用量子统计方法对双原子分子气体振动热容量的研究

Study on Vibration Heat Capacity of Diatomic Molecular Gas by Quantum Statistical Method

基于对长期一直采用包含无限多振动能级的简谐振子模型(SHO)对双原子分子气体振动热容量处理情况和解析结果的分析,指出了这类方法存在的缺陷.认为具有若干高阶修正的非简谐振动能级完全集才是双原子分子振动的实际描述,导致不是无限项求和也不能将求和转换为积分,而必须从基本的统计原理和有限项统计分析出发获得热力学量的数值解.以HCl气体为例进行了分析计算,得到的结果表明,现在的方法更合理逻辑更严密,结果比无限多简谐振动能级导致的结果明显更好符合实验数据.

Based on the analysis of the treatment of the vibration heat capacity of diatomic molecular gas and the analytical results of the simple harmonic oscillator model(SHO)which has been used for a long time and contains infinitely many vibration energy levels,the defects of this method are pointed out.It is considered that the complete set of non-harmonic vibration levels with some higher order corrections is the actual description of diatomic molecular vibration levels,which leads to that the numerical solution of thermodynamic quantities must be obtained from the basic statistical principles and finite statistical analysis,instead of the infinite summation and the conversion of summation into integral.Taking the HCl gas as an example,the analysis results show that the current method is more reasonable and more rigorous,compared with the experimental data,and the AM data are obviously better than the SHO results.