Search Results (9)

Atmospheric climate science lacks the capacity to integrate thermodynamics with the gravitational potential of air in a classical quantum theory. To what extent can we identify Carnot’s ideal heat engine cycle in reversible isothermal and isentropic phases between dual temperatures partitioning heat flow with coupled work processes in the atmosphere? Using statistical action mechanics to describe Carnot’s cycle, the maximum rate of work possible can be integrated for the working gases as equal to variations in the absolute Gibbs energy, estimated as sustaining field quanta consistent with Carnot’s definition of heat as caloric. His treatise of 1824 even gave equations expressing work potential as a function of differences in temperature and the logarithm of the change in density and volume. Second, Carnot’s mechanical principle of cooling caused by gas dilation or warming by compression can be applied to tropospheric heat–work cycles in anticyclones and cyclones. Third, the virial theorem of Lagrange and Clausius based on least action predicts a more accurate temperature gradient with altitude near 6.5–6.9 °C per km, requiring that the Gibbs rotational quantum energies of gas molecules exchange reversibly with gravitational potential. This predicts a diminished role for the radiative transfer of energy from the atmosphere to the surface, in contrast to the Trenberth global radiative budget of ≈330 watts per square metre as downwelling radiation. The spectral absorptivity of greenhouse gas for surface radiation into the troposphere enables thermal recycling, sustaining air masses in Lagrangian action. This obviates the current paradigm of cooling with altitude by adiabatic expansion. The virial-action theorem must also control non-reversible heat–work Carnot cycles, with turbulent friction raising the surface temperature. Dissipative surface warming raises the surface pressure by heating, sustaining the weight of the atmosphere to varying altitudes according to latitude and seasonal angles of insolation. New predictions for experimental testing are now emerging from this virial-action hypothesis for climate, linking vortical energy potential with convective and turbulent exchanges of work and heat, proposed as the efficient cause setting the thermal temperature of surface materials. Full article

After a brief review of Carnot’s everlasting contributions to the foundations of thermodynamics, we critically examine the consequences of the Carnot theorem, which leaves behind some lingering questions and confusion that persist even today. What is the one significant aspect of the Carnot cycle that leads to this theorem? When does the working substance play an important role for an engine and what is its correlation with the protocol of operational details? Do all reversible engines working between the same two temperatures have the same maximum efficiency of the Carnot engine as Fermi has suggested? Are all heat engines equivalent to a Carnot engine in disguise? Our new perspective allows for the clarification of these questions with a positive answer for the last question. Recognizing that Carnot eventually abandoned the caloric theory, we use a result by Carnot and simple dimensional analysis to show how the first law, the concept of entropy, and the efficiency of the Carnot engine could have been germinated by Carnot in his time. This then demonstrates that Carnot had good understanding of entropy before its invention by Clausius. We suggest that both should be credited with inventing entropy by calling it Carnot–Clausius entropy. We also clarify some fundamental misconceptions plaguing reversible regenerators and their irreversible replacement by heat exchangers in the field. Full article

The status of the Second Law of Thermodynamics, even in the 21st century, is not as certain as when Arthur Eddington wrote about it a hundred years ago. It is not only about the truth of this law, but rather about its strict and exhaustive formulation. In the previous article, it was shown that two of the three most famous thermodynamic formulations of the Second Law of Thermodynamics are non-exhaustive. However, the status of the statistical approach, contrary to common and unfounded opinions, is even more difficult. It is known that Boltzmann did not manage to completely and correctly derive the Second Law of Thermodynamics from statistical mechanics, even though he probably did everything he could in this regard. In particular, he introduced molecular chaos into the extension of the Liouville equation, obtaining the Boltzmann equation. By using the H theorem, Boltzmann transferred the Second Law of Thermodynamics thesis to the molecular chaos hypothesis, which is not considered to be fully true. Therefore, the authors present a detailed and critical review of the issue of the Second Law of Thermodynamics and entropy from the perspective of phenomenological thermodynamics and statistical mechanics, as well as kinetic theory. On this basis, Propositions 1–3 for the statements of the Second Law of Thermodynamics are formulated in the original part of the article. Proposition 1 is based on resolving the misunderstanding of the Perpetuum Mobile of the Second Kind by introducing the Perpetuum Mobile of the Third Kind. Proposition 2 specifies the structure of allowed thermodynamic processes by using the Inequality of Heat and Temperature Proportions inspired by Eudoxus of Cnidus’s inequalities defining real numbers. Proposition 3 is a Probabilistic Scheme of the Second Law of Thermodynamics that, like a game, shows the statistical tendency for entropy to increase, even though the possibility of it decreasing cannot be completely ruled out. Proposition 3 is, in some sense, free from Loschmidt’s irreversibility paradox. Full article

Increasing interest has been shown in the subject of non-additive entropic forms during recent years, which has essentially been due to their potential applications in the area of complex systems. Based on the fact that a given entropic form should depend only on a set of probabilities, its time evolution is directly related to the evolution of these probabilities. In the present work, we discuss some basic aspects related to non-additive entropies considering their time evolution in the cases of continuous and discrete probabilities, for which nonlinear forms of Fokker–Planck and master equations are considered, respectively. For continuous probabilities, we discuss an H-theorem, which is proven by connecting functionals that appear in a nonlinear Fokker–Planck equation with a general entropic form. This theorem ensures that the stationary-state solution of the Fokker–Planck equation coincides with the equilibrium solution that emerges from the extremization of the entropic form. At equilibrium, we show that a Carnot cycle holds for a general entropic form under standard thermodynamic requirements. In the case of discrete probabilities, we also prove an H-theorem considering the time evolution of probabilities described by a master equation. The stationary-state solution that comes from the master equation is shown to coincide with the equilibrium solution that emerges from the extremization of the entropic form. For this case, we also discuss how the third law of thermodynamics applies to equilibrium non-additive entropic forms in general. The physical consequences related to the fact that the equilibrium-state distributions, which are obtained from the corresponding evolution equations (for both continuous and discrete probabilities), coincide with those obtained from the extremization of the entropic form, the restrictions for the validity of a Carnot cycle, and an appropriate formulation of the third law of thermodynamics for general entropic forms are discussed. Full article

This paper started with the explanation of the conditions for using the momentum equation and with the presentation of the actuator disc theory. Focusing on the flow model used in actuator disk theory, both the Froude-Rankine theorem and Betz’s law have been examined. It has been found that the Froude-Rankine theorem is not justified because a stream-tube that is used as the control volume does not really exist (pseudo stream-tube). The theorem is also not justified because an unfounded velocity (v₂) is used to connect the thrust of the actuator disc with the total power loss. Two flaws have been identified in Betz’s law. First, the use of both the unjustified Froude-Rankine theorem and the incorrect flow model totally violates the condition of determining the thrust of the actuator disc using the momentum equation. Second, the unfounded velocity (v₂) from the Froude-Rankine theorem is misinterpreted and used for the volumetric flow rate through the actuator disc. These two main flaws lead to diverse computational contradictions and paradoxes, particularly when considering the case of an impermeable circular disc. The flaws in Betz’s law become evident when the law is applied to a rectangular actuator plate of infinite length. The possible solution for the actuator disc flow has been presented. This includes the additional consideration of energy dissipation in the flow downstream of the actuator disc, similar to the method used to calculate the Borda-Carnot shock loss. Full article

Nonequilibrium temperature is a topic of research with continuously growing interest because of recent improvements in and applications of nonequilibrium thermodynamics, with particular regard to information theory, kinetic theory, nonequilibrium molecular dynamics, superfluids, radiative systems, etc. All studies on nonequilibrium temperature have pointed out that the definition of nonequilibrium temperature must be related to different aspects of the system, to the energy of the system, and to the energy fluxes between the system and its environment. In this paper, we introduce a definition of nonequilibrium temperature based on the Gouy–Stodola and Carnot theorems in order to satisfy all these theoretical requirements. The result obtained links nonequilibrium temperature to the electromagnetic outflow, generated by irreversibility during microscopic interaction in the system; to the environmental temperature; to the mean energy; and to the geometrical and physical characteristics of the system. Full article

The goal of this comment note is to express my concerns about the recent paper by Tian Zhao et al. (Entropy 2018, 20, 542). It is foreseen that this comment will stimulate a fruitful discussion of the issues involved. The principle of the least thermodynamic action is applicable for the analysis of the Carnot cycle using the entropy (not heat) generation extrema theorem. The transversality conditions of the variational problem provide the rectangular shape of the ST diagram for the Carnot cycle. Full article

The present age, which can be called the Information Age, has a core technology constituted by bits transported by photons. Both concepts, bit and photon, originated in the past century: the concept of photon was introduced by Planck in 1900 when he advanced the solution of the blackbody spectrum, and bit is a term first used by Shannon in 1948 when he introduced the theorems that founded information theory. The connection between Planck and Shannon is not immediately apparent; nor is it obvious that they derived their basic results from the concept of entropy. Examination of other important scientists can shed light on Planck’s and Shannon’s work in these respects. Darwin and Fowler, who in 1922 published a couple of papers where they reinterpreted Planck’s results, pointed out the centrality of the partition function to statistical mechanics and thermodynamics. The same roots have been more recently reconsidered by Jaynes, who extended the considerations advanced by Darwin and Fowler to information theory. This paper investigates how the concept of entropy was propagated in the past century in order to show how a simple intuition, born in the 1824 during the first industrial revolution in the mind of the young French engineer Carnot, is literally still enlightening the fourth industrial revolution and probably will continue to do so in the coming century. Full article

Closed, steady or cyclic thermodynamic systems, which have temperature variations over their boundaries, can represent an extremely large range of plants, devices or natural objects, such as combined heating, cooling and power plants, computers and data centres, and planets. Energy transfer rates can occur across the boundary, which are characterized as heat or work. We focus on the finite time thermodynamics aspects, on energy-based performance parameters, on rational efficiency and on the environmental reference temperature. To do this, we examine the net work rate of a closed, steady or cyclic system bounded by thermal resistances linked to isothermal reservoirs in terms of the first and second laws of thermodynamics. Citing relevant references from the literature, we propose a methodology that can improve the thermodynamic analysis of an energy-transforming or an exergy-destroying plant. Through the reflections and analysis presented, we have found an explanation of the second law that clarifies the link between the Clausius integral of heat over temperature and the reference temperature of the Gouy–Stodola theorem. With this insight and approach, the specification of the environmental reference temperature in exergy analysis becomes more solid. We have explained the relationship between the Curzon Ahlborn heat engine and an irreversible Carnot heat engine. We have outlined the nature of subsystem rational efficiencies and have found Rant’s anergy to play an important role. We postulate that heat transfer through thermal resistance is the sole basis of irreversibility. Full article