Open systems defined

Figure 2.1 Flow (open) system defined for combustion.

The saturation parameter defined by (2.11) for the open two-level system is more general than that defined in Vol. 1, (3.67d) for a closed two-level system. The difference lies in the definition of the mean relaxation probability, which is P = (Pi + P2)/2 in the closed system but R = PiP2/(Pi -I- P2) in the open system. We can close our open system defined by the rate equations (2.8a-2.8c) by setting Cl = R2N2, C2 = PiVi, and Ni + N2 = N = const, (see Fig. 2.2b). The rate equations then become identical to Vol. 1, (3.66) and R converts to P. 

We deal directly with the general case. Consider an open system defined by the domain of external coordinates, with boundary consisting of an inlet domain which admits the particle-fluid mixture into the system, and an outlet domain through which the mixture exits the system. We... 

We make use of the previously defined parameters of the one-compartment open system (eq. (39.6)). 

Whether a reaction is spontaneous or not depends on thermodynamics. The cocktail of chemicals and the variety of chemical reactions possible depend on the local environmental conditions temperature, pressure, phase, composition and electrochemical potential. A unified description of all of these conditions of state is provided by thermodynamics and a property called the Gibbs free energy, G. Allowing for the influx of chemicals into the reaction system defines an open system with a change in the internal energy dt/ given by ... 

The first and most critical step in developing a geochemical model is conceptualizing the system or process of interest in a useful manner. By system, we simply mean the portion of the universe that we decide is relevant. The composition of a closed system is fixed, but mass can enter and leave an open system. A system has an extent, which the modeler defines when he sets the amounts of fluid and mineral considered in the calculation. A system s extent might be a droplet of rainfall, the groundwater and sediments contained in a unit volume of an aquifer, or the world s oceans. 

There is no restriction against applying polythermal models in open systems. In this case, the modeler defines mass transfer as well as the heating or cooling rate in terms of . Realistic models of this type can be hard to construct (e.g., Bowers and Taylor, 1985), however, because the heating or cooling rates need to be balanced somehow with the rates of mass transfer. 

The rate of feed vf (in mol 1 1 s ) of the reactant into the reaction medium is now the critical parameter to adjust for a favourable outcome of a cyclisa-tion experiment. A kinetic treatment of the open system under influxion incurs the same difficulties already discussed for the closed system in Section 2. However, when the higher-order polymerisation terms are relatively unimportant and the overall process is described to a useful approximation by (6), an exact mathematical solution is possible (Galli and Mandolini, 1975). After a relatively short initial time9, the concentration of M reaches a steady value [M]st given by (72), where (3 defined by (73) is a dimensionless parameter... 

The charge associated with a given atom is an often used and important concept, but one that has physical meaning only when defined for a bounded, open system. The atomic charge for an atom A, denoted by q(A), is defined as q(A) = ZA-N(A), the dif-... 

A control volume is a volume specified in transacting the solution to a problem typically involving the transfer of matter across the volume s surface. In the study of thermodynamics it is often referred to as an open system, and is essential to the solution of problems in fluid mechanics. Since the conservation laws of physics are defined for (fixed mass) systems, we need a way to transform these expressions to the domain of the control volume. A system has a fixed mass whereas the mass within a control volume can change with time. 

In open systems consisting of several components the thermodynamic properties of each component depend on the overall composition in addition to T and p. Chemical thermodynamics in such systems relies on the partial molar properties of the components. The partial molar Gibbs energy at constantp, Tand rij (eq. 1.77) has been given a special name due to its great importance the chemical potential. The corresponding partial molar enthalpy, entropy and volume under the same conditions are defined as... 

In order to define the surface tension we will consider the change in internal energy connected with a reversible change in the system. For an open system dU is given by eq. (1.79) as... 

Since the definitions given by Equations 2.5 and 2.6 require the energy to be well defined for noninteger number of electrons and to be differentiable with respect to N, let us present first the extension of DFT to open systems that can exchange electrons with its environment, developed by Perdew, Parr, Levy, and Balduz (PPLB) [23]. 

The inverse of H determines the geometric compliance matrix (Nalewajski, 1993, 1995, 1997, 1999, 2000, 2002b, 2006a,b Nalewajski and Korchowiec, 1997 Nalewajski et al., 1996, 2008) describing the open system in the Qi,F)-representation. The relevant thermodynamic potential is defined by the total Legendre transform of the system BO potential, which replaces the state-parameters (N, Q) with their energy conjugates (/a, F), respectively ... 

An electrocyclic reaction is defined as a concerted closure of a ring starting from a conjugated open system in which a k orbital is converted into a o orbital. It is therefore an example of intramolecular cycloaddition or retroaddition. 

Following the mass-flux equations developed for open-system magma ehambers by DePaolo (1981), we will define a flux ratio of Fe(II) into tbe pool relative to Fe(III) out of tbe pool as ... 

But the major physical problem remained open Could one prove rigorously that the systems studied before 1979—that is, typically, systems of N interacting particles (with N very large)—are intrinsically stochastic systems In order to go around the major difficulty, Prigogine will take as a starting point another property of dynamical systems integrability. A dynamical system defined as the solution of a system of differential equations (such as the Hamilton equations of classical dynamics) is said to be integrable if the initial value problem of these equations admits a unique analytical solution, weekly sensitive to the initial condition. Such systems are mechanically stable. In order to... 

The domain of living organisms is unified by the commonality of cells and in terms of mutual energy dependence. Living organisms are open systems that create order at the expense of disorder in the environment. Life can be defined by a series of characteristics, including evolved programs and chemical properties. 

Given that, in the snbsnrface, we are dealing with an open system, the fundamental eqnation may be applied only when the macroscopic system is decoupled in isolated, well-defined systems. As an example, we can consider that an adiabatic zone of the snbsnrface solid phase is in contact with an aqneous solntion throngh a rigid barrier, snrronnded by an insnlating wall. 

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