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On the Logic of a Prior Based Statistical Mechanics of Polydisperse Systems: The Case of Binary Mixtures
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 cir...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2019
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7515103/ https://www.ncbi.nlm.nih.gov/pubmed/33267313 http://dx.doi.org/10.3390/e21060599 |
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author | Paillusson, Fabien |
author_facet | Paillusson, Fabien |
author_sort | Paillusson, Fabien |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-7515103 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75151032020-11-09 On the Logic of a Prior Based Statistical Mechanics of Polydisperse Systems: The Case of Binary Mixtures Paillusson, Fabien Entropy (Basel) Article 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. MDPI 2019-06-16 /pmc/articles/PMC7515103/ /pubmed/33267313 http://dx.doi.org/10.3390/e21060599 Text en © 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Paillusson, Fabien On the Logic of a Prior Based Statistical Mechanics of Polydisperse Systems: The Case of Binary Mixtures |
title | On the Logic of a Prior Based Statistical Mechanics of Polydisperse Systems: The Case of Binary Mixtures |
title_full | On the Logic of a Prior Based Statistical Mechanics of Polydisperse Systems: The Case of Binary Mixtures |
title_fullStr | On the Logic of a Prior Based Statistical Mechanics of Polydisperse Systems: The Case of Binary Mixtures |
title_full_unstemmed | On the Logic of a Prior Based Statistical Mechanics of Polydisperse Systems: The Case of Binary Mixtures |
title_short | On the Logic of a Prior Based Statistical Mechanics of Polydisperse Systems: The Case of Binary Mixtures |
title_sort | on the logic of a prior based statistical mechanics of polydisperse systems: the case of binary mixtures |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7515103/ https://www.ncbi.nlm.nih.gov/pubmed/33267313 http://dx.doi.org/10.3390/e21060599 |
work_keys_str_mv | AT paillussonfabien onthelogicofapriorbasedstatisticalmechanicsofpolydispersesystemsthecaseofbinarymixtures |