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

Optimal performance analysis of irreversible cycles used as heat pumps and refrigerators

A general irreversible cycle model is used to investigate the optimal performance of a class of heat-driven pumps affected by the three main irreversibilities, which are finite-rate heat transfer between the working fluid and the external heat reservoirs, internal dissipation due to the working fluid and heat leakage between heat reservoirs. The coefficient of performance of the cycle system is taken as an objective function for optimization. Some equivalent parameters are introduced so that the relevant calculation is simplified. The coefficient of performance versus dimensionless heating load curves describing the general performance characteristics of heat-driven heat pumps are plotted. The optimal temperatures of the working fluid at the maximum coefficient of performance are determined. Moreover, it is expounded that the irreversible cycle model is very useful. The optimal performance not only of a class of irreversible heat-driven refrigerators but also of an irreversible Carnot heat pump and refrigerator may be directly analysed by using the cycle model. The results obtained may provide some new theoretical bases for the optimal design and operation of two classes of real heat pump and refrigerator systems driven by ‘low-grade’ heat energy and ‘high-grade’ work.The present research was supported by the Natural Science Foundation of Fujian, People’s Republic of China

Performance analysis of an irreversible quantum heat engine working with harmonic oscillators

The cycle model of a regenerative quantum heat engine working with many noninteracting harmonic oscillators is established. The cycle consists of two isothermal and two constant-frequency processes. The performance of the cycle is investigated, based on the quantum master equation and semigroup approach. The inherent regenerative losses in the two constant-frequency processes are calculated. The expressions of several important performance parameters such as the efficiency, power output, and rate of the entropy production are derived for several interesting cases. Especially, the optimal performance of the cycle in high-temperature limit is discussed in detail. The maximum power output and the corresponding parameters are calculated. The optimal region of the efficiency and the optimal ranges of the temperatures of the working substance in the two isothermal processes are determined

关于非理想气体卡诺循环的一点讨论

《物理通报》1992年4期发表了《非理想气体卡诺循环》一文-([1]),对理想气体卡诺循环效率η=1-((T_2)/(T_1))(1)的证明提出如下两个问题:“1.由于理想气体绝热方程PV-γ=常量是假定γ=(C_P)/(C_V)为一与温度无关的常数而得到的一近似方程,故容易使人怀疑由绝热方程所得到的证明结果也同样具有近似性

The general performance characteristics of an irreversible absorption heat pump operating between four temperature levels

An irreversible cycle model of an absorption heat pump operating between four temperature levels is set up and used to analyse the performance of the heat pump affected by the irreversibility of finite-rate heat transfer and the internal irreversibilities of the working material. The coefficient of performance of the heat pump is optimized for a given specific heating load. A fundamental optimum relation is derived, from which the characteristic curves of the dimensionless specific heating load versus the coefficient of performance are generated. The influence of the internal irreversibilities on the performance of the system is discussed. The optimal distribution of the heat-transfer areas of the heat exchangers is determined. Some special cases are analysed. The results obtained can describe the optimal performance of a four-temperature-level absorption heat pump affected simultaneously by the internal and external irreversibilities and can provide the theoretical bases for the optimal design and operation of real absorption heat pumps operating between four temperature levels

THE MAXIMUM POWER OUTPUT AND MAXIMUM EFFICIENCY OF AN IRREVERSIBLE CARNOT HEAT ENGINE

The effect of thermal resistance, heat leakage and internal irreversibility resulting from the working fluid on the performance of a Carnot heat engine is investigated using a new cyclic model. The power output and efficiency of the heat engine are adopted as objective functions for heat engine optimization. The optimal performance of the heat engine is analysed systematically. Some significant results are obtained. For example, the maximum power output and maximum efficiency are determined. The efficiency of the heat engine at maximum power output and the power output of the heat engine at maximum efficiency are also calculated. Curves of the power output varying with the efficiency of the heat engine are obtained. These curves can indicate clearly the rational regions of efficiency and power output for an irreversible Carnot heat engine. It is pointed out that all the conclusions concerning a reversible Carnot heat engine, an endoreversible Carnot heat engine only affected by thermal resistance and an irreversible Carnot heat engine with internal irreversibility and/or heat leakage can be deduced from the results in this paper

A universal model of an irreversible combined Carnot cycle system and its general performance characteristics

A universal model of ann-stage combined Carnot cycle system is established. Several major irreversibilities which often exist in real thermodynamic cycles, such as finite-rate heat transfer in the heat-exchange processes, heat leak losses of the heat source, and internal dissipation of the working fluid, are included in the model so that many models of irreversible and endoreversible Carnot cycles which appear in the literature can be regarded as special cases of the universal cycle model. The efficiency, power output and rate of heat input are optimized. Some characteristic curves of the cycle system are presented. Some important performance bounds are given. The optimal combined conditions between two adjacent cycles in the combined cycle system are determined. The optimal performance of an arbitrary-stage irreversible, endoreversible, and reversible combined Carnot cycle system can be directly derived for specific choices of some parameters. The results obtained here are of general significance for both physics and engineering

The optimum performance characteristics of a four-temperature-level irreversible absorption refrigerator at maximum specific cooling load

An irreversible cycle model of an absorption refrigerator operating between four temperature levels is established and used to analyse the performance of the refrigerator affected by the irreversibility of finite-rate heat transfer and the internal irreversibilities of the working substance. The specific cooling load of the refrigerator is taken as an objective function for optimization. The maximum specific cooling load is determined. Other main parameters of the refrigerator at maximum specific cooling load are calculated. The optimal distribution relation of the heat-transfer areas of the heat exchangers is derived. Several special cases are discussed in detail so that some important conclusions relative to absorption refrigerators in the literature may be derived directly from the present paper. Moreover, the influence of the internal irreversibilities on the performance of the system is analysed. The results obtained here can describe the optimal performance of a four-temperature-level absorption refrigerator affected simultaneously by the internal and external irreversibilities and provide the theoretical bases for the optimal design and operation of real absorption refrigerators operating between four temperature levels

The efficiency of an irreversible combined cycle at maximum specific power output

An irreversible combined cycle is used to analyse the performance of a two-stage combined heat engine system. The specific power output of the system is adopted as an objective function for optimization. The maximum specific power output and the corresponding efficiency are derived. The optimally combined conditions of two irreversible cycles are determined. Several special cases are discussed. The results obtained are compared with those of a single-stage irreversible heat engine. Moreover, it is expounded that the performance of a two-stage irreversible combined cycle may be described by an equivalent simplified cycle system and the optimal performance of an n-stage irreversible combined heat engine system is given. The aim of this research is to provide some new significant conclusions and redress some errors existing in a related investigation

NEW PERFORMANCE BOUNDS OF A CLASS OF IRREVERSIBLE REFRIGERATORS

A general description is developed for a class of irreversible refrigerators operating between two heat reservoirs. This description is applied to refrigerators having thermal resistances between the working fluid of refrigerators and the heat reservoirs, heat leaks between the heat reservoirs, and internal dissipations of the working fluid in order to obtain the maximum performance coefficient and the performance coefficient versus cooling rate characteristics of such refrigerators. This description is also applied to optimizing the key performance parameters of such refrigerators. Some new performance bounds of of refrigerators are determined