To the 150th anniversary of the masterpiece by J. W. Gibbs on the equilibrium of heterogeneous substances, which is based on the mechanical theory of heat published 160 years ago by R. Clausius and the concept of entropy introduced by him

Abstract

The article briefly presents the life of Josiah Willard Gibbs (1839–1903), the essence of his main work published between 1875-1878 and its impact. The method developed for calculating the phase equilibrium of multi-component, multi-phase material systems and its key elements are described: the molar Gibbs energy formula, the basic condition for equilibrium (minimum of the average molar Gibbs energy of the system), the condition for heterogeneous equilibria (the partial
molar Gibbs energy of each component must be the same in all phases of the system), and the phase rule (the system can have a maximum of C + 2 phases in equilibrium with each other at the same time, where C is the number of independent components (elements) and 2 refers to the two non-compositional state parameters, pressure and temperature). It is presented that Gibbs’ chemical thermodynamics is based on Clausius’ mechanical thermodynamics (and the first two laws of
thermodynamics) and would be unthinkable without the entropy he introduced (1865).
It is mentioned that Nernst’s third law, introduced in 1905, was also needed for practical calculations, according to which the entropy of perfect, one-component solid crystals tends to zero as the temperature approaches 0 K. Finally, it is shown that practical calculations require computers, which appeared in the 1970s; the practical models needed for the calculations were created by the Calphad community. Metallurgical developments are now unimaginable without Calphad software, the theoretical foundations of which were laid by Gibbs as early as the 19th century.