### 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 μ 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.

Original language | English |
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Pages (from-to) | 63-68 |

Number of pages | 6 |

Journal | Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics |

Volume | 44 |

Issue number | 2 |

DOIs | |

Publication status | Published - May 1 2013 |

Externally published | Yes |

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### Keywords

- Clausius (thermodynamical)/statistical entropy
- Extensivity
- Gibbs paradox
- Thermodynamic limit

### ASJC Scopus subject areas

- History
- Physics and Astronomy(all)
- History and Philosophy of Science