有限重力空间中理想费米气体热力学性质的研究

Study of Thermodynamic Properties of an Ideal Fermi Gas in Finite Gravitational Field

用半经典(托马斯-费米)近似法,研究了有限重力场中理想费米气体的热力学性质,导出了总能、费米能、化学势和热容量的一般解析表达式,并且给出了化学势、热容量在高温和低温近似下的解析表达式,然后以电子气为例进行了具体计算。把这些结果和自由费米气体以及无限重力空间费米气体相应的热力学量进行了比较,探讨了有限重力势场对体系性质的影响。

The properties of an ideal Fermi gas in finite gravitational field are studied, based on the semiclassical （Thomas - Fermi） approximation. The general analytical expressions of the total energy, Fermi energy, chemical potential and heat capacity are derived. Moreover, the analytical expressions of the chemical potential and heat capacity in the high - and low - temperature approximations are given, and then, the example of electron gas is used to calculate exactly. All these results are compared with those of free Fermi gas and Fermi gas in infinite gravitational field. The effects of finite gravitational field on properties of Fermi gas are discussed.