Multiphase system, Gibbs rule

From the thermodynamic point of view, this is a multiphase system for which, at equilibrium, the Gibbs equation (A.20) must apply at each interface. Because there is no charge transfer in and out of layer (4) (an ideal insulator) the sandwich of the layers (3)/(4)/(5) also represents an ideal capacitor. It follows from the Gibbs equation that this system will reach electrostatic equilibrium when the switch Sw is closed. On the other hand, if the switch Sw remains open, another capacitor (l)/( )/(6) is formed, thus violating the one-capacitor rule. The signifies the undefined nature of such a capacitor. The open switch situation is equivalent to operation without a reference electrode (or a signal return). Acceptable equilibrium electrostatic conditions would be reached only if the second capacitor had a defined and invariable geometry. 

As with all multiphase systems, the Gibbs phase rule provides a useful tool for determining the number of intensive variables (ones that do not depend on system mass) that can be fixed independently ... 

Useful insights into the thermodynamics of a multiphase reacting system can be obtained by analyzing the situation when chemical and phase equilibrium (C PE) are achieved simultaneously. The Gibbs rule can be used to find the degrees of freedom F ... 

How must the Gibbs phase rule be modified to take account of the following cases (a) A multiphase system is placed between two charged parallel condenser plates (b) One or more of the components is absent from one or more of the phases present (c) Several distinct regions of the system are maintained at different pressures by means of semipermeable membranes Document your answers fully. 

Distinguish between intensive and extensive variables, giving examples of each. Use the Gibbs phase rule to determine the number of degrees of freedom for a multicomponent multiphase system at equilibrium, and state the meaning of the value you calculate in terms of the system s intensive variables. Specify a feasible set of intensive variables that will enable the remaining intensive variables to be calculated. 

The Gibbs phase rule gives the degrees of freedom of a multiphase system in equilibrium, or the number of intensive (size-independent) system variables that must be specified before the others can be determined. 

SPECIFICATION OF THE EQUILIBRIUM THERMODYNAMIC STATE OF A MULTICOMPONENT, MULTIPHASE SYSTEM THE GIBBS PHASE RULE... 

Specification of the Equilibrium Thermodynamic State of a Multicomponent, Multiphase System the Gibbs Phase Rule 387... 

Gibbs phase-rule states how many degrees of freedom/fully describe a multicomponent and multiphase system ... 

The Gibbs phase rule describes how many state variables of a multiphase system may vary independently (degrees of freedom of... 

The Gibbs phase rule gives the number of independent intensive variables in a multicomponent multiphase system at equilibrium ... 

Although occasionally papers appear speaking of the inapplicability of Gibbs phase rule [Li, 1994, 13] or beyond the Gibbs phase rule [Mladek et al, 2007], this invariably means no more than that one of the ceteris paribus conditions Gibbs already mentioned is not fulfilled for example, the phase rule doesn t cover systems in which rigid semi-permeable walls allow the development of pressure differences in the system. Gibbs explicitly allows for the possible presence of other thermodynamic fields. An extended phase rule has been proposed for, inter alia, capillary systems (in which the number and curvature of interfaces/phases play a role), multicomponent multiphase systems for which relative phase sizes are relevant [Van Poolen, 1990], colloid systems (for which, even if in equilibrium, it is not always easy to say how many phases are present), unusual crystalline materials, and more. 

Fig. 3.5 (a) Schematic representatirai of the Gibbs rule for a multiphase system, (b) voltage plateaus appear between the phase instabilities... 

Gibb s Phase Rule. The phase rule derived by W. J. Gibbs applies to multiphase equilibria in multicomponent systems, in the absence of chemical reactions. It is written as... 

The mathematical basis of classic thermodynamics was developed by J. Willard Gibbs in his essay [1], On the Equilibrium of Heterogeneous Substances, which builds on the earlier work of Kelvin, Clausius, and Helmholtz, among others. In particular, he derived the phase mle, which describes the conditions of equilibrium for multiphase, multicomponent systems, which are so important to the geologist and to the materials scientist. In this chapter, we will present a derivation of the phase rule and apply the result to several examples. 

The equilibrium interfaces of fluid systems possess one variant chemical potential less than isolated bulk phases with the same number of components. This is due to the additional condition of heterogeneous equilibrium and follows from Gibbs phase rule. As a result, the equilibrium interface of a binary system is invariant at any given P and T, whereas the interface between the phases a and /3 of a ternary system is (mono-) variant. However, we will see later that for multiphase crystals with coherent boundaries, the situation is more complicated. 

The lacking special description of the Gibbs phase rule in MEIS that should be met automatically in case of its validity is very important for solution of many problems on the analysis of multiphase, multicomponent systems. Indeed, without information (at least complete enough) on the process mechanism (for coal combustion, for example, it may consist of thousands of stages), it is impossible to specify the number of independent reactions and the number of phases. Prior to calculations it is difficult to evaluate, concentrations of what substances will turn out to be negligibly low, i.e., the dimensionality of the studied system. Besides, note that the MEIS application leads to departure from the Gibbs classical definition of the notion of a system component and its interpretation not as an individual substance, but only as part of this substance that is contained in any one phase. For example, if water in the reactive mixture is in gas and liquid phases, its corresponding phase contents represent different parameters of the considered system. Such an expansion of the space of variables in the problem solved facilitates its reduction to the CP problems. 

Multiphase phenomenon is more frequently encountered in multicomponent mixtures, such as reaction mixtures. From a thermodynamic perspective, multiphase phenomena exist because multiple phases reduce the Gibbs free energy of the system. More components mean more ways and phases in which to partition this energy. Due to the Gibbs phase rule, a third component extends multiphase equilibrium as seen in binary mixtures, such as LLV and SLV equihbrium, from a lirte to a region of pressure and concentration at a given temperature. 

If a multiphase multicomponent system is to be at equilibrium (no change with time of the intensive variables) obviously temperature and pressure must be the same for all phases and also the chemical compositions (mole fractions of each constituent). In any given phase there are (C—1) independent mole fractions (their sum is unity by definition), so there are P.(C—1) composition variables involved and thus [P.(C—1) -1-2] intensive variables in total. But if chemical equUibrium in all phases simultaneously is to hold, the chemical potential of each constituent (a function of the composition) must be the same in each phase thus there are C.(P—1) independent constraints on the composition variables arising from the equilibrium condition (the chemical potential in one of the phases is used as the reference standard for the other phases). Thus F = [P.(C—1) -1-2] — [C.(P—1)] =C—P-F2. This is the famous Gibbs Phase Rule. 

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