocatalytic reactions are in a certain contrast with the linear algebra of reaction stoichiometry, on whose basis rate equations respecting the permanence of atoms are constructed. These mathematical models of chemical reactions are termed conservative.Using a non-equilibrium thermodynamics-based theory of chemical kinetics, this paper demonstrates how to properly introduce an autocatalytic step into a (conservative) rate equation. Further, rate equations based on chemical potentials or affinities are derived, and conditions for the consistency of rate equations with entropic inequality (the second law of thermodynamics) are illustrated.<br><div><br></div>

scholarly journals Non-Equilibrium Thermodynamics View on Kinetics of Autocatalytic Reactions—Two Illustrative Examples

Molecules ◽  
2021 ◽  
Vol 26 (3) ◽  
pp. 585
Author(s):  
Miloslav Pekař
Keyword(s):  
Second Law Of Thermodynamics ◽  
Mass Action ◽  
Rate Equations ◽  
Equilibrium Thermodynamics ◽  
Mass Action Kinetics ◽  
Autocatalytic Reactions ◽  
Chemical Potentials ◽  
Entropic Inequality ◽  
Reaction Stoichiometry ◽  
Non Equilibrium

Autocatalytic reactions are in certain contrast with the linear algebra of reaction stoichiometry, on which rate equations respecting the permanence of atoms are constructed. These mathematical models of chemical reactions are called conservative. Using a non-equilibrium thermodynamics-based theory of chemical kinetics, it is shown how to introduce autocatalytic step into such (conservative) rate equation properly. Further, rate equations based on chemical potentials or affinities are derived, and conditions for the consistency of rate equations with the entropic inequality (the second law of thermodynamics) are illustrated. The theory illustrated here can be viewed as a tool for verifying and generalizing traditional mass-action kinetics by means of modern non-equilibrium thermodynamics, which is able to deal also with such rather problematic cases.

Constitutive Relations of Thermal and Mass Diffusion

2020 ◽  
Vol 45 (1) ◽  
pp. 27-38 ◽  
Author(s):  
Antonio Bertei ◽  
Andrea Lamorgese ◽  
Roberto Mauri
Keyword(s):  
Chemical Potential ◽  
Constitutive Relations ◽  
Potential Gradient ◽  
Mass Diffusion ◽  
Composition Gradient ◽  
Special Focus ◽  
Coupling Coefficients ◽  
Equilibrium Thermodynamics ◽  
Coupling Terms ◽  
Non Equilibrium

AbstractNon-equilibrium thermodynamics provides a general framework for the description of mass and thermal diffusion, thereby including also cross-thermal and material diffusion effects, which are generally modeled through the Onsager coupling terms within the constitutive equations relating heat and mass flux to the gradients of temperature and chemical potential. These so-called Soret and Dufour coefficients are not uniquely defined, though, as they can be derived by adopting one of the several constitutive relations satisfying the principles of non-equilibrium thermodynamics. Therefore, mass diffusion induced by a temperature gradient and heat conduction induced by a composition gradient can be implicitly, and unexpectedly, predicted even in the absence of coupling terms. This study presents a critical analysis of different formulations of the constitutive relations, with special focus on regular binary mixtures. It is shown that, among the different formulations presented, the one which adopts the chemical potential gradient at constant temperature as the driving force for mass diffusion allows for the implicit thermo-diffusion effect to be strictly absent while the resulting Dufour effect is negligibly small. Such a formulation must be preferred to the other ones since cross-coupling effects are predicted only if explicitly introduced via Onsager coupling coefficients.

scholarly journals Effective chemical potential for non-equilibrium systems and its application to molecular beam epitaxy of Bi2Se3

2019 ◽  
Vol 1 (2) ◽  
pp. 470-475 ◽  
Author(s):  
Na Wang ◽  
Damien West ◽  
Wenhui Duan ◽  
S. B. Zhang
Keyword(s):  
Molecular Beam Epitaxy ◽  
Molecular Beam ◽  
Chemical Potential ◽  
Chemical Potentials ◽  
Non Equilibrium

Schematic illustration of cluster/island distribution and the corresponding chemical potentials in three different stages of Bi2Se3 growth.

Non-Equilibrium Thermodynamic Analysis of Flash Evaporation Process in Vacuum Ice Making

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Lingeng Zou ◽  
Xuelai Zhang
Keyword(s):  
Steady State ◽  
Water Vapor ◽  
Temperature Difference ◽  
Liquid Water ◽  
Chemical Potential ◽  
Evaporation Process ◽  
Flash Evaporation ◽  
Equilibrium Thermodynamics ◽  
Chemical Potential Difference ◽  
Non Equilibrium

AbstractTraditional equilibrium thermodynamics can only solve a few equilibrium processes composed of continuous stable equilibrium states. However, the vacuum flash evaporation process is a typical unsteady process. The study of non-equilibrium thermodynamics of the two-phase flow model is helpful to improve our understanding of the basic law of the flash evaporation process. Based on the theory of non-equilibrium thermodynamics, the flash chamber in the vacuum flash ice making system was studied in this paper, and the possibility of non-equilibrium steady state evaporation with superheat was obtained. The chemical potential difference between liquid water and water vapor under non-equilibrium steady state conditions was determined, and the corresponding evaporation entropy was calculated. It is shown that the results obtained by equilibrium thermodynamics are only related to the temperature difference, while the results obtained by non-equilibrium thermodynamics are not only related to the temperature difference, but also the state of the evaporation process. This is because non-equilibrium thermodynamics considers the cooling of liquid water and the evaporation of water vapor as a whole, taking into account the interaction between the two processes. However, the traditional equilibrium thermodynamics theory divides the steady state evaporation process into two independent processes and ignores the influence of each other.

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