Fundamentals of Thermodynamic Stability

2005 ◽  
Author(s):  
Eldred H. Chimowitz
Keyword(s):  
Thermodynamic Stability ◽  
Stability Theory ◽  
Stable State ◽  
Second Law Of Thermodynamics ◽  
Entropy Change ◽  
Second Law ◽  
Adiabatic Process ◽  
Chemical Transformations ◽  
Thermodynamic Potentials ◽  
Ideal Tool

The second law of thermodynamics states that the entropy change in any spontaneous adiabatic process is greater than or equal to zero. It is a disarmingly simple statement but one that is a cornerstone of scientific theories. It is instrumental in describing the extent and direction of all physical and chemical transformations and contains within it the essential ideas for developing thermodynamic stability theory. Stability theory concerns itself with answering questions such as (1) What is a stable thermodynamic state? (2) Which conditions define the limit to this state beyond which the system becomes unstable? (3) How does the instability manifest itself ? In a real sense, stability theory provides the underlying framework for a macroscopic understanding of phase transitions and critical phenomena, the subject of this text. Many of the results of stability theory related to phase equilibria are well known; an example is the condition that, for a pure fluid in a stable state, the quantity −(∂P/∂V )T,N must be greater than or equal to zero, with the equality condition holding at the limit of stability. Many other facets of thermodynamic stability theory, however, are relatively unfamiliar. For example, any of the well-known thermodynamic potentials E, H, A, and G can be used to develop stability criteria for a given system. Are these criteria always equivalent, or do some take precedence over others? If so, what are the implications of this for understanding phase transformations in physicochemical systems? It is questions of this sort that we take up in this chapter, where we lay the macroscopic foundations for the material developed throughout the rest of the text. In this analysis, we rely heavily upon results taken from linear algebra, a branch of mathematics that provides an ideal tool for developing a comprehensive description of thermodynamic stability concepts. The combination of the first and second law of thermodynamics for a closed system leads to the well-known equation: . . . dE = T dS − PdV . . . . . . (1.1) . . . where E(S, V ) represents the system energy as a function of the independent variables S and V.

The Limits of the Spreading and Sharing Metaphor

2017 ◽  
pp. 140-143
Author(s):  
Alberto Gianinetti
Keyword(s):  
Physical Function ◽  
Second Law Of Thermodynamics ◽  
Entropy Change ◽  
Second Law ◽  
Available Energy ◽  
Great Utility ◽  
Sharing Function

Some phenomena, though representing instances of entropy change, appear to defy the description of entropy as a function of energy spreading and sharing. Despite its great utility such a description is sometimes difficult to apply because a function levelling down available energy not always exactly acts as a spreading and sharing function. The concept of a physical function levelling down available energy is therefore preferable to understand entropy and the second law of thermodynamics because it has a more general value.

First and second laws of thermodynamics: relationship, “inconsistency”, hidden effects

2020 ◽  
pp. 63-73
Author(s):  
A. M. Savchenko ◽  
Yu. V. Konovalov ◽  
A. V. Laushkin
Keyword(s):  
Free Energy ◽  
Internal Energy ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Entropy Of Mixing ◽  
Ideal Mixing ◽  
Laws Of Thermodynamics ◽  
Relationship Of ◽  
The Relationship

The relationship of the first and second laws of thermodynamics based on their energy nature is considered. It is noted that the processes described by the second law of thermodynamics often take place hidden within the system, which makes it difficult to detect them. Nevertheless, even with ideal mixing, an increase in the internal energy of the system occurs, numerically equal to an increase in free energy. The largest contribution to the change in the value of free energy is made by the entropy of mixing, which has energy significance. The entropy of mixing can do the job, which is confirmed in particular by osmotic processes.

The Analogical Turn (1884–1887)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Boltzmann Equation ◽  
Statistical Mechanics ◽  
Mechanical System ◽  
Thermal Equilibrium ◽  
Special Kind ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Equipartition Theorem ◽  
Royal Road ◽  
H Theorem

This chapter recounts how Boltzmann reacted to Hermann Helmholtz’s analogy between thermodynamic systems and a special kind of mechanical system (the “monocyclic systems”) by grouping all attempts to relate thermodynamics to mechanics, including the kinetic-molecular analogy, into a family of partial analogies all derivable from what we would now call a microcanonical ensemble. At that time, Boltzmann regarded ensemble-based statistical mechanics as the royal road to the laws of thermal equilibrium (as we now do). In the same period, he returned to the Boltzmann equation and the H theorem in reply to Peter Guthrie Tait’s attack on the equipartition theorem. He also made a non-technical survey of the second law of thermodynamics seen as a law of probability increase.

First and Second Law Analysis of a Flat Plate Collector Working With Nanofluids

2018 ◽  
Author(s):  
M. T. Nitsas ◽  
I. P. Koronaki ◽  
L. Prentza
Keyword(s):  
Flat Plate ◽  
Second Law Of Thermodynamics ◽  
Climatic Conditions ◽  
Working Fluid ◽  
Second Law ◽  
Inlet Temperature ◽  
Water Tank ◽  
Systems Quality ◽  
Typical Day ◽  
Flat Plate Collector

The utilization of solar energy in thermal energy systems was and always be one of the most effective alternative to conventional energy resources. Energy efficiency is widely used as one of the most important parameters in order to evaluate and compare thermal systems including solar collectors. Nevertheless, the first law of thermodynamics is not solely capable of describing the quantitative and qualitative performance of such systems and thus exergy efficiency is used so as to introduce the systems’ quality. In this work, the performance of a flat plate solar collector using water based nanofluids of different nanoparticle types as a working fluid is analyzed theoretically under the climatic conditions in Greece based on the First and Second Law of Thermodynamics. A mathematical model is built and the model equations are solved iteratively in a MATLAB code. The energy and exergy efficiencies as well as the collector losses coefficient for various parameters such as the inlet temperature, the particles concentration and type are determined. Moreover, a dynamic model is built so as to determine the performance of a flat plate collector working with nanofluids and the useful energy that can be stored in a water tank. The exergy destruction and exergy leakage are determined for a typical day in summer during which high temperatures and solar intensity values are common for the Greek climate.

Entropy Optimization in Nonlinear Mixed Convective Flow of Nanomaterials Through Porous Space

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tasawar Hayat ◽  
Ikram Ullah ◽  
Ahmad Alsaedi ◽  
Shaher Momani
Keyword(s):  
Convective Flow ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Porous Space ◽  
Arrhenius Activation Energy ◽  
Suction Parameter ◽  
Electrically Conducting ◽  
Entropy Optimization ◽  
Dimensionless Variables ◽  
Mixed Convective Flow

Abstract Our intention in this article is to investigate entropy optimization in nonlinear mixed convective unsteady magnetohydrodynamic flow of nanomaterials in porous space. An exponentially stretched sheet creates the liquid flow. Nanomaterial is considered electrically conducting. The concentration and energy expressions comprise viscous dissipation, Joule heating, thermophoresis and Brownian motion aspects. Arrhenius activation energy is considered. Computation of entropy generation based upon the second law of thermodynamics is made. Nonlinear partial expressions are obtained via suitable dimensionless variables. Resultant expressions are tackled by the OHAM technique. Features of numerous variables on entropy, temperature, velocity and concentration are graphically visualized. Skin friction and the temperature gradient at the surface are also elaborated. Comparative analysis is deliberated in tabulated form to validate the previously published outcomes. Velocity is reduced significantly via the suction parameter. The entropy rate increases for higher values of Brinkman, Biot and Hartmann numbers.

Supradegeneracy and the Second Law of Thermodynamics

2020 ◽  
Vol 45 (2) ◽  
pp. 121-132
Author(s):  
Daniel P. Sheehan
Keyword(s):  
Steady State ◽  
Statistical Mechanics ◽  
Population Inversion ◽  
Laboratory Experiments ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Boltzmann Factor ◽  
Energy Currents ◽  
Non Equilibrium

AbstractCanonical statistical mechanics hinges on two quantities, i. e., state degeneracy and the Boltzmann factor, the latter of which usually dominates thermodynamic behaviors. A recently identified phenomenon (supradegeneracy) reverses this order of dominance and predicts effects for equilibrium that are normally associated with non-equilibrium, including population inversion and steady-state particle and energy currents. This study examines two thermodynamic paradoxes that arise from supradegeneracy and proposes laboratory experiments by which they might be resolved.

scholarly journals Can Quantum Correlations Lead to Violation of the Second Law of Thermodynamics?

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 573
Author(s):  
Alexey V. Melkikh
Keyword(s):  
Quantum Entanglement ◽  
Local Equilibrium ◽  
Heat Engine ◽  
Thermodynamic Quantity ◽  
Second Law Of Thermodynamics ◽  
Quantum Correlations ◽  
Von Neumann Entropy ◽  
Second Law ◽  
Carnot Cycle ◽  
Technical Discussion

Quantum entanglement can cause the efficiency of a heat engine to be greater than the efficiency of the Carnot cycle. However, this does not mean a violation of the second law of thermodynamics, since there is no local equilibrium for pure quantum states, and, in the absence of local equilibrium, thermodynamics cannot be formulated correctly. Von Neumann entropy is not a thermodynamic quantity, although it can characterize the ordering of a system. In the case of the entanglement of the particles of the system with the environment, the concept of an isolated system should be refined. In any case, quantum correlations cannot lead to a violation of the second law of thermodynamics in any of its formulations. This article is devoted to a technical discussion of the expected results on the role of quantum entanglement in thermodynamics.

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