Statistic Characteristics of Quantum Gases in a Confined Space

Abstract

With the help of the Euler-MacLaurin formula, the statistic characteristics of quantum gases confined in a rectangular box are investigated by using a unified way. Three components of the pressure tensor and the internal energy of the system are analytically derived. The important relation between the pressure tensor and the internal energy is strictly proved. It is pointed out that these results are different from those obtained in literature and textbooks under the thermodynamic limit condition. Moreover, the pressure of the system is rationally introduced with the help of the property of the diagonal tensor, so that some thermodynamic functions of the system may be conveniently obtained. The statistic characteristics of quantum and classical gases confined in some different containers are discussed, the influence of the size effect of the containers on the properties of gases is analyzed and some new significant results are obtained.