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对E=sum from i=1 to N(p_i~2/2m)的理想气体系统态密度的计算是通过对多维球体积的计算实现的,但是对于E=C sum from i=1 to N(P_i)的理想气体系统,此种方法已无能为力了,特别是对于一般情况更无从入手,Pathria又通过这Laplace交换,由配分函数求态密度,但必须先求出配分函数,所以不能给出E=C sum from i=1 to N(P_i~l)一类系统的普遍公式.本文对该类系统的态密度计算给出了普遍适用的方法,并得到一般公式.由此给出该类系统在l为任意值时能量与T的关系,以及物态方程与l大小无关的结论.在l=1,2等特殊情况下所得结果与已有结论完全一致.因此,该一般公式对此类系统热力学量的计算和统计性质的研究无疑是一发展.
The calculation of the ideal gas system state density for E = sum from i = 1 to N (p_i ~ 2 / 2m) is achieved by calculating the multidimensional sphere volume but for E = C sum from i = 1 to N (P_i ), This method has been powerless, especially for the general situation even more difficult to start, Pathria and the Laplace exchange by the partition function to find the density, but must first find the partition function, it can not be given E = C universal from i = 1 to N (P_i ~ l). In this paper, we give a general applicable method for calculating the density of states in this kind of system and get the general formula. The relation between the energy and T and the equation of state have nothing to do with the size of L. The results obtained in the special case of l = 1, 2 and so on are completely consistent with the previous conclusions, therefore, the general formula for such systems The calculation of thermodynamic quantities and the study of statistical properties are undoubtedly a development.