T he properties of ideal Fermi gas are studied under the finite gravitational field of generalized uncertainty principle . The internal energy and the constant volume heat capacity in which the analytical expressions under the condition of low temperature are given . Meanwhile , the specific simulation calculation of copper electron gas is given as an example . T he effects of the generalized uncertainty principle on the properties of the systems are discussed .%采用半经典（T homas-Fermi）近似方法，研究了有限重力场中广义测不准原理下理想费米气体的性质。得到了内能和定容热容在低温情况下的解析表达式，同时以铜电子气为例进行了具体模拟计算，并与不考虑广义测不准原理时的结果进行了比较分析，讨论了了广义测不准原理对体系性质的影响。
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