论范德瓦尔斯a和b参数与温度的关系

范德瓦尔斯方程中a、b参数是否与温度相关,不但不同文献中的说法互不相同,而且有同一文献前后的结论相互矛盾.本文分析了这个令人迷惑的问题.在热力学中a和b参量被处理为与温度无关,它仅仅在临界点附近有效并可以把范德瓦尔斯方程表述为对应态定律;在更加广泛的温度区间a、b参量和温度有关,但是范德瓦尔斯方程却丧失了其独特性.统计物理文献把a和b参量处理成为位力展开的一种拟合方程,发现一般情况下两个参数都依赖于温度,仅仅在特殊情况下和温度无关,以说明对应态定律成立的条件.热力学和统计物理关于a和b参量是否依赖于温度相互矛盾的表述,源于这两个理论中范德瓦尔斯状态方程适用范围不同.

On temperature dependence of the van der Waals a and b parameter

On the problem whether the van der Waals parameters a and b depend on temperature, different literature gives different answer, and even the same literature in different pages gives contrary answer. In thermodynamics, they are approximately treated as constants due to matching the thermodynamic coordinates of the critical point and van der Waals equation of state can be expressed as the corresponding state law. Once the parameters a and b depend on the temperature, the corresponding state law does not hold true, and other peculiarities of the van der Waals equation of state is lost accordingly. In statistical mechanics, we usually obtain a Virial expansion of the equation of state;once the van der Waals equation is used to interpolate to this expansion, they are temperature-dependent except some special cases. Therefore, the different statements on temperature dependence of the van der Waals a and b parameter in thermodynamics and statistical mechanics are in fact originates from implicit assumption of the same application domain of the van der Waals equation of state in two different disciplines.