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.
It is well established that at early times, long before the time of radiation-matter equality, the universe could have been well described by a spatially flat, radiation only model. In this letter we consider the whole primeval universe as a black body radiation (BBR) system in an n−dimensional Euclidean space. We propose that the (3 + 1) − d nature of the universe could be the result of a kind of thermodynamic selection principle stemming from the second law of thermodynamics. In regard the three spatial dimensions we suggest that they were chosen by means of the minimization of the Helmholtz free energy per hypervolume unit, while the time dimension, as it is well known was the result of the principle of increment of entropy for closed systems; that is, the so-called arrow of time.
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 parameter's 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.
A working fluid performs a Brayton cycle that is fed by a heat input from a solar power tower and from a combustion chamber, which burns natural gas. This hybrid system is described by a complete model that includes all the main losses and irreversibility sources (optical and thermodynamic). Numerical implementation and validation is performed based on a Spanish commercial plant. On-design computations are carried out varying the pressure ratio for four working fluids (dry air, nitrogen, carbon dioxide, and helium), for different number of stages and for recuperative and non-recuperative configurations. When adjusting the pressure ratio, an improvement of about 7 % in overall thermal efficiency is predicted for a dry air single-stage recuperative configuration with respect to a standard commercial gas turbine. A study about the main energy losses in each plant subsystem for some particular plant layouts is accomplished. A two-compression and expansion stages recuperative Brayton cycle working with air is expected to give overall thermal efficiencies about 0.29 at design conditions, which is about a 47% increase with respect to the simplest single-stage configuration. It is stressing that fuel consumption from the reheaters maybe higher than that of the main combustion chamber for multistage layouts. Off-design hourly curves of output records for the four seasons throughout a day are analyzed. Greenhouse emissions are also analyzed. Specific carbon dioxide emissions are smaller for helium than for dry air, when they both work in a single-stage non-recuperative configuration.
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