Gibbs paradox as a derivative of composition entropy

Abstract

In science, sometimes so-called «problem problems» arise, over the solution of them struggle for a long time several generations of scientists. Possessing deep knowledge and developed intuition, they sometimes predict the result of a problem, but cannot find a solution to it. Among such problems of science, one can certainly include the problem that entered physics under the name «Gibbs paradox». Gibbs predicted all the properties of the entropy of a mixture. He showed that when two different gases are mixed, the entropy of the mixture exceeds the sum of the initial entropies of the components by an amount that called the jump of entropy. What is the physical nature of this jump, he could not explain. The fact is that this jump of entropy behaves in a rather strange way. Its magnitude does not depend on the nature of gases, for a mixture of them of any arbitrary chemical composition, it has the same value. For more than a century there has been a paradox Gibbs associated with the fundamental parameter of physical systems ― entropy, and so far no one has been able to clarify this paradox or at least find out due to what reasons it is formed. Ill. 2. Ref. 8.