固体热容的统计探讨

Exploration of Heat Capacity of Solid by Statistical Methods

根据热力学统计物理理论,主要讨论在低温下,固体的热容随温度的变化规律。一种统计方法是:将固体原子系统看作近独立粒子系统,统计运算固体热容随温度的变化,称为爱因斯坦理论;另一种方法则是:应用系综统计理论,统计运算固体热容随温度的变化情况,称为德拜理论。对两理论的结果进行比较,德拜理论在定量上与实验符合的更好些,而爱因斯坦理论与实验,只是定性上相符合。可以看出,在处理有相互作用的复杂系统时,系综统计理论的方法更占优势,最终统计的结果也更与实验相符。

In this paper, we analyze the dependence of heat capacity of solid on low temperature based on the theory of thermodynamics and statistical mechanics. There are mainly two statistic methods; one is that the heat capacity of solid is statistically calculated when the solid atomic system is in the quasi - independent particle system, this kind of methods is known as Einstein theory. The other is that the heat capacity of solid is statistically calculated based on the ensemble statistics theory, and is known as Debye theory. We compared the results derived from the two theories mentioned above and fred the results from Debye theory are in quantitative agreement with the experimental resuits. But the results from Einstein theory are just in qualitative agreement with the experimental results. So, we can conclude here that in dealing with the complex system, ensemble statistical theory is a better choice and the final statistical results are more in line with the experimental results.