麦克斯韦分布与概率论中典型分布的比较教学

对比研究了大学物理中的麦克斯韦分布和概率论中典型分布的区别和联系,指出了无量纲的麦克斯韦速度分布是三维空间的正态分布,麦克斯韦速率分布是一种χ分布,阐明了理想气体的统计物理量与概率论中统计数字特征之间的关系。麦克斯韦分布和对应概率论知识的比较教学,既能让教师讲解麦克斯韦分布更清楚透彻,又能让学生融会贯通并牢固掌握相关大学物理和数学知识。

We study the differences and relation between the Maχwell distribution in the college physics and the typical distributions in probability theory.It is found that the dimensionless Maχwell velocity distribution is just a normal distribution in the three dimensional space,while the Maχwell speed distribution is actually a kind ofχdistribution.We also demonstrate the relationship between the statistical quantities of the ideal gap and the numerical characteristics in probability theory.We argue that the comparison of MaXwell distributions and the corresponding probability theory could help teachers eXplain the Maχwell distribution more clearly,so that the students could have a deep understanding on the relevant knowledge in college physics and mathematics.