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

School of Mathematics and Physics, University of Lincoln, Lincoln LN6 7TS, UK
Entropy 2019, 21(6), 599; https://doi.org/10.3390/e21060599
Received: 30 May 2019 / Revised: 12 June 2019 / Accepted: 14 June 2019 / Published: 16 June 2019
(This article belongs to the Special Issue Applications of Statistical Thermodynamics)
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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. View Full-Text
Keywords: mixtures; entropy; polydispersity; binomial distribution mixtures; entropy; polydispersity; binomial distribution
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Paillusson, F. On the Logic of a Prior Based Statistical Mechanics of Polydisperse Systems: The Case of Binary Mixtures. Entropy 2019, 21, 599.

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