Search Results (16)

The contributions of Thermodynamics to Economics have been masterfully pioneered by P. A. Samuelson in his Foundations of Economic Analysis, adapting the Le Châtelier Principle to relate changes in economic variables. Recent contributions have been given, including the economic counterparts of energy, temperature, reversibility, and irreversibility, the Carnot engine, entropy, entropy generation, and the four Laws of Thermodynamics. Starting from them, toward a more efficient (more perfect) economy, the present work aims at (i) showing the contribution of negotiation to a more perfect economy; (ii) proposing endoreversible economic processes, and evaluating their efficiency at maximum merchandise wealth delivery; (iii) proposing the dynamic economic processes’ analysis based on the Economics analogue of specific heat, closely related to the demand elasticity coefficient; (iv) exploring ways to maximize merchandise wealth delivery instead of maximizing merchandise economic entropy generation (financial value generation) in dynamic processes; and (v) defining and evaluating the Economics analogue of exergy, the maximum potential of economic systems to deliver merchandise wealth. Full article

The article discusses the current challenges facing the energy sector in the context of climate policy, technological transformation, and the urgent need to increase energy efficiency while reducing greenhouse gas emissions. Modern thermal energy conversion technologies are analyzed, including supercritical steam and gas–steam cycles, as well as distributed systems using renewable fuels and microturbines. Particular attention is given to innovative systems with isothermal expansion, which theoretically allow operation close to the efficiency limit defined by the Carnot cycle. The study presents calculation results for conventional systems (steam, gas with regeneration, and Organic Rankine Cycle) and proposes a novel isothermal air turbine cycle. In a combined gas–steam configuration, the proposed cycle achieved an efficiency exceeding 43% at a relatively low heat source temperature of 700 K, clearly outperforming conventional steam and ORC systems under the same thermal conditions. The use of a simple working medium (air), combined with the potential for integration with renewable energy sources, makes this concept a promising and viable alternative to traditional Rankine and Brayton cycles in thermally constrained applications. Full article

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

Sadi Carnot’s seminal work laid the foundation for exploring the effects of thermodynamics across diverse domains of physics, stretching from quantum to cosmological scales. Here, we build on the principles of the original Carnot heat engine, and apply it in the context of a particular toy model black brane. This theoretical construct of an effectively two-dimensional, stable, and stationary gravitational object in four-dimensional spacetime derives from a hypothetical flat planet collapsed under the influence of gravity. By constructing a thermodynamic cycle involving three such black branes, we explore the possibility of energy extraction or mining, driven by the temperature gradients and gravitational potential differences characteristic of curved spacetime. Analytic solutions obtainable within this toy model illuminate key aspects of black hole thermodynamics in general, particularly for spacetimes that are not asymptotically flat. Central to these findings is the relation between gravitationally induced temperature ratios and entropy changes, which collectively offer a novel perspective on obtainable energy transfer processes around gravitational structures. This analysis highlights potential implications for understanding energy dynamics in gravitational systems in general, including for black hole evaporation and experimentally implemented black hole analogues. The presented findings not only emphasise the universality of the thermodynamic principles first uncovered by Carnot, but also suggest future research directions in gravitational thermodynamics. 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

Advances in applied mechanics have facilitated a better understanding of the recycling of heat and work in the troposphere. This goal is important to meet practical needs for better management of climate science. Achieving this objective may require the application of quantum principles in action mechanics, recently employed to analyze the reversible thermodynamics of Carnot’s heat engine cycle. The testable proposals suggested here seek to solve several problems including (i) the phenomena of decreasing temperature and molecular entropy but increasing Gibbs energy with altitude in the troposphere; (ii) a reversible system storing thermal energy to drive vortical wind flow in anticyclones while frictionally warming the Earth’s surface by heat release from turbulence; (iii) vortical generation of electrical power from translational momentum in airflow in wind farms; and (iv) vortical energy in the destructive power of tropical cyclones. The scalar property of molecular action (@_t ≡ ∫mvds, J-sec) is used to show how equilibrium temperatures are achieved from statistical equality of mechanical torques (mv² or mr²ω²); these are exerted by Gibbs field quanta for each kind of gas phase molecule as rates of translational action (d@_t/dt ≡ ∫mr²ωdϕ/dt ≡ mv²). These torques result from the impulsive density of resonant quantum or Gibbs fields with molecules, configuring the trajectories of gas molecules while balancing molecular pressure against the density of field energy (J/m³). Gibbs energy fields contain no resonant quanta at zero Kelvin, with this chemical potential diminishing in magnitude as the translational action of vapor molecules and quantum field energy content increases with temperature. These cases distinguish symmetrically between causal fields of impulsive quanta (Σhν) that energize the action of matter and the resultant kinetic torques of molecular mechanics (mv²). The quanta of these different fields display mean wavelengths from 10⁻⁴ m to 10¹² m, with radial mechanical advantages many orders of magnitude greater than the corresponding translational actions, though with mean quantum frequencies (v) similar to those of radial Brownian movement for independent particles (ω). Widespread neglect of the Gibbs field energy component of natural systems may be preventing advances in tropospheric mechanics. A better understanding of these vortical Gibbs energy fields as thermodynamically reversible reservoirs for heat can help optimize work processes on Earth, delaying the achievement of maximum entropy production from short-wave solar radiation being converted to outgoing long-wave radiation to space. This understanding may improve strategies for management of global changes in climate. Full article

We present a quantum Otto engine model alternatively driven by a hot and a cold heat reservoir and consisting of two isochoric and two adiabatic strokes, where the adiabatic expansion or compression is realized by adiabatically changing the shape of the potential. Here, we show that such an adiabatic deformation may alter operation mode and enhance machine performance by increasing output work and efficiency, even with the advantage of decreasing work fluctuations. If the heat engine in the sudden limit operates under maximal power by optimizing the control parameter, the efficiency shows certain universal behavior, ${\eta }^{*}={\eta }_C/2+{\eta }_C^2/8+O\left({\eta }_C^3\right)$, where ${\eta }_C=1-{\beta }_h^r/{\beta }_c^r$ is the Carnot efficiency, with ${\beta }_h^r({\beta }_c^r$) being the inverse temperature of the hot (cold) reservoir. However, such efficiency under maximal power can be produced by our machine model in the regimes where the machine without adiabatic deformation can only operate as a heater or a refrigerator. Full article

In the present study, the evaluation of potential improvement of the overall efficiency of a common PV panel, valorizing the heat extracted by a heat exchanger that is integrated on its back side, either into work using an endoreversible Carnot engine or into cold by using an endoreversible tri-thermal machine consisting of a heat-driven refrigeration machine operating between three temperature sources and sink (such as a liquid/gas absorption machine), was carried out. A simplified thermodynamic analysis of the PV/thermal collector shows that there are two optimal operating temperatures ${\tilde{T}}_h$ and $T_h^{*}$ of the panels, which maximize either the thermal exergy or the overall exergy of the PV panel, respectively. The cold produced by the endoreversible tri-thermal machine during the operating conditions of the PV/thermal collector at ${\tilde{T}}_h$ is higher with a coefficient of performance (COP) of 0.24 thanks to the higher heat recovery potential. In the case of using the cold produced by a tri-thermal machine to actively cool of an additional PV panel in order to increase its electrical performances, the operating conditions at the optimal temperature $T_h^{*}$ provide a larger and more stable gain: the gain is about 12.2% compared with the conventional PV panel when the operating temperature of the second cooled panel varies from 15 to 35 °C. Full article

Originally, the Carnot cycle was a theoretical thermodynamic cycle that provided an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of work to the system. The first aim of this paper is to introduce and study the economic Carnot cycles concerning Roegenian economics, using our thermodynamic–economic dictionary. These cycles are described in both a $\mathbf{Q}-\mathbf{P}$ diagram and a $\mathbf{E}-\mathbf{I}$ diagram. An economic Carnot cycle has a maximum efficiency for a reversible economic “engine”. Three problems together with their solutions clarify the meaning of the economic Carnot cycle, in our context. Then we transform the ideal gas theory into the ideal income theory. The second aim is to analyze the economic Van der Waals equation, showing that the diffeomorphic-invariant information about the Van der Waals surface can be obtained by examining a cuspidal potential. Full article

Despite the remarkable success of Carnot’s heat engine cycle in founding the discipline of thermodynamics two centuries ago, false viewpoints of his use of the caloric theory in the cycle linger, limiting his legacy. An action revision of the Carnot cycle can correct this, showing that the heat flow powering external mechanical work is compensated internally with configurational changes in the thermodynamic or Gibbs potential of the working fluid, differing in each stage of the cycle quantified by Carnot as caloric. Action (@) is a property of state having the same physical dimensions as angular momentum (mrv = mr²ω). However, this property is scalar rather than vectorial, including a dimensionless phase angle (@ = mr²ωδφ). We have recently confirmed with atmospheric gases that their entropy is a logarithmic function of the relative vibrational, rotational, and translational action ratios with Planck’s quantum of action ħ. The Carnot principle shows that the maximum rate of work (puissance motrice) possible from the reversible cycle is controlled by the difference in temperature of the hot source and the cold sink: the colder the better. This temperature difference between the source and the sink also controls the isothermal variations of the Gibbs potential of the working fluid, which Carnot identified as reversible temperature-dependent but unequal caloric exchanges. Importantly, the engine’s inertia ensures that heat from work performed adiabatically in the expansion phase is all restored to the working fluid during the adiabatic recompression, less the net work performed. This allows both the energy and the thermodynamic potential to return to the same values at the beginning of each cycle, which is a point strongly emphasized by Carnot. Our action revision equates Carnot’s calorique, or the non-sensible heat later described by Clausius as ‘work-heat’, exclusively to negative Gibbs energy (−G) or quantum field energy. This action field complements the sensible energy or vis-viva heat as molecular kinetic motion, and its recognition should have significance for designing more efficient heat engines or better understanding of the heat engine powering the Earth’s climates. Full article

The seminal Navier–Stokes equations were stated even before the creation of the foundations of thermodynamics and its first and second laws. There is a widespread opinion in the literature on thermodynamic cycles that the Navier–Stokes equations cannot be taken as a thermodynamically correct model of a local “working fluid”, which would be able to describe the conversion of “heating” into “working” (Carnot’s type cycles) and vice versa (Afanasjeva’s type cycles). Also, it is overall doubtful that “cycle work is converted into cycle heat” or vice versa. The underlying reason for this situation is that the Navier–Stokes equations come from a time when thermodynamic concepts such as “internal energy” were still poorly understood. Therefore, this paper presents a new exposition of thermodynamically consistent Navier–Stokes equations. Following that line of reasoning—and following Gyftopoulos and Beretta’s exposition of thermodynamics—we introduce the basic concepts of thermodynamics such as “heating” and “working” fluxes. We also develop the Gyftopoulos and Beretta approach from 0D into 3D continuum thermodynamics. The central role within our approach is played by “internal energy” and “energy conversion by fluxes.” Therefore, the main problem of exposition relates to the internal energy treated here as a form of “energy storage.” Within that context, different forms of energy are discussed. In the end, the balance of energy is presented as a sum of internal, kinetic, potential, chemical, electrical, magnetic, and radiation energies in the system. These are compensated by total energy flux composed of working, heating, chemical, electrical, magnetic, and radiation fluxes at the system boundaries. Therefore, the law of energy conservation can be considered to be the most important and superior to any other law of nature. This article develops and presents in detail the neoclassical set of Navier–Stokes equations forming a thermodynamically consistent model. This is followed by a comparison with the definition of entropy (for equilibrium and non-equilibrium states) within the context of available energy as proposed in the Gyftopoulos and Beretta monograph. The article also discusses new possibilities emerging from this “continual” Gyftopoulos–Beretta exposition with special emphasis on those relating to extended irreversible thermodynamics or Van’s “universal second law”. Full article

Stirling engines have a high potential to produce renewable energy due to their ability to use a wide range of sustainable heat sources, such as concentrated solar thermal power and biomass, and also due to their high theoretical efficiencies. They have not yet achieved widespread use and commercial Stirling engines have had reduced efficiencies compared to their ideal values. In this work we show that a substantial amount of the reduction in efficiency is due to the operation of Stirling engines using sinusoidal motion and quantify this reduction. A discrete model was developed to perform an isothermal analysis of a 100cc alpha-type Stirling engine with a 90 ${}^{\circ }$ phase angle offset, to demonstrate the impact of sinusoidal motion on the net work and thermal efficiency in comparison to the ideal cycle. For the specific engine analyzed, the maximum thermal efficiency of the sinusoidal cycle was found to have a limit of 34.4%, which is a reduction of 27.1% from Carnot efficiency. The net work of the sinusoidal cycle was found to be 65.9% of the net work from the ideal cycle. The model was adapted to analyze beta and gamma-type Stirling configurations, and the analysis revealed similar reductions due to sinusoidal motion. Full article

The nature of thermal phenomena is still elusive and sometimes misconstrued. Starting from Lavoisier, who presumed that caloric as a weightless substance is conserved, to Sadi Carnot who erroneously assumed that work is extracted while caloric is conserved, to modern day researchers who argue that thermal energy is an indistinguishable part of internal energy, to the generalization of entropy and challengers of the Second Law of thermodynamics, the relevant thermal concepts are critically discussed here. Original reflections about the nature of thermo-mechanical energy transfer, classical and generalized entropy, exergy, and new entransy concept are reasoned and put in historical and contemporary contexts, with the objective of promoting further constructive debates and hopefully resolve some critical issues within the subtle thermal landscape. Full article

The difference between quantum isoenergetic process and quantum isothermal process comes from the violation of the law of equipartition of energy in the quantum regime. To reveal an important physical meaning of this fact, here we study a special type of quantum heat engine consisting of three processes: isoenergetic, isothermal and adiabatic processes. Therefore, this engine works between the energy and heat baths. Combining two engines of this kind, it is possible to realize the quantum Carnot engine. Furthermore, considering finite velocity of change of the potential shape, here an infinite square well with moving walls, the power output of the engine is discussed. It is found that the efficiency and power output are both closely dependent on the initial and final states of the quantum isothermal process. The performance of the engine cycle is shown to be optimized by control of the occupation probability of the ground state, which is determined by the temperature and the potential width. The relation between the efficiency and power output is also discussed. Full article

In this work, we present the generalization of some thermodynamic properties of the black body radiation (BBR) towards an n-dimensional Euclidean space. For this case, the Planck function and the Stefan–Boltzmann law have already been given by Landsberg and de Vos and some adjustments by Menon and Agrawal. However, since then, not much more has been done on this subject, and we believe there are some relevant aspects yet to explore. In addition to the results previously found, we calculate the thermodynamic potentials, the efficiency of the Carnot engine, the law for adiabatic processes and the heat capacity at constant volume. There is a region at which an interesting behavior of the thermodynamic potentials arises: maxima and minima appear for the n—dimensional BBR system at very high temperatures and low dimensionality, suggesting a possible application to cosmology. Finally, we propose that an optimality criterion in a thermodynamic framework could be related to the 3—dimensional nature of the universe. Full article