论范德瓦尔斯a 和b 参数与温度的关系
收稿日期: 2020-05-28
修回日期: 2020-08-03
网络出版日期: 2021-01-11
基金资助
国家自然科学基金( 11675051) 资助
On temperature dependence of the van der Waals a and b parameter
Received date: 2020-05-28
Revised date: 2020-08-03
Online published: 2021-01-11
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.
张子奕, 李心宇, 王鑫, 刘全慧 . 论范德瓦尔斯a 和b 参数与温度的关系[J]. 大学物理, 2021 , 40(01) : 66 -69 . DOI: 10.16854 /j.cnki.1000-0712.200208
gives different answer，and even the same literature in different pages gives contrary answer. In thermody
namics，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 temperaturedependent
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.
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