Zijun Yan

The effect of heat‐transfer law on performance of a two‐heat‐source endoreversible cycle

In this paper it is shown that the optimal two‐heat‐source endoreversible cycle is the endoreversible Carnot cycle for a class of heat‐transfer laws. The relation between optimal efficiency and power output of the cycle is derived. By use of this relation, we discuss the optimal performance of an endoreversible Carnot cycle for three common heat‐transfer laws, and reveal the dependence of performance on the heat‐transfer law and the heat‐transfer coefficient. A number of new universal results are derived, and some major conclusions derived in several references are also deduced.

Equivalent combined systems of three-heat-source heat pumps

In this paper, the equivalent combined systems of three‐heat‐source heat pumps are studied. It is pointed out that there may be three combined ways for us to conceive a reversible three‐heat‐source heat pump as a combined system having a reversible Carnot heat pump driven by a reversible Carnot engine. Whereas for an endoreversible three‐heat‐source heat pump affected by the heat resistances, there is only one combined way for us to conceive it as a combined system having an endoreversible Carnot heat pump driven by an endoreversible Carnot engine. Then, the fundamental optimum formula of a three‐heat‐source heat pump is derived simply and directly by using those of two‐heat‐source cycles. The optimal peformance of an endoreversible three‐heat‐source heat pump is thus discussed. The inherent relation between the two‐ and the three‐heat‐source cycles as well as the fundamental distinction between the reversible and the endoreversible three‐heat‐source cycles is also revealed. These results may enrich the theory of finite time thermodynamics, and provide some new theoretical bases for the exploitation and application of three‐heat‐source apparatus such as chemical heat pumps, absorption heat pumps, and so on.

Efficiency bound of a solar-driven Stirling heat engine system

A solar-driven Stirling engine is modelled as a combined system which consists of a solar collector and a Stirling engine. The performance of the system is investigated, based on the linearized heat loss model of the solar collector and the irreverisible cycle model of the Stirling engine affected by finite-rate heat transfer and regenerative losses. The maximum efficiency of the system and the optimal operating temperature of the solar collector are determined. Moreover, it is pointed out that the investigation method in the present paper is valid for other heat loss models of the solar collector as well, and the results obtained are also valid for a solar-driven Ericsson engine system using an ideal gas as its engine work substance.

Optimal performance of a generalized Carnot cycle for another linear heat transfer law

The optimal performance of an engine operating between a finite high‐temperature source and an infinite low‐temperature reservoir is studied. It is assumed that there exists only the irreversibility of heat conduction in the cycle and heat transfer obeys another linear law [i.e., the heat‐flux q∝Δ(1/T)] instead of Newton’s law. It is shown that the optimal configuration of the cycle is composed of two adiabatic processes and two isoheat‐flux processes in which the difference of the reciprocal temperature of the working fluid and reservoirs must be maintained constant. Moreover, the relation between the optimal power output and the efficiency of such a cycle is derived, and some new results are deduced from it. The results are compared with the optimal performance of a generalized Carnot cycle for Newton’s heat transfer law. Consequently, the common character and the main difference of a generalized Carnot cycle for the two different heat transfer laws are expounded.

Density of states and thermodynamic properties of an ideal system trapped in any dimension

The density of states and thermodynamic properties of an ideal gas system trapped in a generic power-law potential in an n-dimensional space are studied. A unified description for the Bose, Fermi and classical gases is given by using the grand potential of the system. Consequently, not only the results in current textbooks of statistical mechanics but also some new general important conclusions, such as the conditions for the occurence of Bose-Eisntein condensation in a trapped Bose system in any dimensional space, can be derived directly using the results of this paper.

FLUCTUATIONS OF THERMODYNAMIC QUANTITIES CALCULATED FROM THE FUNDAMENTAL EQUATION OF THERMODYNAMICS

On the basis of the probability distribution of the various values of the fluctuation and the fundamental equation of thermodynamics of any given system, a simple and useful method of calculating the fluctuations is presented. By using the method, the fluctuations of thermodynamic quantities can be directly determined from the fundamental equation of thermodynamics. Finally, some examples are given to illustrate the use of the method.

AN EQUIVALENT THEOREM OF THE NERNST THEOREM

It is proved that on the basis of the second law of thermodynamics, the Nernst theorem and the conclusion that the heat capacities tend to zero as the temperature approaches absolute zero can be derived from each other. In the process of the proof, it is not necessary to appeal to the unattainability of absolute zero. Therefore, the conclusion that the heat capacities tend to zero as the temperature approaches absolute zero is an equivalent theorem of the Nernst theorem.