重力场中稀薄气体的密度分布:对玻尔兹曼分布律公式的商榷和改进

The Distribution of the Thin Gas in Gravitational Field: The Modification to the Formula of Boltzmann Distribution

重力场中的理想气体密度随高度减小,其分布规律服从玻尔兹曼分布律公式.按照玻尔兹曼分布律公式,无论高度如何,理想气体密度不会降低为零,即重力场中理想气体没有上边界。然而,有明显的证据可以证明这一结论是不正确的。文章认为:玻尔兹曼分布律公式是不精确的,其误差起源于重力场中容器顶部稀薄理想气体的不连续性,即不能将稀薄气体再看作连续介质。文章讨论了这一误差的产生原因并提出了对玻尔兹曼分布律进行改进的初步修正公式。

In gravitational fieldt,he density of the idea gas contained in a rigidity recipient decreases with height according Boltzmann distribution.The density of the gas never minish to zero no matter how much the height.It is to say that,in gravitational field the idea gas has no up interface.However,There are some prominent evidence against this conclusion,and the author argue that the Boltzmann distribution is not a precision one.The error due to the discontinuity of the gas rareness in the upside of the recipient.In this paper,author analysed the mistake in the expression of the Boltzmann distribution and an abecedarian reformative formula is proposed to modify Boltzmann distribution.