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 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 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].

Surfaces, Interfaces, and Changing Shapes in Multilayered Films

MRS Bulletin ◽  
1999 ◽  
Vol 24 (2) ◽  
pp. 39-43 ◽  
Author(s):  
Daniel Josell ◽  
Frans Spaepen
Keyword(s):  
Free Energy ◽  
Excess Free Energy ◽  
External Pressure ◽  
Electronic Density ◽  
Spherical Drop ◽  
Crystal Anisotropy ◽  
Fundamental Quantity ◽  
The Difference ◽  
Image Position ◽  
Work Done

It is generally recognized that the capillary forces associated with internal and external interfaces affect both the shapes of liquid-vapor surfaces and wetting of a solid by a liquid. It is less commonly understood that the same phenomenology often applies equally well to solid-solid or solid-vapor interfaces.The fundamental quantity governing capillary phenomena is the excess free energy associated with a unit area of interface. The microscopic origin of this excess free energy is often intuitively simple to understand: the atoms at a free surface have “missing bonds”; a grain boundary contains “holes” and hence does not have the optimal electronic density; an incoherent interface contains dislocations that cost strain energy; and the ordering of a liquid near a solid-liquid interface causes a lowering of the entropy and hence an increase in the free energy. In what follows we shall show how this fundamental quantity determines the shape of increasingly complex bodies: spheres, wires, thin films, and multilayers composed of liquids or solids. Crystal anisotropy is not considered here; all interfaces and surfaces are assumed isotropic.Consideration of the equilibrium of a spherical drop of radius R with surface free energy γ shows that pressure inside the droplet is higher than outside. The difference is given by the well-known Laplace equation:This result can be obtained by equating work done against internal and external pressure during an infinitesimal change of radius with the work of creating a new surface.

Introduction

2003 ◽  
Author(s):  
Rob Cross ◽  
Andrew Parker
Keyword(s):  
New Product Development ◽  
Flexible Structures ◽  
Knowledge Work ◽  
Informal Networks ◽  
Work Processes ◽  
Knowledge Intensive ◽  
Management Advice ◽  
Intensive Work ◽  
Work Done ◽  
Second Wave

Spend some time in most any organization today and you are sure to hear of the importance of networks, in one form or another, for getting work done. In this age of increasingly organic, flat, and flexible structures, many managers and scholars are using networks as a central organizing metaphor for twenty-first-century firms (e.g., Dimagio, 2001; Nohria & Ghoshal, 1997). In large part, this focus seems a product of two trends. First, over the past decade or so initiatives such as de-layering, TQM, reengineering, team-based structures, and outsourcing, to name a few, have been undertaken to promote organizational flexibility and efficiency (Hirschhorn & Gilmore, 1992; Hammer & Champy, 1993; Mohrman, Cohen, & Mohrman, 1995; Kerr & Ulrich, 1995). One outcome of these restructuring efforts is that information flow and work increasingly occur through informal networks of relationships rather than through channels tightly prescribed by formal reporting structures or detailed work processes. Along with the drive to more organic structures in organizations we have also seen a rise in the prevalence and value of knowledge-intensive work (Quinn, 1992; Drucker, 1993). Early initiatives to support knowledge workers focused heavily on databases and organizational processes to ensure the capture and sharing of lessons and reusable work products (e.g., Stewart, 1997; O’Dell & Grayson, 1998; Ruggles, 1998; Davenport, Delong, & Beers, 1998). However, these investments rarely, if ever, had the intended impact on the effectiveness and efficiency of knowledge work. As a result, a “second wave” of knowledge-management advice is coming forth that pays a great deal more attention to knowledge embedded within employees and relationships in organizations (e.g., Brown & Duguid, 2000; Cross & Baird, 2000; Dixon, 2000; Von Krogh et al., 2000; Cohen & Prusak, 2001). Among other things, this work has illustrated the importance of trust and informal networks for knowledge creation and sharing within organizations. We suggest that in today’s de-layered, knowledge-intensive settings, most work of importance is heavily reliant on informal networks of employees within organizations. For example, networks sitting across core work processes, weaving together new product development initiatives or integrating strategic initiatives such as alliances or mergers can be critical to organizational effectiveness.

scholarly journals Crystal Period Vectors under External Stress in Statistical Physics

2019 ◽  
Author(s):  
Gang Liu
Keyword(s):  
General Equation ◽  
Statistical Physics ◽  
Continuous Media ◽  
External Pressure ◽  
External Stress ◽  
Cell Edge ◽  
Newtonian Dynamics ◽  
Work Done ◽  
Crystal Cells

A basic and general equation to determine their period vectors (cell edge vectors) is necessary in physics, especially when crystals are under external stress. It has been derived in Newtonian dynamics in these years. Since statistical physics should also generate such, here we derive it. By extending the normal way for crystals under external pressure, regarding crystal cells as being filled with continuous media, writing the work done by the external stress on the crystal explicitly, and deriving the forces on the surfaces of the cells by the external stress, we arrived at the equation for the period vectors, which is in principle the same as the above mentioned counterpart achieved in Newtonian dynamics. It should be applicable when crystals are under different pressures in different directions, like in piezoelectric and piezomagnetic phenomena.

scholarly journals Crystal Period Vectors under External Stress in Statistical Physics

2019 ◽  
Author(s):  
Gang Liu
Keyword(s):  
General Equation ◽  
Statistical Physics ◽  
Continuous Media ◽  
External Pressure ◽  
External Stress ◽  
Cell Edge ◽  
Newtonian Dynamics ◽  
Work Done ◽  
Crystal Cells ◽  
Special Case

A basic and general equation to determine period vectors (cell edge vectors) is necessary in physics, especially when crystals are under external stress. It has been derived in Newtonian dynamics. Since statistical physics should also generate such equation, we will provide a derivation. By extending the normal derivation for crystals under external pressure, regarding crystal cells as being filled with continuous media, formulating the work done by the external stress on the crystal explicitly, and deriving the forces on the surfaces of the cells by the external stress, we arrived at the equation for the period vectors, which is in principle the same as the above mentioned counterpart achieved in Newtonian dynamics. Everything also restores when the external stress reduces to the special case of external pressure. It should be applicable when crystals are under different pressures in different directions, like in piezoelectric and piezomagnetic phenomena.

XXI. The direct influence of gradual variations of temperature upon the rate of beat of the dog’s heart

1883 ◽  
Vol 174 ◽  
pp. 663-688 ◽  
Keyword(s):  
Arterial Pressure ◽  
Pulse Rate ◽  
Venous Pressure ◽  
Practical Importance ◽  
The Body ◽  
Full Account ◽  
Heart Beating ◽  
External Conditions ◽  
Work Done ◽  
Made In

In the year 1881 I briefly described (1) a method of experimenting by which the heart and lungs of a Dog or Cat could be completely isolated physiologically from the remainder of the body of the animal, and kept alive some hours for study in an apparently normal condition, the heart beating regularly and maintaining a good arterial pressure. Since then I have been at work investigating the influence of various conditions upon the pulse-rate of Dogs’ hearts so isolated; while under my supervision several of my pupils have been engaged in studying the work done in a unit of time by such hearts under different external conditions. As regards the effects of variations of arterial pressure upon the pulse-rate of the isolated Dog’s heart, my results have already been published (2); and detailed observations as to the influence of variations in venous pressure will shortly be printed. But in so far as the influence of temperature variations upon the cardiac rhythm is concerned, only a brief preliminary announcement (3) has been made. In the present paper I propose to give a full account of my experiments upon this subject, which is one that, apart from and in addition to its purely physiological interest, has considerable practical importance in connexion with inquiries as to the immediate cause of the quick pulse so constantly found in warm-blooded animals suffering from fever.

The Mean Air Flow as Lagrangian Dynamics Approximation and Its Application to Moist Convection

2016 ◽  
Vol 73 (11) ◽  
pp. 4407-4425 ◽  
Author(s):  
Olivier M. Pauluis
Keyword(s):  
Atmospheric Carbon Dioxide ◽  
Energy Transport ◽  
Potential Temperature ◽  
Carnot Cycle ◽  
Moist Convection ◽  
Lagrangian Dynamics ◽  
Thermodynamic Cycles ◽  
The Mean ◽  
Work Done ◽  
Dynamics Approximation

Abstract This paper introduces the Mean Airflow as Lagrangian Dynamics Approximation (MAFALDA), a new method designed to extract thermodynamic cycles from numerical simulations of turbulent atmospheric flows. This approach relies on two key steps. First, mean trajectories are obtained by computing the mean circulation using height and equivalent potential temperature as coordinates. Second, thermodynamic properties along these trajectories are approximated by using their conditionally averaged values at the same height and θe. This yields a complete description of the properties of air parcels that undergo a set of idealized thermodynamic cycles. MAFALDA is applied to analyze the behavior of an atmosphere in radiative–convective equilibrium. The convective overturning is decomposed into 20 thermodynamic cycles, each accounting for 5% of the total mass transport. The work done by each cycle can be expressed as the difference between the maximum work that would have been done by an equivalent Carnot cycle and a penalty that arises from the injection and removal of water at different values of its Gibbs free energy. The analysis indicates that the Gibbs penalty reduces the work done by all thermodynamic cycles by about 55%. The cycles are also compared with those obtained for doubling the atmospheric carbon dioxide, which in the model used here leads to an increase in surface temperature of about 3.4 K. It is shown that warming greatly increases both the energy transport and work done per unit mass of air circulated. As a result, the ratio of the kinetic energy generation to the convective mass flux increases by about 20% in the simulations.

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.

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