Coupling, thermodynamic

In this section, a general formulation will be given for the effect of bubble residence-time and bubble-size distributions on simultaneous and thermodynamically coupled heat- and mass-transfer in a multicomponent gas-liquid dispersion consisting of a large number of spherical bubbles. Here one can... 

C14-0117. The notion of thermodynamic coupling of a nonspontaneous process with a spontaneous process is not restricted to chemical reactions. Identify the spontaneous and nonspontaneous portions of the following coupled processes (a) Water behind a dam passes through a turbine and generates electricity, (b) A gasoline engine pumps water from a valley to the top of a hill. 

The empirical valence bond (EVB) method of Warshel [19] has features of both the structurally and thermodynamically coupled QM/MM method. In the EVB method the different states of the process studied are described in terms of relevant covalent and ionic resonance structures. The potential energy surface of the QM system is calibrated to reproduce the known experimental... 

In this chapter the basic theory of the structurally coupled QM/MM is summarized. This is followed by some technical points important in the practical use of the method. In particular, details about the treatment of the QM/MM boundary are discussed. The thermodynamically coupled quantum mechanical/ free energy (QM/FE) method is then introduced. Some representative applications of QM/MM methods are then described. The examples are selected to provide a representative picture of the potential applications of QM/MM methods on studies of reaction mechanisms. Here there is special emphasis on recent advances in the computational methodologies and in the future developments needed to improve the applicability of the methods. 

The general features discussed so far can explain the complexity of these reactions alone. However, thermodynamic and kinetic couplings between the redox steps, the complex equilibria of the metal ion and/or the proton transfer reactions of the substrate(s) lead to further complications and composite concentration dependencies of the reaction rate. The speciation in these systems is determined by the absolute concentrations and the concentration ratios of the reactants as well as by the pH which is often controlled separately using appropriately selected buffers. Perhaps, the most intriguing task is to identify the active form of the catalyst which can be a minor, undetectable species. When the protolytic and complex-formation reactions are relatively fast, they can be handled as rapidly established pre-equilibria (thermodynamic coupling), but in any other case kinetic coupling between the redox reactions and other steps needs to be considered in the interpretation of the kinetics and mechanism of the autoxidation process. This may require the use of comprehensive evaluation techniques. 

CHAPTER 2 IRREVERSIBLE THERMODYNAMICS COUPLED FORCES AND FLUXES... 

The second law requires that the total entropy production in a system of several reactions be positive for a closed system removed from equilibrium. However, in the case of thermodynamic coupling of reactions (26), it is not necessary that individual reaction entropy productions be positive. Apparently such reaction systems have not yet been considered in connection with natural water systems. 

GEMC utilizes two simulation subsystems ( boxes ) though physically separate, the two boxes are thermodynamically coupled through the MC algorithm, which allows them to exchange both volume and particles subject to the constraint that the total volume and number of particles remain fixed. Implementing these updates (in a way that respects detailed balance) ensures that the two systems will come to equilibrium at a common temperature, pressure, and chemical potential. The temperature is fixed explicitly in the MC procedure but the procedure itself selects the chemical potential and pressure that will secure equilibrium. 

With its unique simplified approach to thermodynamics coupled with its discussions of the historical and conceptual development of the field, this text is ideal for both undergraduate and (graduate students in physical chemistry, chemical engineering, thermal physics, and materials sciences. 

Mobility close to bulk water for part and perhaps most of hydration water. Mobile bound ligand r = 7 x 10"10 s. Enzymatic activity l/10th solution value. Full internal motions of protein. Dynamic and thermodynamic coupling between hydration water and protein... 

This phenomenon shows that decrease or absorption of entropy in subsystem II may be compensated by a larger entropy production in subsystem I. This is possible only if subsystems I and n are coupled by some suitable coupling mechanisms leading to dS dS I <7.S II>0. With thermodynamic coupling a process in subsystem n may progress in a direction contrary to that determined by its own thermodynamic force. Some biological reactions represent coupled reactions for which the total entropy production is positive. 

We consider the general balance equations of mass and energy in the absence of chemical reactions, and electrical, magnetic and viscous effects. The partial differential equations of these general balance equations represent the mathematically and thermodynamically coupled phenomena, which may describe some complex behavior due to interactions among various forces and flows within a system. 

Equation (7.206) disregards the small contribution to the heat flow arising from the kinetic energy of the Brownian particles. Equation (7.206) is mathematically and thermodynamically coupled and describes specifically the coupled evolutions of the temperature field and the velocity-coordinate probability distribution of the Brownian particles. However, for larger times than the characteristic time /3 1, the system is in the diffusion and thermal diffusion regime. 

Some structures can only originate in a dissipative (nonequilibrium) medium and be maintained by a continuous supply of energy and matter. Such dissipative structures exist only within narrow limits due to the delicate balance between reaction rates and diffusion. If one of these factors is changed, then the balance is affected and the whole organized structure collapses. In a system of two simultaneous reactions, thermodynamic coupling allows one of the reactions to progress in a direction contrary to that imposed by its own affinity, provided that the total dissipation is positive. 

Table 9.1. Parameters for some exothermic reactions used in the thermodynamically coupled model...

Equations (9.69) and (9.70) represent the modeling of reaction-diffusion systems with the thermodynamically coupled heat and mass flows excluding the coupling effects due to reaction. After combining Eqs. (9.64), (9.69), and (9.70) steady-state balance equations with the coupled heat and mass transfer become... 

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