Gibbs paradox - Wikipedia
Gibbs paradox. In statistical mechanics, a semi-classical derivation of entropy that does not take into account the indistinguishability of particles yields an expression for entropy which is not extensive (is not proportional to the amount of substance in question).
2.12: Entropy of Mixing and the Gibbs Paradox
Sep 3, 2024 · This is known as the Gibbs paradox. The resolution of the Gibbs paradox is to include the indistinguishability correction, which renders \(S\) extensive, in which case \(S(T,V,N)=2S(T,\half V,\half N)\).
The Gibbs Paradox: Early History and Solutions - PMC
The history of thermodynamics has three famous “paradoxes”: Josiah Willard Gibbs’s mixing paradox of 1876, Josef Loschmidt reversibility paradox of the same year, and Ernst Zermelo’s recurrence paradox of 1896.
17.8: Entropy of Mixing, and Gibbs' Paradox - Physics LibreTexts
Sep 10, 2020 · Gibbs’ Paradox arises when the two gases are identical. The above analysis does nothing to distinguish between the mixing of two different gases and the mixing of two identical gases.
The Gibbs paradox in statistical mechanics. 1. Introduction. The Gibbs paradox involves the contrast between mixing two quantities of (ideal) gases of a dierent kind and that of mixing two quantities of the same gas. In the case of dierent gases, mixing is accompanied by an entropy increase S = 2R log 2; in the case of same gases there is no ...
The Gibbs paradox is usually broken down into two puzzles: Why is the entropy of the mixing of two gases independent of their degree of similarity—and only zero when the gases are the same? (the discontinuity puzzle). How, in classical statistical mechanics, can an extensive entropy function be defined? (the extensivity puzzle).
Gibb's paradox - University of Texas at Austin
A paradox arises if we try to treat molecules as if they were distinguishable. This is called Gibb's paradox, after the American physicist Josiah Gibbs who first discussed it. The resolution of Gibb's paradox is quite simple: treat all molecules of the same species as if they were indistinguishable.
The Gibbs Paradox - PMC - National Center for Biotechnology …
Jul 25, 2018 · The Gibbs paradox is usually broken down into two puzzles: (i) Why is the entropy of the mixing of two gases independent of their degree of similarity—and only zero when the gases are the same? (the discontinuity puzzle). (ii) How, in classical statistical mechanics, can an extensive entropy function be defined? (the extensivity puzzle).
present note we consider the "Gibbs Paradox" about entropy of mixing and logically inseparable topics of reversibility and the extensive property entropy. For 80 years it has seemed natural that, to find what Gibbs had say about this, one should turn to his Statistical Mechanics.
Mixing indistinguishable systems leads to a quantum Gibbs paradox - Nature
Mar 5, 2021 · Nature Communications - The Gibbs paradox stems from the entropy change upon mixing two gases. Here, by considering bosonic and fermionic statistics, the authors show that an observer unable to...