Paillusson Fabien
School of Mathematics and Physics, University of Lincoln, Lincoln LN6 7TS, UK.
Entropy (Basel). 2019 Jun 16;21(6):599. doi: 10.3390/e21060599.
Most undergraduate students who have followed a thermodynamics course would have been asked to evaluate the volume occupied by one mole of air under standard conditions of pressure and temperature. However, what is this task exactly referring to? If air is to be regarded as a mixture, under what circumstances can this mixture be considered as comprising only one component called "air" in classical statistical mechanics? Furthermore, following the paradigmatic Gibbs' mixing thought experiment, if one mixes air from a container with air from another container, all other things being equal, should there be a change in entropy? The present paper addresses these questions by developing a prior-based statistical mechanics framework to characterise binary mixtures' composition realisations and their effect on thermodynamic free energies and entropies. It is found that (a) there exist circumstances for which an ideal binary mixture is thermodynamically equivalent to a single component ideal gas and (b) even when mixing two substances identical in their underlying composition, entropy increase does occur for finite size systems. The nature of the contributions to this increase is then discussed.
大多数修读过热力学课程的本科生都曾被要求计算在标准压力和温度条件下一摩尔空气所占的体积。然而，这项任务究竟指的是什么呢？如果将空气视为一种混合物，在经典统计力学中，在何种情况下这种混合物可以被视为仅由一种称为“空气”的组分组成呢？此外，遵循典型的吉布斯混合思想实验，如果将一个容器中的空气与另一个容器中的空气混合，在其他条件相同的情况下，熵会发生变化吗？本文通过建立一个基于先验的统计力学框架来描述二元混合物的组成实现及其对热力学自由能和熵的影响，从而解决这些问题。研究发现：（a）存在某些情况，在此情况下理想二元混合物在热力学上等同于单一组分理想气体；（b）即使混合两种在基本组成上相同的物质，对于有限尺寸的系统，熵也确实会增加。然后讨论了这种增加的贡献的性质。
