本文利用Stirling公式的精确形式严格求解了N个气体分子在一长方形容器中左、右两半分布的热力学概率问题，定量验证了玻尔兹曼对热力学第二定律微观本质的统计解释. 结果显示占微观态总数95%的态分布在平衡态附近±N的区间，即，相对涨落与N呈1/N的标度关系. 本文讨论了常用的Stirling近似引发的困惑和谬误.

 In this work，the thermodynamic probability problem of N gas molecules distributed in the left and right halves of a rectangular container is rigorously solved using the exact form of Stirlings formula，which quantitatively verifies Boltzmanns statistical interpretation of the microscopic nature of the second law of thermodynamics. It is shown that 95% of the total microscopic states are distributed in the ±Ninterval near the equilibrium state，i.e.，the relative fluctuations are 1/Nwith respect to N. Confusion and errors caused by the common Stirling approximation are discussed.