Gibbss phase law

For phases that are in equilibrium with one another, the Gibbs phase law holds ... 

J. W. Gibbs Publishes On the equilibrium of heterogeneous substances ,which contains Gibbs phase law 1876... 

This is the mathematical expression of the Gibbs phase law. It is an explicit and simple guide in the study of phase equilibria. 

The phase diagrams of two-component systems are represented in the two-dimensional space, where the composition is shown on the x axis (in molar or in mass fractions) in agreement with the lever rule, and the temperature is given on the y axis (in °C or in Kelvin). They are the so-called isobaric diagrams, since the constant pressure, mostly the atmospheric one, is assumed. The Gibbs phase law attains thus the form... 

This problem is important because the determination of a base will enable us to calculate the dimension of the vector space, which is, specifically, the number of transformations, which plays a part in Gibbs phase law, for determining the number of independent components (see section 2.3). This number can also be used (see Chapter 3) to calculate the associated values and the equilibrium constant of the overall transformation. 

When a reversible transition from one monolayer phase to another can be observed in the 11/A isotherm (usually evidenced by a sharp discontinuity or plateau in the phase diagram), a two-dimensional version of the Gibbs phase rule (Gibbs, 1948) may be applied. The transition pressure for a phase change in one or both of the film components can be monitored as a function of film composition, with an ideally miscible system following the relation (12). A completely immiscible system will not follow this ideal law, but will... 

STATIONARY POINTS OF PHASE DIAGRAMS GIBBS-KONOWALOW LAWS... 

The separation of these gases is dictated by the Gibbs phase rule. The degree to which they separate is based on the physical behavior of the liquid and vapor phases. This behavior is governed, as at ambient temperatures, by Raoult s and Dalton s laws. 

There being two components and two phases in the following streams at the bottom, feed and overhead, Gibbs s law states that only two of the three variables (pressure, temperature, and composition) are independent. Therefore, the number of independent variables is only 11. The number of defining equations is two (the conservation of mass and energy), and, therefore, the number of degrees of freedom for this process is 11 - 2 = 9. Consequently, not more than nine automatic controllers can be placed on this process. 

Besides, let us note the automatic observance (certainly with correctly set initial data) and, hence, needlessness of the formalized descriptions in equilibrium modeling of such important regularities of macroscopic system behavior as the Gibbs phase rule, the Le Chatelier-Brown principle, mass action laws, the Henry law, the Raoult law, etc. 

We have given very considerable space to the most recent applications of Thermodynamics to Chemistry. We have, in particular, developed the applications of that admirable phase law, an algebraic theorem conceived by the genius of J. Willard Gibbs and... 

Abstract The Gibbs phase rule relating the number of degrees of freedom / of a system to the number of components c and the number of coexisting phases p is a central, universally used relation, expressed by what is probably the simplest formula in the natural sciences,/ = c — p + 2. Research into the behavior of small systems, notably atomic clusters, has shown in recent years that the phase rule is not as all-encompassing as is often assumed. Small systems can show coexistence of two or more phases in thermodynamic equilibrium over bands of temperature and pressure (with no other forces acting on them). The basis of this apparent violation of the phase rule, seeming almost like violation of a scientific law, is in reality entirely understandable, consistent with the laws of thermodynamics, and even allows one to estimate the upper size limit of any particular system for which such apparent violation could be observed. 

Gibbs phase rule, which pertains to the external intensive values and the composition variables. This law is applicable both to open and to closed... 

Kirschoff, 19 relation, 106 Lagrange multiplier method, 150 law of mass action, 55 linear combination, 36 minimization of the Gibbs energy function, 149 open system, 20 phase law Duhem, 42 Gibbs, 41... 

---