The Fifty-First Solution of the Gibbs Paradox

Despite the fact that the textbooks on thermodynamics and statistical physics regard the Gibbs paradox as resolved long ago, researchers into the history of the matter point out that, although numerous different solutions exist, there is no single, generally accepted solution. It is shown that the Gibbs paradox came as a result of a methodological error and, with this error corrected, the Gibbs paradox disappears. The “secret” of this paradox is that there are two legitimate laws in gas theory: Dalton’s law and Amagat’s law. For all thermodynamic parameters except entropy, these two laws produce the same results. It is only when calculating entropy that the results differ. When Dalton’s law is applied, the Gibbs paradox appears. When Amagat’s law is applied, the paradox disappears. Applying Dalton՚s law to entropy calculations is erroneous, which is indicated by the fact that no researcher has been able to identify the “physical meaning” of the difference in the entropy of a gas mixture before and after mixing.