On the Logic of a Prior Based Statistical Mechanics of Polydisperse Systems: The Case of Binary Mixtures

Paillusson, Fabien (2019) On the Logic of a Prior Based Statistical Mechanics of Polydisperse Systems: The Case of Binary Mixtures. Entropy, 21 (6). p. 599. ISSN 1099-4300

Full content URL: https://doi.org/10.3390/e21060599

DocumentsOthers
On the Logic of a Prior Based Statistical Mechanics of Polydisperse Systems: The Case of Binary Mixtures
Published PDF
[img]
[Download]
[img] HTML
htm - Whole Document
Restricted to Repository staff only
Available under License Creative Commons Attribution 4.0 International.

250kB
[img] PDF
Entropy2019.pdf - Whole Document
Available under License Creative Commons Attribution 4.0 International.

548kB
Item Type:Article
Item Status:Live Archive

Abstract

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.

Keywords:Entropy, Mixtures, Binomial distribution, Mixing
Subjects:F Physical Sciences > F340 Mathematical & Theoretical Physics
G Mathematical and Computer Sciences > G320 Probability
F Physical Sciences > F300 Physics
Divisions:College of Science > School of Mathematics and Physics
ID Code:36251
Deposited On:20 Jun 2019 14:15

Repository Staff Only: item control page