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Clausius versus Sackur-Tetrode entropies

Oikonomou, Thomas and Bagci, Gokhan B (2013) Clausius versus Sackur-Tetrode entropies. [Preprint]

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Abstract

Based on the property of extensivity (mathematically, homogeneity of first degree), we derive in a mathematically consistent manner the explicit expressions of the chemical potential and the Clausius entropy $S$ for the case of monoatomic ideal gases in open systems within phenomenological thermodynamics. Neither information theoretic nor quantum mechanical statistical concepts
are invoked in this derivation. Considering a specific expression of the constant term of $S$, the derived entropy coincides with the Sackur-Tetrode entropy in the thermodynamic limit. We demonstrate however, that the former limit is not contained in the
classical thermodynamic relations, implying that the usual
resolutions of Gibbs paradox do not succeed in bridging the gap between the thermodynamics and statistical mechanics. We finally consider the volume of the phase space as an entropic measure, albeit, without invoking the thermodynamic limit to investigate its relation to the thermodynamic equation of state and observables.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Oikonomou, Thomas
Bagci, Gokhan B
Additional Information: Accepted for publication in Studies in History and Philosophy of Modern Physics Part B
Keywords: Clasius (thermodynamical)/statistical entropy; Gibbs paradox; extensivity; thermodynamic limit
Subjects: Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Depositing User: Dr. Gokhan Bagci
Date Deposited: 22 Feb 2013 22:55
Last Modified: 22 Feb 2013 22:55
Item ID: 9584
Subjects: Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Date: 2013
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/9584

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