Chapter 4 - Solution of the Gibbs Paradox and Related Problems

Abstract

The Gibbs paradox and other misunderstandings connected with entropy arose due to a wrong interpretation of its initial underlying physical meaning. It was insufficiently grounded that entropy represents a kind of energy. From this standpoint, the entropy jump arising at the mixing of different gases at the same temperature and pressure cannot provide energy jump. The energy of a combined system can be equal only to the sum of energies of its components. At that, the additional energy is nowhere to arise from. Obviously, the acceptance of its increase leads to the violation of the energy conservation law. Entropy and the Gibbs paradox are real parameters of physical phenomena and need a correct interpretation, which is among somewhat different physical notions. The basis of these notions is the statement that entropy is not energy. It is unambiguously proved that entropy is a dimensionless characteristic of the uncertainty of the state of any system. It has made it possible to solve unambiguously the Gibbs paradox and overcome other misunderstandings connected with entropy. At the mixing of various gases, the system uncertainty increases, and the entropy jump magnitude depends on the ratio of components in the mixture. Although mixing identical components, the mixture uncertainty remains the same, which determines the absence of entropy jump. The uncertainty of composition of any complex mixture or its entropy can be calculated using the probability of components content. It is considered that entropy is characteristic for dynamic systems only. Here it is proved that any multicomponent static systems can be also characterized by the entropy parameter. In this case, the entropy expresses only the composition uncertainty. An important conclusion that entropy consists of static and dynamic components is substantiated.