用类比法推导分子平均自由程公式的关键问题

CRITICAL ISSUE FOR DERIVING MOLECULAR MEAN FREE PATH FORMULA BY ANALOGY METHOD

为了指出部分学生在用类比法推导分子平均自由程公式时出现的错误并给出正确的推导,采用弹性刚球模型讨论分子之间的相互碰撞过程。用类比法推导分子的平均自由程公式,要解决的关键问题是推导分子的平均相对速率服从麦克斯韦速率分布律。平均相对速率是平均相对速度的大小,因此先由麦克斯韦速度分布律导出处在平衡态的混合理想气体分子相对速度的分布函数,并得出相对速度瓫r也服从麦克斯韦速度分布律,再取特殊情况即得出同种分子碰撞的相对速度分布函数。然后根据麦克斯韦速度分布函数和速率分布函数的关系,导出平均相对速率服从麦克斯韦速率分布律。

To point out the error that in students＇ deriving molecular mean free path formula by analogy method and give the correct deduction, we discuss molecular collision process using elastic hard sphere model . To derive molecular mean free path formula by analogy method, the critical issue is to derive the average relative speed between two molecules is given on the basis of Maxwell speed distribution law. Firstly, we obtain that relative velocity of mixed ideal gas molecule follows Maxwell velocity distribution law. Then we derive that the average relative speed obeys the Maxwell speed distribution law based upon the relationship between Maxwell velocity distribution function and Maxwell speed distribution function.