Identical thermodynamical processes and the generalization of the Clausius inequality

2008 ◽  
Vol 86 (2) ◽  
pp. 369-377 ◽  
Author(s):  
J Anacleto ◽  
J M Ferreira ◽  
A Anacleto
Keyword(s):  
Second Law ◽  
Definition Of ◽  
Thermodynamical Processes ◽  
Clausius Inequality

We stress the advantages of heat and work reservoirs in the formalism of Thermodynamics and using an illustrative example show the need to reformulate the concepts of heat and work to avoid inconsistencies, namely, with regard to the Second Law. To deal with this problem, we use the concept of identical thermodynamical processes and obtain the condition for two such processes to be identical even when the system neighbourhood as a whole cannot be treated as a reservoir. The aforementioned concept is then applied to obtain a standardized definition of heat and work as well as a generalization of the well-known Clausius inequality. Finally, we return to the example given earlier to corroborate the effectiveness of our results.PACS Nos.: 05.70.–a, 44.90.+c, 65.40.Gr

The Second Law of Thermodynamics

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Second Law Of Thermodynamics ◽  
Worked Examples ◽  
Phase Changes ◽  
Second Law ◽  
The Third ◽  
Mathematical Properties ◽  
Third Law Of Thermodynamics ◽  
Third Law ◽  
Definition Of ◽  
Clausius Inequality

The Second Law. The definition of entropy, and its mathematical properties. The Clausius inequality, and the criterion of spontaneity of change in an isolated system. Worked examples of heat flow down a temperature gradient, and the adiabatic expansion of a gas into a vacuum. Combining the First and Second Laws, with worked examples, such as phase changes. Introduction to the Third Law of Thermodynamics. Introduction to T,S diagrams.

Reactions in solution

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Phase Equilibria ◽  
Gas Phase ◽  
First Principles ◽  
Unique Feature ◽  
Life Sciences ◽  
Equilibrium Mixture ◽  
Second Law ◽  
Ideal Solution ◽  
Coupled Reactions ◽  
Definition Of

Another key chapter, examining reactions in solution. Starting with the definition of an ideal solution, and then introducing Raoult’s law and Henry’s law, this chapter then draws on the results of Chapter 14 (gas phase equilibria) to derive the corresponding results for equilibria in an ideal solution. A unique feature of this chapter is the analysis of coupled reactions, once again using first principles to show how the coupling of an endergonic reaction to a suitable exergonic reaction results in an equilibrium mixture in which the products of the endergonic reaction are present in much higher quantity. This demonstrates how coupled reactions can cause entropy-reducing events to take place without breaking the Second Law, so setting the scene for the future chapters on applications of thermodynamics to the life sciences, especially chapter 24 on bioenergetics.

scholarly journals Second Law and Non-Equilibrium Entropy of Schottky Systems --Doubts and Verification--

2018 ◽  
Author(s):  
Wolfgang Muschik
Keyword(s):  
Open Systems ◽  
Embedding Theorem ◽  
Contact Temperature ◽  
Second Law ◽  
Molar Entropy ◽  
Primitive Concept ◽  
Historical Remark ◽  
Clausius Inequality ◽  
Non Equilibrium

Meixner's historical remark in 1969 "... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined...." is investigated from today's insight. Several statements --such as the three laws of phenomenological thermodynamics, the embedding theorem and the adiabatical uniqueness-- are used to get rid of non-equilibrium entropy as a primitive concept. In this framework, Clausius inequality of open systems can be derived by use of the defining inequalities which establish the non-equilibrium quantities contact temperature and non-equilibrium molar entropy which allow to describe the interaction between the Schottky system and its controlling equilibrium environment.

scholarly journals Diffusive Bejan number and second law of thermodynamics toward a new dimensionless formulation of fluid dynamics laws

2019 ◽  
Vol 23 (6 Part B) ◽  
pp. 4005-4022 ◽  
Author(s):  
Michele Trancossi ◽  
Jose Pascoa
Keyword(s):  
Fluid Dynamics ◽  
Entropy Generation ◽  
Fluid Dynamic ◽  
Second Law Of Thermodynamics ◽  
Integral Form ◽  
Second Law ◽  
Bejan Number ◽  
Definition Of ◽  
New Formulation ◽  
Dimensionless Formulation

In a recent paper, Liversage and Trancossi have defined a new formulation of drag as a function of the dimensionless Bejan and Reynolds numbers. Further analysis of this hypothesis has permitted to obtain a new dimensionless formulation of the fundamental equations of fluid dynamics in their integral form. The resulting equations have been deeply discussed for the thermodynamic definition of Bejan number evidencing that the proposed formulation allows solving fluid dynamic problems in terms of entropy generation, allowing an effective optimization of design in terms of the Second law of thermodynamics. Some samples are discussed evidencing how the new formulation can support the generation of an optimized configuration of fluidic devices and that the optimized configurations allow minimizing the entropy generation.

scholarly journals Classical Mechanics as a Fundamental Law of Quantum Mechanics

2020 ◽  
Author(s):  
Yehuda Roth
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Classical Mechanics ◽  
Second Law ◽  
Operator Form ◽  
Fundamental Law ◽  
Third Law ◽  
Definition Of ◽  
Force Operator ◽  
Physical Quantities

n our previous paper, we showed that the so-called quantum entanglement also exists in classical mechanics. The inability to measure this classical entanglement was rationalized with the definition of a classical observer which collapses all entanglement into distinguishable states. It was shown that evidence for this primary coherence is Newton’s third law. However, in reformulating a "classical entanglement theory" we assumed the existence of Newton’s second law as an operator form where a force operator was introduced through a Hilbert space of force states. In this paper, we derive all related physical quantities and laws from basic quantum principles. We not only define a force operator but also derive the classical mechanic's laws and prove the necessity of entanglement to obtain Newton’s third law.

scholarly journals Quantum Thermodynamics in the Refined Weak Coupling Limit

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 725 ◽  
Author(s):  
Ángel Rivas
Keyword(s):  
System Dynamics ◽  
Internal Energy ◽  
Weak Coupling ◽  
Weak Coupling Limit ◽  
Second Law ◽  
Quantum Thermodynamics ◽  
Thermodynamic Framework ◽  
Definition Of

We present a thermodynamic framework for the refined weak coupling limit. In this limit, the interaction between system and environment is weak, but not negligible. As a result, the system dynamics becomes non-Markovian breaking divisibility conditions. Nevertheless, we propose a derivation of the first and second law just in terms of the reduced system dynamics. To this end, we extend the refined weak coupling limit for allowing slowly-varying external drivings and reconsider the definition of internal energy due to the non-negligible interaction.

Thermodynamic Modeling for Discrete-Time Large-Scale Dynamical Systems

2011 ◽  
Author(s):  
Wassim M. Haddad ◽  
Sergey G. Nersesov
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Thermodynamic Modeling ◽  
Discrete Time ◽  
Large Scale ◽  
Type Inequality ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Thermodynamic Models ◽  
Definition Of

This chapter describes the thermodynamic modeling of discrete-time large-scale dynamical systems. In particular, it develops nonlinear discrete-time compartmental models that are consistent with thermodynamic principles. Since thermodynamic models are concerned with energy flow among subsystems, the chapter constructs a nonlinear compartmental dynamical system model characterized by conservation of energy and the first law of thermodynamics. It then provides a deterministic definition of entropy for a large-scale dynamical system that is consistent with the classical thermodynamic definition of entropy and shows that it satisfies a Clausius-type inequality leading to the law of entropy nonconservation. The chapter also considers nonconservation of entropy and the second law of thermodynamics, nonconservation of ectropy, semistability of discrete-time thermodynamic models, entropy increase and the second law of thermodynamics, and thermodynamic models with linear energy exchange.

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