Julian Gonzalez-Ayala

Connection between maximum-work and maximum-power thermal cycles.

A new connection between maximum-power Curzon-Ahlborn thermal cycles and maximum-work reversible cycles is proposed. This linkage is built through a mapping between the exponents of a class of heat transfer laws and the exponents of a family of heat capacities depending on temperature. This connection leads to the recovery of known results and to a wide and interesting set of results for a class of thermal cycles. Among other results it was found that it is possible to use analytically closed expressions for maximum-work efficiencies to calculate good approaches to maximum-power efficiencies. Behind the proposed connection is an interpretation of endoreversibility hypothesis. Additionally, we suggest that certain reversible maximum-work cycles depending on working substance can be used as reversible landmarks for FTT maximum-power cycles, which also depend on working substance properties.

From maximum power to a trade-off optimization of low-dissipation heat engines: Influence of control parameters and the role of entropy generation

For a low-dissipation heat engine model we present the role of the partial contact times and the total operational time as control parameters to switch from maximum power state to maximum Ω trade-off state. The symmetry of the dissipation coefficients may be used in the design of the heat engine to offer, in such switching, a suitable compromise between efficiency gain, power losses, and entropy change. Bounds for entropy production, efficiency, and power output are presented for transitions between both regimes. In the maximum power and maximum Ω trade-off cases the relevant space of parameters are analyzed together with the configuration of minimum entropy production. A detailed analysis of the parameters space shows physically prohibited regions in which there is no longer a heat engine and another region that is physically well behaved but is not suitable for possible optimization criteria.

Carnot-Like Heat Engines Versus Low-Dissipation Models

In this paper, a comparison between two well-known finite time heat engine models is presented: the Carnot-like heat engine based on specific heat transfer laws between the cyclic system and the external heat baths and the Low-Dissipation model where irreversibilities are taken into account by explicit entropy generation laws. We analyze the mathematical relation between the natural variables of both models and from this the resulting thermodynamic implications. Among them, particular emphasis has been placed on the physical consistency between the heat leak and time evolution on the one side, and between parabolic and loop-like behaviors of the parametric power-efficiency plots. A detailed analysis for different heat transfer laws in the Carnot-like model in terms of the maximum power efficiencies given by the Low-Dissipation model is also presented.

On reversible, endoreversible, and irreversible heat device cycles versus the Carnot cycle: a pedagogical approach to account for losses

In this work we analyze the deviations of reversible cycles (for both heat engines and refrigerators) from the corresponding Carnot cycle operating between the same extreme temperatures, and deviations of irreversible cycles from their corresponding reversible realization while putting emphasis on the corresponding losses. The endoreversible models fit in the proposed framework. Two suitable loss factors, which do not need the explicit calculation of entropy variations, are introduced. The behavior of these factors and their interplay allow for a clear and pedagogical visualization of where external and internal irreversibilities are located, and their intensities in terms of the main variables describing the cycle. The analysis could be used as a starting point for more advanced studies on modeling and optimization of real devices and installations.

Local-stability analysis of a low-dissipation heat engine working at maximum power output

In this paper we address the stability of a low-dissipation (LD) heat engine (HE) under maximum power conditions. The LD system dynamics are analyzed in terms of the contact times between the engine and the external heat reservoirs, which determine the amount of heat exchanged by the system. We study two different scenarios that secure the existence of a single stable steady state. In these scenarios, contact times dynamics are governed by restitutive forces that are linear functions of either the heat amounts exchanged per cycle, or the corresponding heat fluxes. In the first case, according to our results, preferably locating the system irreversibility sources at the hot-reservoir coupling improves the system stability and increases its efficiency. On the other hand, reducing the thermal gradient increases the system efficiency but deteriorates its stability properties, because the restitutive forces are smaller. Additionally, it is possible to compare the relaxation times with the total cycle time and obtain some constraints upon the system dynamics. In the second case, where the restitutive forces are assumed to be linear functions of the heat fluxes, we find that although the partial contact time presents a locally stable stationary value, the total cycle time does not; instead, there exists an infinite collection of steady values located in the neighborhood of the fixed point, along a one-dimensional manifold. Finally, the role of dissipation asymmetries on the efficiency, the stability, and the ratio of the total cycle time to the relaxation time is emphasized.

Is the (3 + 1)-d nature of the universe a thermodynamic necessity?

It is well established that at early times, long before the time of radiation-matter density equality, the universe could have been well described by a spatially flat, radiation only model. In this article we consider the whole primeval universe, as a first approach, as a black-body radiation system in an n-dimensional Euclidean space. We propose that the (3 + 1)-dimensional nature of the universe could be the result of a thermodynamic selection principle stemming from the second law of thermodynamics. In regard to the three spatial dimensions we suggest that they were chosen by means of the minimization of the Helmholtz free energy per hypervolume unit following possibly a kind of broken symmetry process, while the time dimension, as is well known, is related with the principle of increment of entropy for closed systems: the so-called arrow of time.

A Possible Cosmological Application of Some Thermodynamic Properties of the Black Body Radiation in n-Dimensional Euclidean Spaces

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.