Gibbs function defined

The corresponding characteristic function will be the Gibbs function defined in the statistical plane by ... 

For large departures from T, we have to fall back on eqn. (5.21) in order to work out Wf. Thermodynamics people soon got fed up with writing H - TS all the time and invented a new term, the Gibbs function G, defined by... 

Among many other valuable results in his memoir on heterogeneous equilibrium is a formulation of the Gibbs free energy, also called the Gibbs function, which is defined by the equation... 

The Clausius-Clapeyron equation provides a relationship between the thermodynamic properties for the relationship psat = psat(T) for a pure substance involving two-phase equilibrium. In its derivation it incorporates the Gibbs function (G), named after the nineteenth century scientist, Willard Gibbs. The Gibbs function per unit mass is defined... 

The energy relations associated with the redox processes in wastewater follow the general rules of thermodynamics (Castellan, 1975 Atkins, 1978). The Gibbs free energy, G, of the system is the major thermodynamic function defining the state — and the change in state — of the biochemical redox processes. At constant temperature and under constant pressure, AG is equal to the maximum work, which can be produced by the redox process ... 

A further complication arises from the AG term in Equation (4.49). The diagram above is clearer than the derivation in reality, the differential quantity 3G/3 only corresponds to the change in Gibbs function AG under certain, well defined, and precisely controlled experimental conditions. 

Writing the equation in this way tells us that if we know the enthalpy of the system, we also know the temperature dependence of G -i-T. Separating the variables and defining Gj as the Gibbs function change at Ti and similarly as the value of G2 at T2, yields... 

The relationship between changes in Gibbs function and temperature (at constant pressure p) is defined using Equation (4.38) ... 

As the procedure is the same for both the Gibbs function and the Helmholtz function, we shall consider in detail only the derivation for the Gibbs function G. After Equation (7.14), we obtained the differential of the function, which was later to be defined as G, as... 

As it has been shown that the Gibbs function for formation of an individual ion has no operational meanings [12], no way exists to determine such a quantity experimentally. However, for the purposes of tabulation and calculation, it is possible to separate AfGm of an electrolyte arbitrarily into two or more parts, which correspond to the number of ions formed, in a way analogous to that used in tables of standard electrode potentials. In both cases, the standard Gibbs function for formation of aqueous H" " is defined to be zero at every temperature ... 

Application to Macromolecular Interactions. Chun describes how one can analyze the thermodynamics of a particular biological system as well as the thermal transition taking place. Briefly, it is necessary to extrapolate thermodynamic parameters over a broad temperature range. Enthalpy, entropy, and heat capacity terms are evaluated as partial derivatives of the Gibbs free energy function defined by Helmholtz-Kelvin s expression, assuming that the heat capacities integral is a continuous function. 

Consider a crystal which is in equilibrium having n chemical components (k = 1,2,..., ). We can define (at any given P and T) a Gibbs function, G, as a homogeneous function that is first order in the amount of components... 

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. 

Gibbs functions for a real salt solution and the corresponding ideal salt solution containing m2 moles of salt in a kilogram of solvent. GE can be calculated for many aqueous salt solutions from published values of 0 and y . In the same way, the corresponding excess enthalpy HE can be defined and this equals the apparent partial molar enthalpy. Thus the properties of salt solutions can be examined in plots of GE, HE, and T SE against m2, where SE is the... 

By elementary theory we can show that the Gibbs function is defined in such a way that the free energy change criterion we are searching for (i.e., dG T,p = 0) may be deduced from the second law of thermodynamics on the condition that T and p are constants. However, only a superficial summary of the fundamental theory is provided as the underlying ideas is quite involved. 

Since Ecell is defined to be positive for a spontaneous reaction, this equation correctly expresses a decrease in Gibbs function, which is the thermodynamic criterion for a spontaneous reaction at constant T and P. It is evident that if AGreact can be calculated from AG j- data, the potential of a cell arranged for reversible operation can be determined conversely, experimental measurements of Ecen permit calculation of AGreact. Both types of calculations are useful in electrochemical work and, thus, in the analysis of corrosion. 

It follows from the discussion in this paragraph that only standard differential thermodynamic functions can be calculated from any chromatographic distribution constant defined in whatever way. Also, it is necessary to always specify the choice of the standard states for the solute in both phases of the system. Without specifying the standard states the data on the thermodynamic functions calculated from chromatographic retention data lack any sense. When choosing certain standard states it may happen that the standard differential Gibbs function is identical with another form of the differential Gibbs function, or includes such a form situations described by equations 46 and 49 may serve as examples. The same also holds true for standard differential volumes, entropies and enthalpies (compare Section 1.8.3). However, every particular situation requires a special treatment. 

E = constant in scaling equation G = Gibbs free energy h = scaling function defined by Equation 8 M = molecular weight n = index of refraction P = pressure... 

We now define a modified Gibbs function to measure changes from the initial standard Gibbs energy and to scale by the temperature and the total initial moles as follows,... 

Planck function - A thermodynamic function defined by T = -GIT, where G is Gibbs energy and T thermodynamic temperature. [2]... 

Gibbs function (Gibbs free energy) Symbol G A thermodynamic function defined by... 

This chapter deals with experimental methods for determining the thermodynamic excess functions of binary liquid mixtures of non-electrolytes. Most of it is concerned with techniques suitable for measurements in the temperature range 250 to 400 K and the pressure range 0 to 100 kPa. Techniques suitable for lower temperatures will be briefly reviewed. Techniques for measuring the molar excess Gibbs function G, the molar excess enthalpy and the molar excess volume will be discussed. The molar excess entropy can only be determined indirectly from either measurements of (7 and at a specific temperature = (If — C /T], or from the temperature dependence of G m [ S m = The molar excess functions have been defined by... 

The molar excess Gibbs function G T,p, x) of a liquid mixture of A -f B containing mole fraction jc of B in the liquid phase at temperature T and pressure is defined by ... 

Chemical potential Defined in terms of Gibbs free energy, it is a measure of how the Gibbs function for a system changes when a specified amount of component is added to the system. 

Another important thing in the synthesis of final products by combustion of metals and nonmetals in nitrogen is the possibility of dissociation of the obtained compounds. The paper [8] was the first to define a change in Gibbs function AG of the system Me-N when determining the direction of the reaction ... 

Basic to the thermodynamic description is the heat capacity which is defined as the partial differential Cp = (dH/dT)n,p, where H is the enthalpy and T the temperature. The partial differential is taken at constant pressure and composition, as indicated by the subscripts p and n, respectively A close link between microscopic and macroscopic description is possible for this fundamental property. The integral thermodynamic functions include enthalpy H entropy S, and free enthalpy G (Gibbs function). In addition, information on pressure p, volume V, and temperature T is of importance (PVT properties). The transition parameters of pure, one-component systems are seen as first-order and glass transitions. Mesophase transitions, in general, were reviewed (12) and the effect of specific interest to polymers, the conformational disorder, was described in more detail (13). The broad field of multicomponent systems is particularly troubled by nonequilibrium behavior. Polymerization thermodynamics relies on the properties of the monomers and does not have as many problems with nonequilibrium. 

As an example let us discuss the triple of independent variables defining the Gibbs function G. Temperature , the coordinates of the electric field vector and... 

The defining equations for higher-order critical points are straightforward in terms of the Gibbs function and the composition variables. For instance, for a... 

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