Conditions for thermodynamic equilibrium

Conditions for thermodynamic equilibrium of the lamella can be derived by considering the lamella plus its environment as an isolated supersystem. Assuming the entropy of the supersystem to be fixed, one knows that the... 

To derive the condition for thermodynamic equilibrium, we start with an isolated system consisting of two subsystems as shown in Figure 5.6. Subsystem A is the one of primary interest in that it is the one in which the chemical process is occurring. Subsystem B is a reservoir in contact with subsystem A in such a way that energy in the form of heat or work can flow between the two subsystems. If left alone, the system will come to equilibrium. Energy will be transferred between the subsystems so that the temperature and pressure will be... 

We have noted previously that the forward and reverse rates are equal at equilibrium. It seems, then, that one could use this equality to deduce the form of the rate law for the reverse reactions (by which is meant the concentration dependences), seeing that the form of the equilibrium constant is defined by the condition for thermodynamic equilibrium. By and large, this method works, but it is not rigorously correct, since the coefficients in the equilibrium condition are only relative, whereas those in the rate law are absolute.19 Thus, if we have this net reaction and rate law for the forward direction,... 

For a nucleus to become useful as a seed for subsequent bubble growth, the size of the nucleus must exceed that of thermodynamic equilibrium corresponding to the state of the liquid. The condition for thermodynamic equilibrium at a vapor-liquid interface in a pure substance can be written as... 

Graphically, the conditions for thermodynamic equilibrium are equal to two points which have a common tangent. These points give the composition of a polymer-rich phase (I) and a solvent-rich phase (II) that can coexist in thermodynamic equilibrium. The summation of such points is also called the coexistence curve or binodal line. 

The condition for thermodynamic equilibrium between phases is that the species chemical potentials are equal in each of the phases. Thus, at equilibrium,... 

In Fig. 21.1, the condition for thermodynamic equilibrium is that the chemical potential of each membrane-permeable ion is identical between the left and right side solutions. The chemical potential /< can be defined either for the 1 1 salt or for the individual ions... 

The condition for thermodynamic equilibrium permits us to attach a thermodynamic significance to the constants in the Arrhenius equation, as we have just demonstrated in the case of reversible reaction systems. There is no real objection to extending this in a formal way to all reactions, so that we can rewrite the Arrhenius equation in the following form ... 

At low concentration (x 1) hydrogen first dissolves in the metal lattice and forms a solid solution phase (a phase). Hydrogen is then randomly distributed in the metal host lattice and the concentration varies slowly with temperature. The a phase has the same crystal structure as the bare metal. The condition for thermodynamic equilibrium is given by ... 

To recover equilibrium thermodynamics from Onsager s theory, first premultiply Eq. (A.15) by R = L and then set A t) — A and A t) = 0 (the conditions for thermodynamic equilibrium in state Fp) in the result. This yields... 

The general derivation of an equation for the potential difference across an interface has been thoroughly treated by Parsons [1] and also by Overbeek [13]. The starting point is the condition for thermodynamic equilibrium between the two bulk phases a and p, given by... 

The most significant consequence of this principle for kineticists is that if in a system at equilibrium there is a flow of reacting molecules along a particular reaction path, there must be an equal flow in the opposite direction. This principle implies that the reaction path established as most probable for the forward direction must also be the most probable path for the reverse reaction. This consequence is also known as the principle of detailed balancing of chemical reactions. Its relationship to the principle of microscopic reversibility has been discussed by Denbigh (19). If we consider a substance that can exist in three intraconvertible isomeric forms, A, B, and C (e.g., frani-butene-2, cw-butene-2, and butene-1), there is more than one independent reaction that occurs at equilibrium. The conditions for thermodynamic equilibrium would be satisfied if there were a steady unidirectional flow at the molecular level around the cycle... 

K is the equilibrium constant for Frenkel disorder. This can be seen if we set the time derivative in eq. (6-2) equal to zero, since this is the condition for thermodynamic equilibrium. On the basis of the simple theory of homogeneous reactions, two limiting cases arise. 1. The electrostatic interaction between electrically charged defects at a separation 2 is negligible compared... 

The concept of chemical potential is very general, applicable to almost any transformation of matter as long as there is a well-defined temperature. We have already seen how the condition for thermodynamic equilibrium for chemical reactions leads to the law of mass action. We shall now see how diffusion, electrochemical reactions and relaxation of polar molecules in the presence of an electric field, can all be viewed as chemical transformations with associated chemical potential and affinity. 

The real three-phase region (tube) is replaced by a triple line (TL) as the new model element for thermodynamic considerations. In theory, its position results from the extrapolation of the three undisturbed D-faces to their common intersection. Accordingly, the tangent lines on these extrapolated D-faces Dsl and Dlv to the point of intersection lead by definition to the thermodynamic contact angle For reasons of exactness, 0 is introduced for the thermodynamic equilibrium of the three-phase system. The static contact angle 0o in Sect. 4.1 refers to the triple line at rest, i.e., to mechanical equilibrium which is a necessary but insufficient condition for thermodynamic equilibrium. 6 is the first excess quantity for the TL. As the position of any of the three D-faces can be chosen arbitrarily, the position of the TL and the value for 8 are arbitrary too. Fortunately, this vagueness is of no serious consequence as long as the two-phase and three-phase boundaries possess microscopic thicknesses. Note that 0 is... 

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