On the incorrectness of the proof of the Gibbs theorem on the entropy of a mixture of ideal gases, which was given by J. W. Gibbs

Abstract

There is the Gibbs theorem in thermodynamics, according to which the entropy of the mixture of ideal gases is equal to the sum of the entropies of the components of the mixture. J. W. Gibbs proved this by a mathematical derivation from the beginnings of thermodynamics and the laws of ideal gases, in particular Dalton's law. This message shows that this proof is mathematically incorrect. It is also shown that the Gibbs theorem cannot be derived mathematically from Dalton's law.

6 pages. The fragments of the article "On the incorrectness of the proofs of the Gibbs theorem on the entropy of a mixture of ideal gases" [In Russian] // Proceeding of Sixth International Scientific-Practical Conference "Mathematics in Modern Technical University". Kyiv. Igor Sikorsky Kyiv Polytechnic Institute. 2018. P.324-330