Clausius vs. Sackur-Tetrode ideal gas entropy in open systems

Details Clausius vs. Sackur-Tetrode ideal gas entropy in open systems Clausius vs. Sackur-Tetrode ideal gas entropy in open systems

2011-08-27

arxiv.org/abs/1108.5442v3

Physics

Condensed Matter

Statistical Mechanics

6 pages

Scientific paper

Based on the properties of homogeneous functions of first degree, we derive in a mathematically consistent manner the explicit expressions of the chemical potential $\mu$ 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/value 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 two aforementioned entropies are distinct in finite systems.

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