scholarly journals The Carnot Cycle, Reversibility and Entropy

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 810
Author(s):  
David Sands
Keyword(s):  
Irreversible Process ◽  
Entropy Change ◽  
External Pressure ◽  
Step Change ◽  
Equilibrium States ◽  
Rate Equations ◽  
Carnot Cycle ◽  
Work Processes ◽  
Reversible Process ◽  
External Conditions

The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still corresponds to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea, current at the time, that heat is motion. It is shown how this view of heat led Clausius to develop the entropy of a body based on the work that could be performed in a reversible process rather than the work that is actually performed in an irreversible process. In consequence, Clausius built into entropy a conflict with energy conservation, which is concerned with actual changes in energy. In this paper, reversibility and irreversibility are investigated by means of a macroscopic formulation of internal mechanisms of damping based on rate equations for the distribution of energy within a gas. It is shown that work processes involving a step change in external pressure, however small, are intrinsically irreversible. However, under idealised conditions of zero damping the gas inside a piston expands and traces out a trajectory through the space of equilibrium states. Therefore, the entropy change due to heat flow from the reservoir matches the entropy change of the equilibrium states. This trajectory can be traced out in reverse as the piston reverses direction, but if the external conditions are adjusted appropriately, the gas can be made to trace out a Carnot cycle in P-V space. The cycle is dynamic as opposed to quasi-static as the piston has kinetic energy equal in difference to the work performed internally and externally.

scholarly journals The Carnot Cycle, Reversibility and Entropy

2021 ◽  
Author(s):  
David Sands
Keyword(s):  
Entropy Change ◽  
External Pressure ◽  
Step Change ◽  
Equilibrium States ◽  
Rate Equations ◽  
Carnot Cycle ◽  
Work Processes ◽  
Reversible Process ◽  
External Conditions ◽  
Work Done

The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still correspond to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea current at the time that heat is motion. It is shown how this view of heat led Clausius to develop the entropy of a body based on the work that could be done in a reversible process rather than the work that was actually done. In consequence, Clausius built into entropy a conflict with energy conservation, which is concerned with actual changes in energy. In this paper, a macroscopic formulation of internal mechanisms of damping based on rate equations for the distribution of energy within a gas. It is shown that work processes involving a step-change in external pressure, however small, are intrinsically irreversible. However, under idealised conditions of zero damping the gas inside a piston expands and traces out a trajectory through the space of equilibrium states. Therefore, the entropy change due to heat flow from the reservoir matches the entropy change of the equilibrium states. This trajectory can traced out in reverse as the piston reverses direction, but if the external conditions are adjusted appro-priately, the gas can be made to trace out a Carnot cycle in P-V space. The cycle is dynamic as opposed to quasi-static as the piston has kinetic energy equal in difference to the work done in-ternally and externally.

scholarly journals Entropy change of an ideal gas determination with no reversible process

2005 ◽  
Vol 27 (2) ◽  
pp. 259-262 ◽  
Author(s):  
Joaquim Anacleto
Keyword(s):  
Irreversible Process ◽  
Entropy Change ◽  
Ideal Gas ◽  
Equilibrium States ◽  
State Function ◽  
Actual Process ◽  
Reversible Process ◽  
Original Process ◽  
First Law Of Thermodynamics ◽  
Entropy Changes

As is stressed in literature [1], [2], the entropy change, deltaS, during a given irreversible process is determined through the substitution of the actual process by a reversible one which carries the system between the same equilibrium states. This can be done since entropy is a state function. However this may suggest to the students the idea that this procedure is mandatory. We try to demystify this idea, showing that we can preserve the original process. Another motivation for this paper is to emphasize the relevance of the reservoirs concept, in particular the work reservoir, which is usually neglected in the literature<A NAME="tx02"></A><A HREF="#nt02">2</A>. Starting by exploring briefly the symmetries associated to the first law of Thermodynamics, we obtain an equation which relates both the system and neighborhood variables and allows entropy changes determination without using any auxiliary reversible process. Then, simulations of an irreversible ideal gas process are presented using Mathematica©, which we believe to be of pedagogical value in emphasizing the exposed ideas and clarifying some possible misunderstandings relating to the difficult concept of entropy [4].

Development of the Concept of Entropy: A Simpler Alternative to Carnot Cycle

2021 ◽  
Vol 30 (6) ◽  
pp. 630-635
Author(s):  
Jamil Ahmad ◽  
Keyword(s):  
Heat Capacity ◽  
Internal Energy ◽  
Irreversible Process ◽  
Entropy Change ◽  
Ideal Gas ◽  
Carnot Cycle ◽  
Total Entropy ◽  
Isothermal Expansion ◽  
The Relationship ◽  
Reversible Work

The relationship between entropy and reversible heat and temperature is developed using a simple cycle, in which an ideal gas is subjected to isothermal expansion and compression and heated and cooled between states. The procedure is easily understood by students if they have knowledge of calculations involving internal energy, reversible work, and heat capacity for an ideal gas. This approach avoids the more time-consuming Carnot cycle. The treatment described here illustrates how the total entropy change resulting from an irreversible process is always positive.

AN IRREVERSIBLE PROCESS REPRESENTED BY A REVERSIBLE ONE

2008 ◽  
Vol 18 (07) ◽  
pp. 2059-2061 ◽  
Author(s):  
ABRAHAM BOYARSKY ◽  
PAWEŁ GÓRA
Keyword(s):  
Differential Equation ◽  
Probability Density ◽  
Irreversible Process ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Probability Density Functions ◽  
Density Functions ◽  
Reversible Process

Chaotic maps on an interval are irreversible in the sense that trajectories of points cannot be reversed. Furthermore, even when one considers trajectories of probabilities or probability density functions (pdf) generated by the chaotic map, the processes are irreversible. In this note we consider the following question: let τ be a chaotic map which takes a pdf f0 to a pdf f1. Does there exist a reversible process that accomplishes the same thing. For example, can we construct a differential equation which takes f0 to f1 and then, on reversal of time, f1 to f0. We present an example which answers this question in the affirmative.

Thermodynamics and foundations of mass-action kinetics

2005 ◽  
Vol 30 (1-2) ◽  
pp. 3-113 ◽  
Author(s):  
Miloslav Pekař
Keyword(s):  
Chemical Kinetics ◽  
Reaction Rate ◽  
Chemical Potential ◽  
Kinetic Equations ◽  
Reaction Rates ◽  
Equilibrium States ◽  
Mass Action ◽  
Rate Equations ◽  
Mass Action Kinetics ◽  
Non Equilibrium

A critical overview is given of phenomenological thermodynamic approaches to reaction rate equations of the type based on the law of mass-action. The review covers treatments based on classical equilibrium and irreversible (linear) thermodynamics, extended irreversible, rational and continuum thermodynamics. Special attention is devoted to affinity, the applications of activities in chemical kinetics and the importance of chemical potential. The review shows that chemical kinetics survives as the touchstone of these various thermody-namic theories. The traditional mass-action law is neither demonstrated nor proved and very often is only introduced post hoc into the framework of a particular thermodynamic theory, except for the case of rational thermodynamics. Most published “thermodynamic'’ kinetic equations are too complicated to find application in practical kinetics and have merely theoretical value. Solely rational thermodynamics can provide, in the specific case of a fluid reacting mixture, tractable rate equations which directly propose a possible reaction mechanism consistent with mass conservation and thermodynamics. It further shows that affinity alone cannot determine the reaction rate and should be supplemented by a quantity provisionally called constitutive affinity. Future research should focus on reaction rates in non-isotropic or non-homogeneous mixtures, the applicability of traditional (equilibrium) expressions relating chemical potential to activity in non-equilibrium states, and on using activities and activity coefficients determined under equilibrium in non-equilibrium states.

scholarly journals On the ambiguity of an ideal gas entropy concept

2020 ◽  
Vol 22 (4) ◽  
pp. 32-42
Author(s):  
V. G. Kiselev
Keyword(s):  
Critical Analysis ◽  
Ideal Gas ◽  
Absolute Temperature ◽  
Carnot Cycle ◽  
Perfect Gas ◽  
Reversible Process ◽  
Thermodynamic Potentials ◽  
Adiabatic Processes ◽  
Isothermal Processes

Based on a critical analysis of the existing characteristics of an ideal gas and the theory of thermodynamic potentials, the article considers its new model, which includes the presence of an ideal gas in addition to kinetic energy of potential (chemical) energy, in the framework of which the isothermal and adiabatic processes in it are studied both reversible and irreversible, in terms of changes in the entropy of the system in question, observed in case. In addition, a critical analysis was made of the process of introducing the concept of entropy by R. Clausius, as a result of which the main requirements for entropy were established, the changes of which are observed in isothermal and adiabatic quasistatic processes, in particular, it was revealed that if in isothermal processes involving one in a perfect gas, the entropy ST is uniquely characterized by the value , regardless of whether the process is reversible or not, then when the adiabatic processes occur, the only requirement made of them is the condition of mutual destruction adiabats in this Carnot cycle. As a result of this circumstance, in fact, in thermodynamics various “adiabatic” entropies are used, namely; const SA = const R ln V  и  C V ln T , and in addition, as established in this paper, CV, which leads, despite the mathematically perfect introduction of the concept of entropy for the Carnot cycle, to the impossibility of its unambiguous interpretation and, therefore, the determination of its physicochemical meaning even for perfect gas. A new concept is introduced in the work: “total” entropy of an ideal gas SS = R ln V + C V , satisfying the criteria of R. Clausius, on the basis of which it was established that this type of entropy multiplied by the absolute temperature characterizes a certain level of potential energy of the system, which can besuccessively converted to work in an isothermal reversible process, with the supply of an appropriate amount of heat, and in the adiabatic reversible process under consideration.

scholarly journals The Electrochemical Reduction Mechanism of ZnFe2O4 in NaCl-CaCl2 Melts

Crystals ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 925
Author(s):  
Chang Liu ◽  
Jinglong Liang ◽  
Hui Li ◽  
Hongyan Yan ◽  
Sijia Zheng ◽  
...  
Keyword(s):  
Electrochemical Reduction ◽  
Thermodynamic Analysis ◽  
Irreversible Process ◽  
Gradual Increase ◽  
Reduction Process ◽  
Reduction Mechanism ◽  
Reversible Process ◽  
Electrochemical Tests ◽  
Oxygen Ions ◽  
One Step

The electrochemical reduction process of ZnFe2O4 in NaCl-CaCl2 melts was studied. Thermodynamic analysis shows that the reduction process of ZnFe2O4 is carried out in multiple steps, and it is difficult to reduce Fe3+ to Fe in one step. Electrochemical tests revealed that the reduction process of ZnFe2O4 includes three steps: First, Fe3+ is reduced to Fe in two steps, then Zn2+ is reduced to Zn in one step. The reduction of Fe3+ on the Mo electrode is a reversible process controlled by diffusion, while the reduction of Zn2+ is an irreversible process controlled by diffusion. The influence of electrolysis voltage and temperature on the process of electric deoxidation has also been studied. It is indicated that properly increasing the temperature is conducive to the diffusion of oxygen ions, thereby increasing the deoxidation rate. With the gradual increase of voltage, the reduction process of ZnFe2O4 is ZnFe2O4 → FeO + ZnO → Fe + ZnO → Fe + Zn.

Pursuing defragmentation at the municipal level: signs of a changing pattern?

Modern Italy ◽  
2017 ◽  
Vol 23 (1) ◽  
pp. 85-102 ◽  
Author(s):  
Silvia Bolgherini ◽  
Mattia Casula ◽  
Mariano Marotta
Keyword(s):  
Local Level ◽  
National Policy ◽  
Step Change ◽  
Quarter Century ◽  
The Past ◽  
Explanatory Factors ◽  
External Conditions ◽  
Descriptive Approach ◽  
National Policy Maker ◽  
Municipal Level

Municipal fragmentation is a real historical issue in Italy but its relevance has been differently perceived over time. With a focus on the municipal unions and amalgamations as the main tools for defragmentation, we will present an overview of the last quarter century (1990–2017) of territorial policy at the local level. The reforms introduced since 2010 marked a step change in this area: in fact, empirical evidence shows that the most recent defragmentation attempts have had a certain success. This article, by maintaining a descriptive approach, will try to answer why the most recent defragmentation policy achieved some results, in contrast to those of the past. Some explanatory factors will be presented by reviewing the stances of the main actors in this policy field and their interaction with national policy-maker goals and approaches as well as with normative elements and external conditions.

Relaxation times obtained from the rate equations using path probability method for the spin-1 Ising model

2019 ◽  
Vol 33 (22) ◽  
pp. 1950258 ◽  
Author(s):  
Rıza Erdem ◽  
Songül Özüm
Keyword(s):  
Ising Model ◽  
Relaxation Times ◽  
Phenomenological Theory ◽  
Equilibrium States ◽  
Time Dependent ◽  
Rate Equations ◽  
Probability Method ◽  
Temperature Variations ◽  
Path Probability Method ◽  
Good Agreement

We have presented the time-dependent behaviors of a spin-1 Ising model (with both bilinear and biquadratic interactions) in the neighborhood of the equilibrium states via the path probability method. The rate equations as introduced by Keskin and co-workers (1989) have been linearized to obtain the characteristic relaxation times. The temperature variations of these times were produced in accordance with the Tanaka and Mannari’s work (1976) on the equilibrium properties. Results are compared to one using Onsager’s phenomenological theory and a good agreement is achieved.

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