Entropy change of an ideal gas determination with no reversible process

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].

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The Carnot Cycle, Reversibility and Entropy

Entropy ◽

10.3390/e23070810 ◽

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.

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Mixing indistinguishable systems leads to a quantum Gibbs paradox

Nature Communications ◽

10.1038/s41467-021-21620-7 ◽

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.

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On the ambiguity of an ideal gas entropy concept

Proceedings of the higher educational institutions ENERGY SECTOR PROBLEMS ◽

10.30724/1998-9903-2020-22-4-32-42 ◽

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.

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

Natural Science and Advanced Technology Education ◽

10.53656/nat2021-6.01 ◽

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.

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“TERPI” AS A QUANTITY OF THERMODYNAMIC POTENTIAL ENERGY SUPPLEMENTARY TO THE CONCEPT OF WORK AND HEAT

Indonesian Journal of Chemistry ◽

10.22146/ijc.21887 ◽

2010 ◽

Vol 3 (2) ◽

pp. 67-69

Author(s):

RHA Sahirul Alim

Keyword(s):

Energy Flow ◽

Thermodynamic Potential ◽

Electrochemical Cell ◽

Ideal Gas ◽

Work Flow ◽

Second Law ◽

Energy Potential ◽

Reversible Process ◽

Gas System ◽

Thermodynamic Processes

Isothermal reversible thermodynamic processes were studied, where there will not occur flow of heat (q) in the system in accord with the second law of thermodynamic. It appear that the energy flow in the system cannot be explained adequately by considering the flow of P,V - work, usually indicated by w, in accordance with the first law, that is, ΔU = q + w with q = 0. Therefore, it is necessary to have another kind of work energy (potential) which is not electrical to explain such as the experiment of Boyle that results in the formula PV = C for a close ideal gas system undergoing an isothermal and reversible process. In this paper, a new work potential which is called ";;terpi";; is introduced, and is abbreviated as τ (tau) and defined as: dτ ≡ - T dSrev = - dqrev. Therefore, dt is also not an exact differential as dw and dq. For any isothermal reversible process, it can be written: τ = -TΔSrev, and for redox reaction, such as an electrochemical cell, it is noteworthy to distinguish between τ system (τsyst) and τ reaction (τr) which combine together to become an electrical work flow, (wel) done by the system on the surrounding, so that: ΔGr = τsyst + τr = v F E Furthermore, the studies of phase transitions, which occur isothermally, were also considered, e.g. the evaporation of a liquid into vapour at a certain T. The heat given to this process cannot freely flow isothermally, but first it must be changed into terpy and then added to the enthalpy of the vapour following the equation: τvap = -TΔSvap = -ΔHvap. Keywords: thermodynamics, heat, work, isothermal, reversible

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The Carnot Cycle, Reversibility and Entropy

10.20944/preprints202106.0038.v1 ◽

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.

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On the Preparation of Bovine α-Thrombin

Thrombosis and Haemostasis ◽

10.1055/s-0038-1646669 ◽

1978 ◽

Vol 39 (01) ◽

pp. 193-200 ◽

Cited By ~ 7

Author(s):

Erwin F Workman ◽

Roger L Lundblad

Keyword(s):

Immobilized Enzyme ◽

Catalytic Properties ◽

Specific Activity ◽

Guanidine Hydrochloride ◽

Low Molecular Weight ◽

Reversible Process ◽

Gel Beads ◽

Tissue Thromboplastin ◽

C 50 ◽

Hydrolysis Of

SummaryAn improved method for the preparation of bovine α-thrombin is described. The procedure involves the activation of partially purified prothrombin with tissue thromboplastin followed by chromatography on Sulfopropyl-Sephadex C-50. The purified enzyme is homogeneous on polyacrylamide discontinuous gel electrophoresis and has a specific activity toward fibrinogen of 2,200–2,700 N.I.H. U/mg. Its stability on storage in liquid media is dependent on both ionic strenght and temperature. Increasing ionic strength and decreasing temperature result in optimal stability. The denaturation of α-thrombin by guanidine hydrochloride was found to be a partially reversible process with the renatured species possessing properties similar to “aged” thrombin. In addition, the catalytic properties of a-thrombin covalently attached to agarose gel beads were also examined. The activity of the immobilized enzyme toward fibrinogen was affected to a much greater extent than was the hydrolysis of low molecular weight, synthetic substrates.

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