Thermodynamic conditions for

Part of the gas can escape from the solution at a specific concentration and a fixed temperature, as the pressure level falls to under P < Pg. This takes place in two phases appearance of nuclei, and growth of bubbles of the free gas phase. Thermodynamic conditions for stable nucleation are formulated in [1], They are analogous to the conditions for starting the boiling of low-molecular liquids. The following changes take... 

Passivation is defined as the state where even though a metal electrode fulfills the thermodynamic condition for dissolution (solution composition, electrode potential, etc.), a corrosive reaction scarcely proceeds. 

A great many electrolytes have only limited solubility, which can be very low. If a solid electrolyte is added to a pure solvent in an amount greater than corresponds to its solubility, a heterogeneous system is formed in which equilibrium is established between the electrolyte ions in solution and in the solid phase. At constant temperature, this equilibrium can be described by the thermodynamic condition for equality of the chemical potentials of ions in the liquid and solid phases (under these conditions, cations and anions enter and leave the solid phase simultaneously, fulfilling the electroneutrality condition). In the liquid phase, the chemical potential of the ion is a function of its activity, while it is constant in the solid phase. If the formula unit of the electrolyte considered consists of v+ cations and v anions, then... 

Bernard, G. Hocine, R. Lupis, C.H.P. Thermodynamic conditions for spinodal decomposition in a multicomponent system. Transactions of the metallurgical society of AIME. 1967, 239, 1600-1604. 

In the intermediate state (line b) the free energy curve also delivers the points that satisfy the thermodynamic conditions for equilibrium [51-54]. Thus the chemical potentials of each component (polymer or solvent) must be the same in both phases I and II). For a polymer-solvent system, this is mathematically... 

For heavily doped n-type semiconductors, the flat band is nearly coincident with the conduction band, while for heavily doped p-type semiconductors the flat band lies very close to the valence band edge. A necessary thermodynamic condition for the photoproduction of hydrogen and oxygen is that the p-type conduction band must be at or above the H7H2 half cell potential, while n-type valence band must lie below the 02/0H half cell potential. 

The thermodynamic conditions for spherical flaw growth were derived in Ref. 113 for a body with a sinusoidally displaced boundary. The final expression for the oscillatory displacement u = u0 sin mt is given as ... 

Dilute aqueous solutions of strong acids (e.g. HCl or H2SO4) contain sufficient concentrations of hydrated protons to oxidize many metals, to produce their most stable states in solution. The only thermodynamic condition for metal oxidation is that the reduction potential of the metal ion produced should be negative. In general, for the metal ion M + undergoing reduction to the metal, if the standard reduction potential for the half-reaction ... 

Then the general thermodynamic condition for equilibrium in a reaction involving charged particles and electrons is... 

Use of consistent thermodynamic conditions for enhancer formulations Permeation enhancement efficacy of a CPE is a function of its chemical potential, temperature, pressure, and cosolvent amongst other thermodynamic parameters. These thermodynamic conditions need to be standardized for all the enhancers that are being tested to create direct comparison of their efficacies in increasing skin permeation. 

The stoichiometric coefficients i9, are positive for products and negative for reactants. The Gibbs energy of the system of products and reactants must be minimal at equilibrium. If this condition is combined with the mass balance that is imposed by eq.(2.4-3) we get the general thermodynamic condition for chemical equilibrium ... 

Finding Work of Compression with a Thermodynamic Chart Hydrogen sulfide is to be compressed from 100°F and atmospheric pressure to SOpsig. The isentropic efficiency is 0.70. A pressure-enthalpy chart is taken from Starling (Fluid Thermodynamic Properties for Light Petroleum Systems, Gulf, Houston, TX, 1973). The work and the complete thermodynamic conditions for the process will be found. 

The thermodynamic condition for solubility is the negative change in Gibbs free energy. With low-molecular solutes this is easily fulfilled because of the large entropy... 

These studies throw light on the initial aggregation phenomena, which results in micelles and may also (17) constitute the necessary basis for understanding the subsequent agglomeration to liquid crystals. Very little is known about the thermodynamic conditions for the latter associations. Instead we must rely on empirical data to illuminate the basic mechanisms which determine the association behavior of those substances in concentrated systems. Valuable information for understanding the drastic influence of weak intermolecular forces on the association structures (Figure 1) is obtained from the pronounced temperature dependence of the solubilization which was observed early by Shinoda (29). He and his collaborators (30, 31, 32 33) have since developed this subject. 

Forces of interphase tension oti/t2 act at the contact surface between the two liquid phases of Ba(OH)2 (or Ca(OH)2) and -CV,Hi4. The thermodynamic condition for a liquid to spread over the surface of another liquid is [19]... 

All of the above actualizes the question about detection of thermodynamic conditions for conjugation reactions (4.2) and (4.7). Thermodynamic study of these reactions shows that the under-mentioned conditions (refer to Table 4.1) are quite executable and the equilibrium yield of N20, for example, equals 60%, whereas in the overall reaction (3) it equals 100%, but this reaction not known to be conjugated. 

In Section 7.1 we discussed the thermodynamic condition for a stable mixture given in the Flory-Huggins equation (Eq. 7.1-6), where AS denotes the increase of entropy due to mixing. This equation is based on Boltzmann s principle stating that the entropy of a... 

When a nonvolatile solute is dissolved in a volatile solvent, the solution is at equilibrium with the vapor phase. The thermodynamic condition for this equilibrium is ... 

Wc have so far studied only perfect gases and have not taken up imperfect gases, liquids, and solids. Before we treat them, it is really necessary to understand what happens when two or more phases are in equilibrium with each other, and the familiar phenomena of melting, boiling, and the critical point and the continuity of the liquid and gaseous states. We shall now proceed to find the thermodynamic condition for the coexistence of two phases and shall apply it to a general discussion of the forms of the various thermodynamic functions for matter in all three states. 

If the adsorption reaction can indeed be represented as a purely mechanical interaction, then from the thermodynamic conditions for equilibrium of systems in purely hydrostatic states of stress, we can deduce... 

The condition for the critical solubility point Tc can easily be derived from the thermodynamic conditions for a critical point ... 

The thermodynamic condition for secondary wetting described by equation (H.2) is expected to hold for many metal combinations and more seldomly for metal/ceramic couples. In practice, a detailed study of this phenomenon is difficult to perform because other phenomena can complicate the analysis. For example, dissolution of the solid in the liquid or diffusion of a component of the liquid in the solid could occur during prolonged experiments. In the last case, the liquid volume... 

Example 13.6 Order in time Thermodynamic conditions for chemical oscillations Consider the following set of reactions... 

Chain growth can only occur under suitable thermodynamic conditions. For the chains to have required properties, some chemical conditions must also be fulfilled. The possibility of the technical control of propagation depends on the rates of the respective reactions, i. e. on the kinetics of the process. 

If metals and alloys are brought in contact with gaseous, liquid or solid chemical agents, and if the thermodynamic conditions for a reaction are favorable, one observes a more or... 

An organic donor ligand (b -> c - d) like imidazole working as o-donor and jt-acceptor is the thermodynamic condition for binding and activating small molecules like O2 (c - e)... 

The thermodynamic condition for equilibrium of reaction step j at a point in a reactor system is... 

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