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].

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.

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.

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 Mixing indistinguishable systems leads to a quantum Gibbs paradox

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Benjamin Yadin ◽  
Benjamin Morris ◽  
Gerardo Adesso
Keyword(s):  
Statistical Mechanics ◽  
Thought Experiment ◽  
Entropy Change ◽  
Ideal Gas ◽  
Gibbs Paradox ◽  
Quantum Case ◽  
Entropy Increase ◽  
Level Of Knowledge ◽  
Different Gases ◽  
As If

AbstractThe classical Gibbs paradox concerns the entropy change upon mixing two gases. Whether an observer assigns an entropy increase to the process depends on their ability to distinguish the gases. A resolution is that an “ignorant” observer, who cannot distinguish the gases, has no way of extracting work by mixing them. Moving the thought experiment into the quantum realm, we reveal new and surprising behaviour: the ignorant observer can extract work from mixing different gases, even if the gases cannot be directly distinguished. Moreover, in the macroscopic limit, the quantum case diverges from the classical ideal gas: as much work can be extracted as if the gases were fully distinguishable. We show that the ignorant observer assigns more microstates to the system than found by naive counting in semiclassical statistical mechanics. This demonstrates the importance of accounting for the level of knowledge of an observer, and its implications for genuinely quantum modifications to thermodynamics.

Ideal gas processes – and two ideal gas case studies too

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Case Studies ◽  
Constant Pressure ◽  
Ideal Gas ◽  
Heat Capacities ◽  
Carnot Cycle ◽  
State Function ◽  
Ideal Gases ◽  
First Case ◽  
The Ideal

This chapter brings together, and builds on, the results from previous chapters to provide a succinct, and comprehensive, summary of all key relationships relating to ideal gases, including the heat and work associated with isothermal, adiabatic, isochoric and isobaric changes, and the properties of an ideal gas’s heat capacities at constant volume and constant pressure. The chapter also has two ‘case studies’ which use the ideal gas equations in broader, and more real, contexts, so showing how the equations can be used to tackle, successfully, more extensive systems. The first ‘case study’ is the Carnot cycle, and so covers all the fundamentals required for the proof of the existence of entropy as a state function; the second ‘case study’ is the ‘thermodynamic pendulum’ – a system in which a piston in an enclosed cylinder oscillates to and fro like a pendulum under gravity, in both the absence, and presence, of friction.

The First Law of Thermodynamics

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Internal Energy ◽  
Heat Capacities ◽  
Dissipative Process ◽  
Constant Volume ◽  
Irreversible Processes ◽  
State Function ◽  
Thermodynamic Cycles ◽  
First Law Of Thermodynamics

The First Law of Thermodynamics, and how the First Law relates a change in a state function, internal energy, to changes in the path functions work and heat. Thermodynamic cycles. Heat capacities at constant volume, and the definition CV = (∂U/∂T)V. Mathematics of internal energy. Examples of the application of the First Law to isothermal, isobaric, isochoric and adiabatic changes. Reversible and irreversible paths. Mixing and friction as irreversible processes. Proof that that any path involving friction (or any other dissipative process) must be irreversible, implying that all real paths are irreversible.

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.

Analysis of Emission Rate Measurements in a Material Showing a Meyer-Neldel- Rule

2003 ◽  
Vol 799 ◽  
Author(s):  
Richard S. Crandall
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Emission Rate ◽  
Deep Level ◽  
Entropy Change ◽  
Emission Data ◽  
Entropy Changes ◽  
Deep Traps ◽  
Transient Spectroscopy ◽  
Transition Entropy

ABSTRACTThis paper presents data showing a Meyer-Neldel rule (MNR) in InGaAsN alloys. It is shown that without this knowledge, significant errors can be made using Deep-Level Transient-Spectroscopy (DLTS) emission data to determine capture cross sections. The errors arise because of the neglect of significant transition entropy changes associated with multiphonon excitation of charge from deep traps. Ignoring the entropy change results in cross section values ranging over five orders-of-magnitude in InGaAsN alloys and 18 orders-of-magnitude in CuInGaSe alloys. Only by correctly accounting for the MNR and the accompanying entropy changes in analyzing the DLTS data will the correct value of the cross section be obtained.

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