量纲分析在热力学统计物理中的教学应用

Application on Dimensional Analysis in the Teaching of Thermodynamics and Statistical Physics

热力学统计物理是一门综合性较强的课程,涉及力学、热学、电磁学、光学、量子力学等内容.它的教与学难度较大,特别是宏观物理量与微观物理量之间的关系复杂并难以理解.而量纲分析却能较好地解决这个问题.它基于物理量的量纲,很容易就能确定各个物理量之间的关系或者验证公式的正确性.通过3个问题的求解,即理想气体的碰壁数、光子气体的物态方程、零温时自由电子气体的简并压.文章介绍了量纲分析在热力学统计物理中的具体应用.可以看到,量纲分析有助于学生理解物理规律及其对应的数学表达式,也有助于学生分析问题和解决问题的能力培养.

Thermodynamics and statistical physics is a comprehensive course,involving mechanics,thermotics,electromagnetism,optics,quantum mechanics and so on.This course is difficult to teach and study.Especially the relationship between macro physical quantity and micro physical quantity is complex and difficult to understand.However,dimensional analysis can solve this problem.Based on the dimension of physical quantities,it is easy to find the relationship between various physical quantities or verify the correctness of the formula.This paper introduces the application of dimensional analysis in thermodynamics and statistical physics through the solution of three problems,namely,the wall collision number of ideal gas,the state equation of photon gas and the degenerate pressure of free electron gas at zero temperature.It can be seen that dimensional analysis helps students understand the laws of physics and their corresponding mathematical expressions,and also helps students cultivate their ability to analyze and solve problems.