Total free energy of system

Free energy of A = Ga Free energy of B = Gb Total free energy of system = G =... 

The total free energy of the system is then made up of the molar free energy times the total number of moles of the liquid plus G, the surface free energy per unit area, times the total surface area. Thus... 

The calculation is based on the rule of thermodynamics, which states that a system will be in equilibrium when the Gibbs free energy is at a minimum. Cl The objective then is the minimization of the total free energy of the system and the calculation of equilibria at constant temperature and volume or at constant pressure. It is a complicated and lengthy calculation but, fortunately, several computer programs are now available that considerably simplify the task. PI... 

Note that the total free energy of the system always increases on addition of component i and when its surface area is increased. 

Let ns now examine the effect of adsorption on the interfacial energy (y). If a solnte i is positively adsorbed with a snrface density of F we wonld expect the surface energy to decrease on increasing the bulk concentration of this component (and vice versa). This situation is illustrated in Figure 3.2, where the total free energy of the system and... 

The driving force for sintering is the reduction in the total free energy of the particulate system, AG, which is composed of free energy changes of volume, AGy, boundaries, AGb, and surfaces, AGt. 

From a thermodynamic consideration by Gibbs,225 one can expect surface segregation to occur if the total free energy of a system can be lowered by segregation of a species to the surface. For a dilute solution of B in A, this condition is described as... 

Biopolymers are, of course, poly electrolytes. This means that electrostatic repulsion between them, as well as the contribution of counterions to the total free energy of the system, are to be included amongst the key factors affecting the character of the biopolymer interactions, and hence the stability of mixed biopolymer solutions with respect to phase separation (Antipova and Semenova, 1997 Grinberg and Tolstoguzov, 1997 Polyakov et al., 1997 Semenova, 1996 Wassennan et al., 1997). For... 

Let us now first consider the situation in which equilibrium of reaction Eq. 8-6 is not yet reached. From Eqs. 3-20 and 3-21 (Chapter 3) it is easy to see that if the reaction proceeds by the increment dnT, the change in the total free energy of the system considered is given by ... 

Some readers will recognize this development as the calculus of variations [7]. A functional is a function of a function in this case, T takes the function (r,t0) and maps it to a scalar value that is numerically equal to the total free energy of the system. 

The effect of solvent on the total free energy of a BA/solvent system is represented in Figure 22 for a polar solvent such as propylene carbonate. A corresponding plot for BA in a nonpolar solvent is given in Figure 23. These zero order (uncoupled) curves for the various configurations correspond to the following equations. 

The chemical potential is thus identical with the partial molar-free energy, Gt, of component i. The total free energy of a closed system is therefore... 

In what follows, we only need to refer to (not mpl) and therefore drop the superscript for brevity. Since In V(m) is extensive, we can write In V(m) = Ns(m), where s is the entropy of mixing per particle expressed as a function of the moment m (or, more generally, of the full set of normalized moments). The total free energy of the system then takes the form... 

Assuming that the total free energy of the system is equal to the sum of the free energy of the individual components (Trivedi and V fells, 2000), the solubility of a compound in a binary mixture of water and an organic solvent can be described as... 

The equilibrium dimensions rm and lm of the inverted domain correspond to the minimum of the total free energy of the tip array-sample system, Wtotai The calculated domain sizes at the energy minimum are shown in Figure 10.17 as a function of the distance p0 between two adjacent tips. 

In the model, the total free energy of the system is decomposed into six terms. The first term accounts for the entropy of the condensed counterions [48]... 

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