On the equivalence of the Nernst theorem and its consequence

One general consequence of the Nernst theorem is derived, i.e., the various heat capacities of a thermodynamic system under different constraints approach zero as the temperature approaches absolute zero. The temperature dependence of the heat capacity of any thermodynamic system at ultra-low temperatures is revealed through this consequence. Moreover, the general form and the simplest expression of the heat capacities of thermodynamic systems at ultra-low temperatures are deduced. Some significant discussion and results are given. One new research method is provided by using this consequence. Finally, the equivalence between the Nernst theorem and its consequence is rigorously proved, so that this consequence may be referred to another description of the third law of thermodynamics

Casimir effect of an ideal Bose gas trapped in a generic power-law potential

The Casimir effect of an ideal Bose gas trapped in a generic power-law potential and confined between two slabs with Dirichlet, Neumann, and periodic boundary conditions is investigated systematically, based on the grand potential of the ideal Bose gas, the Casimir potential and force are calculated. The scaling function is obtained and discussed. The special cases of free and harmonic potentials are also discussed. It is found that when T<Tc (where Tc is the critical temperature of Bose-Einstein condensation), the Casimir force is a power-law decay function; when T>Tc, the Casimir force is an exponential decay function; and when T>>Tc, the Casimir force vanishes.Comment: 5 pages, 1 figur

Solar-driven sodium thermal electrochemical converter coupled to a Brayton heat engine: Parametric optimization

[EN]A novel high-efficiency device comprised of three subsystems, a solar collector, a sodium thermal electrochemical converter, and a non-recuperative Brayton heat engine, is modeled by taking into account the main internal and external irreversibility sources. The model extends previous works in which the heat waste of the electrochemical converter is used as heat input in a Brayton gas turbine to study its performance and feasibility when a solar energy input is added. The operative working temperatures of three subsystems are determined by energy balance equations. The dependence of the efficiency and power output of the overall system on the solar concentration ratio, the current density, the thickness of the electrolyte, and the adiabatic pressure ratio (or temperature ratio) of the Brayton cycle is discussed in detail. The maximum efficiencies and power output densities are calculated and the states of the maximum efficiency-power density are determined under different given solar concentration ratios. The parametric optimum selection criteria of a number of critical parameters of the overall system are provided and the matching problems of the three subsystems are properly addressed. It is found that under a solar concentration around 1350, the maximum efficiency and power output density of the proposed hybrid system can reach, respectively, 29.6% and 1:23 105 W/m2. These values amount approximately 32.7% and 156% compared to those of the solar-driven sodium thermal electrochemical converter system without the bottoming Brayton cycle. The Pareto front obtained from numerical multiobjective and multi-parametric methods endorses previous findings.China Scholarship Council under the State Scholarship Fund (No. 201806310020), People’s Republic of China

Influence of heat- and mass-transfer coupling on the optimal performance of a non-isothermal chemical engine

The cyclic model of a non isothermal chemical engine operated between two reservoirs with different temperatures and chemical potentials is established in which the irreversibilities resulting from the heat and mass transfer between the working fluid and the reservoirs are taken into account Expressions for the power output and efficiency of the engine are analytically derived and used to analyze the performance characteristics of the engine at the maximum power output The general characteristics of the efficiency of the engine are searched in detail The optimal criteria for some important parameters such as the power output and efficiency are obtained and the reasonably operating region of the engine is determined Some interesting cases are specially discussed The results obtained here can reveal the performance characteristics of a non isothermal chemical engine affected by the irreversibilities of heat and mass transfer couplingNational Natural Science Foundation, People's Republic of China [10875100

Self-similar motion for modeling anomalous diffusion and nonextensive statistical distributions

We introduce a new universality class of one-dimensional iteration model giving rise to self-similar motion, in which the Feigenbaum constants are generalized as self-similar rates and can be predetermined. The curves of the mean-square displacement versus time generated here show that the motion is a kind of anomalous diffusion with the diffusion coefficient depending on the self-similar rates. In addition, it is found that the distribution of displacement agrees to a reliable precision with the q-Gaussian type distribution in some cases and bimodal distribution in some other cases. The results obtained show that the self-similar motion may be used to describe the anomalous diffusion and nonextensive statistical distributions.Comment: 15pages, 5figure

Local axisymmetry-breaking–induced transition of trapped-particle orbit and loss channels in quasi-axisymmetric stellarators

The transition of trapped-particle orbit topologies has been investigated in quasi-axisymmetric (QA) configurations, such as the Chinese First Quasi-axisymmetric Stellarator (CFQS). It is found that the axisymmetry-breaking phenomenon in QA configurations is of great significance at some specific locations, which could easily induce blocked particles to transit into localized particles. A novel aspect is presented to interpret the transition mechanism of trapped-particle orbit topologies in this paper, i.e., as the amplitudes of non-axisymmetric field increase along the radius direction, the region of large toroidal inhomogeneity is gradually generated, which makes the length of the trapped-particle trajectory substantially short, and hence, may restrict particles to a single helical field period. Meanwhile, at such locations the "pseudo-axisymmetric" field results in coupling of the maximum radial drift and the minimum poloidal drift, which enables the transition of trapped-particle orbit topologies considerably and forms specific loss channels, degrading plasma confinement. These results may shed light on the optimization of QA configurations via avoidance of such coupling with respect to energetic particle confinement. Moreover, this work is also relevant to the generation of inhomogeneity of particle flux deposition on the devertor plates

Performance optimum analysis and load matching of an energy selective electron heat engine

A new model of the energy selective electron (ESE) heat engine with a variable bias voltage resulting from a variable load resistance is established. Analytical expressions for the power output and efficiency of the system are derived, based on the Fermi-Dirac distribution of electrons. The general performance characteristics of the system are revealed. The effects of the energy level of the central position of the filter, chemical potential, and load resistance on the performance of the system are discussed in detail. It is found that as long as the position of the filter is suitably designed, the maximum electric current may be obtained at zero load. The optimal values of two important parameters. the energy level of the central position of the filter and chemical potential or load resistance, are calculated for differently operating states, and consequently, two important criteria on the parametric optimum design are obtained. These results obtained here may provide some guidance for the optimum design of ESE heat engines. (C) 2012 Elsevier Ltd. All rights reserved.National Natural Science Foundation [11175148]; Xiamen Natural Science Foundation, People's Republic of China [3502z20110004