Total Gibbs energy

The foUowiag criterion of phase equUibrium can be developed from the first and second laws of thermodynamics the equUibrium state for a closed multiphase system of constant, uniform temperature and pressure is the state for which the total Gibbs energy is a minimum, whence... 

The general criterion of chemical reaction equiUbria is the same as that for phase equiUbria, namely that the total Gibbs energy of a closed system be a minimum at constant, uniform T and P (eq. 212). If the T and P of a siagle-phase, chemically reactive system are constant, then the quantities capable of change are the mole numbers, n. The iadependentiy variable quantities are just the r reaction coordinates, and thus the equiUbrium state is characterized by the rnecessary derivative conditions (and subject to the material balance constraints of equation 235) where j = 1,11,.. ., r ... 

In the case of a siagle-phase, multicomponent system undergoiag just a single reaction, the total Gibbs energy is as foUows ... 

Complex Clieinical-Reaction Equilibria When the composition of an equilibrium mixture is determined by a number of simultaneous reactions, calculations based on equilibrium constants become complex and tedious. A more direct procedure (and one suitable for general computer solution) is based on minimization of the total Gibbs energy G in accord with Eq. (4-271). The treatment here is... 

E is Young s modulus and Vav is die average molar volume. Summing these terms the total Gibbs energy change accompanying the fluctuation, AG is... 

It follows that the total Gibbs energy change will be negative, and a fluctuation will be stable, when a wavelength component of the flucmation spectrum conesponds to the relationship... 

Figure 2.14 The contribution from the order-disorder transition of CaCC>3(s) to the total Gibbs energy and entropy [25],...

Figure 3.11 shows the G/x diagram at 600 K. If an alloy of composition xq were single phase it would have a Gibbs energy Go- However, if it could form a mixture of two phases, one with composition x and the other with composition x, it could lower its total Gibbs energy to G, where G is defined by the equation... 

The excess term should allow the total Gibbs energy to be fitted to match that of Eq. (6.3) while at the same time incorporating a return to the inclusion of f 6) and f i) in the lattice stabilities. With the increased potential for calculating metastable Debye temperatures and electronic specific heats from first principles (Haglund et al. 1993), a further step forward would be to also replace Eq. (6.5) by some function of Eq. (6.8). 

CALPHAD methods attempt to provide a true equilibrium calculation by considering the Gibbs energy of all phases and minimising the total Gibbs energy of the system (G). In this circumstance G can be calculated either from knowledge of the chemical potential (Gi) of component i, by... 

The equilibrium conditions for phase equilibria can be derived in the simplest way using the Gibbs energy G. According to the second law of thermodynamics, the total Gibbs energy of a closed system at constant temperature and pressure is minimum at equilibrium. If this condition is combined with the condition that the total number of moles of component i is constant in a closed system... 

Here the subscript i designates a particular component in a solution which also contains solvent and, perhaps, other components. To be precise, Gl is a partial molar Gibbs energy, i.e., the changes in total Gibbs energy of a very large volume of solution when one mole of the component is added. 

Let us assume that the martensite particle has grown in the form of an oblate spheroid, the volume of which is (4-n/3with c as the semi-thickness of the spheroid. The total Gibbs energy change for the formation of this particle includes a chemical, an elastic, and an interface energy term. It can be appropriately written as... 

If this strain energy of the coherent a-a system is added to the other Gibbs energy contributions, both the total Gibbs energy and the spinodal curve are shifted as shown schematically in Figure 12-10. 

In Sec. 13.8 it is shown that the total Gibbs energy of a closed system at constant T and P must decrease during an irreversible process and that the condition for equilibrium is reached when... 

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