Potentials Gibbs thermodynamic potential

Feistel R (2003) A new extended Gibbs thermodynamic potential of seawater. Prog Ocean 58 43-114... 

Equilibrium hydrogen concentration m(P, T) was determined from the lattice constant a(P,T) of hydrogen unit cell at minimum value of the Gibbs thermodynamical potential G P. T) = F(P, T) + PV ... 

Feistel, R., Hagen E., 1998. A Gibbs thermodynamic potential of sea ice. Cold Regions Science and Technology, 28, 83-142. 

Feistel, R., 2005. Numerical implementation and oceanographic application of the Gibbs thermodynamic potential of seawater. Ocean Science, 1, 9-16, http //www.ocean-science.net/os/l/9. 

Feistel, R., Hagen, E., 1995. On the GIBBS thermodynamic potential of seawater. Progress in Oceanography, 36, 249-327. 

The formation of an individual particle at constant temperature and pressure requires additional work equal to a change in the Gibbs thermodynamic potential of the system, Since the state of matter and... 

A ol,P) is the Gibbs thermodynamic potential associated with 3, F is the usual Helmholtz free energy and N is the average number of particles in the system compatible with the value of a ... 

Gibbs thermodynamic potential per unit volume and qs specifies the thermodynamic portion of the 5-th step in the variation of the reaction s Gibbs free energy. 

Secondary twinning is not accompanied by ary shape change of the crystal. It is only possible if the Gibbs thermodynamic potential decreases. Following tensor coordinates of and 5, change sign (see coordinates in brackets) in second twin crystal... 

Let us denote the value of the Gibbs thermodynamic potential per unit volume for the first G(l) and second G(2) twin crystal. Twinning is possible under the condition (see Eqs. (5.80) and (5.81))... 

X-cut of quartz belongs to the mostly used quartz elements for piezoelectric transducers. Uniaxial stress Ti 0 in the x-axis direction does not induce arty twinning because the conditionEq. (7.3) is not satisfied. Gibbs thermodynamic potential does not change under this uniaxial stress. But the twinning is experimentally observed at room temperature for stresses 5-9 x 10 Pa in the laboratory samples as well as for transducers. This must be a consequence of multiaxial stress created due... 

So far, we use the model that assumes the fact that critical nuclei of aU phases, allowed by the phase diagram, appear at once (the unlimited nucleation model). It is known that the growth of a new phase from the nucleus is energetically favorable only in the case of nucleus size exceeding some critical value la, determined from the extremum condition of Gibbs thermodynamic potential. In a one-component substance, the extremum condition is expressed simply by the derivative of G with respect to the nucleus size being equal to zero ... 

Thermodynamics only considers the initial and final states of a system, which are characterized by special thermodynamic parameters. Usually, temperature, pressure, volume, and such characteristic junctions as enthalpy, entropy, internal energy, Helmholtz free energy, Gibbs thermodynamic potential act as such parameters of state. Just these functions and their values characterize the thermodynamic state of a system and... 

The investigation above is due initially to Gibbs (Scient. Papers, I., 43—46 100—134), although in many parts we have followed the exposition of P. Saurel Joum. Phys. diem., 1902, 6, 474—491). It is chiefly noteworthy on account of the ease with which it permits of the deduction, from purely thermodynamic considerations, of all the principal properties of the critical point, many of which were rediscovered by van der Waals on the basis of molecular hypotheses. A different treatment is given by Duhem (Traite de Mecanique chimique, II., 129—191), who makes use of the thermodynamic potential. Although this has been introduced in equation (11) a the condition for equilibrium, we could have deduced the second part of that equation directly from the properties of the tangent plane, as was done by Gibbs (cf. 53). 

The application of n additional thermodynamic potentials (of electric, magnetic or other origin) implies that the Gibbs phase rule must be rewritten to take these new potentials into account ... 

Once the cluster expansion of the partition function has been made the remaining thermodynamic functions can be obtained as cluster expansions by taking suitable derivatives. Of particular interest are the expressions for the equilibrium concentrations of intrinsic point defects for the various types of lattice disorder. Since the partition function is a function of Nx, N2, V, and T, it is convenient for the derivation of these expressions to introduce defect chemical potentials for each of the species in the set (Nj + N2) defined, by analogy with ordinary Gibbs chemical potentials (cf. Section I), by the relation... 

Gibbs equation, which is perfectly general, may be deduced readily from the potential functions of Gibbs Thermodynamics, p. 221) and Duhem Le Potential Thermodynamique, Paris 1886), or in the following manner. 

According to Gibbs, any constituent of a system in equilibrium must have the same thermo-dynamic potential in all the phases of which it is a component. Hence, when equilibrium has been established across an interface between a metal and an electrolyte containing its ions, the thermo-d3mamic potential f Me iona of the metallic ions must be the same in both. In general the thermodynamic potential of a constituent which is electrically neutral may be said to depend only on its concentration G and its environment, but if it is an ion the electrical potential of the ]... 

An extremely useful quantity in the thermodynamic treatment of multicomponent phase equilibria is the chemical potential. The chemical potential for component /, is the partial molal Gibbs free energy with respect to component i at constant pressure and temperature ... 

The subject of interest is a gel swollen by solvent. Let F be the Gibbs free energy change after mixing of solvent and an initially unstrained polymer network [1]. When the gel is isotropic and is immersed in a pure solvent with a fixed pressure Po, F is a thermodynamic potential dependent on the temperature T, the pressure p inside the gel, and the solvent particle number Ns inside the gel. It satisfies... 

OTHER THERMODYNAMIC POTENTIALS GIBBS AND HELMHOLTZ FREE ENERGY... 

After discussing the thermodynamic properties of the boundary, let us concentrate on the change in thermodynamic potentials across the boundary. For this, we formulate the Gibbs energy for the bulk phase a of an ionic crystal as the sum... 

The Gibbs Tree energy, which is also called (he Gibbs function and the thermodynamic potential, is most generally understood when the term free energy is used without qualification. It is defined by the equation. 

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