Subsystem available energy

Let us consider a part of discrete system with random fluxes. Since the free energy of a system with random fluxes is very large (in comparison with system close equilibrium), subsystems possessing the most large energy cannot be neglected, and one should evaluate their parameters. The minimum of available energy of subsystems with random fluxes can be approximately assumed equal zero. 

Analysis of Sub-processes. To determine the locations and magnitudes of the consumptions which comprise A5, one need only subdivide the system appropriately into subsystems, and then repeat the foregoing procedure. Thus, the boiler in this problem can be broken down into three separate processes 1) combustion, 2) heat transfer, and 3) dissipation of the stack gases. Each can be analyzed for its second law efficiency and the amount of available energy it consumes. 

System Available Energy. The available energy as commonly defined Q) and symbolized by A is a special case of system available energy, B. (As will be seen, A is called the subsystem available energy in this paper.)... 

Subsystem Available Energies. The purpose of this section is to show that subsystem available energies, A, can be defined such that the system available energy, B, of any system is equal to the sum of the subsystem available energies. That is, for any breakdown of the system into distinct subsystems... 

Consider the composite system shown in Fig. 3 where subsystems A and B can exchange entropy, volume, and components i = 1, The available energy of A is the same as that of... 

This definition allows Eq. 11 to be expressed in terms of subsystem available energies... 

Finally, it will be shown that subsystem available energy is an extensive property i.e., that A = A + Ag. 

Thus, for any object, its subsystem available energy equals the sum of the subsystem available energies of its parts, proving that A is extensive. 

It can also be shown (2J that the subsystem available energy changes as a result of transports and/or destructions of subsystem available energy i.e. 

The remainder of this article addresses the selection of available energy systems and subsystems as well as the choice of dead states for analyses of practical problems. 

The Selection of Reference Datums for Subsystem Available Energy. 

The definition of subsystem available energy, A, which is an extensive property, is crucial to practical Second Law efficiency analysis. Before a process, device, or system can be analyzed, it is necessary to ascertain (or assume or approximate) the dead states of all relevant materials and equipment. 

With this selection of Tf, Pf, and the total zAj, sunned over all the subsystems j besides tne ambient environment, does not represent the absolute system available energy. Rather... 

Consider an example of Evans, et al., which consists of three subsystems in an overall system, as shown in Figure 3a (14). Figure 3b shows the system with the subsystems separated and ready for economic optimization with the X s representing unit available energy values at the points indicated. To do this rigorously, the capital costs and input available energy rate of each subsystem must be expressed as functions of the output available energy rate and the decision variables X particular to that subsystem. 

Let us consider only two special cases among those considered by Evans, et al. (14). For the case in which the subsystem capital costs are insensitive to the output available energy rate and each subsystem cost depends only on the thermodynamic efficiency mi, then the result of the mathematical optimization is that Xj = cj,... 

Consider the situation where the subsystem capital costs increase linearly with output available energy,... 

It should be mentioned that other methods of design optimization, employing the Second Law for costing, have been used. For example, without explicitly determining the cost of available energy at each juncture of a system, in 1949 Benedict (see 19) employed the Second Law for optimal design. He determined the "work penalties" associated with the irreversibilities in an air separation plant. That is, the additional input of shaft power to the compressors required as a consequence of irreversibilities was determined from the entropy production in each subsystem. Associated with additional shaft power requirements are the costs of the power itself and the increased capital for larger compressors. 

Maintenance and Operation Decisions. The determination of an appropriate cost of available energy at various junctures of a system in a manner similar to that described above for Design Optimization is useful not only in design but also allows decisions regarding the repair or replacement of a specific subsystem to be readily made (9, 10). The amortized cost of such improvements can be easily compared with the cost of the additional available energy that will be dissipated if a component is left to operate in the given condition. The proper decision then becomes very apparent. 

As shown in Figure 1, the D C approach involves division of a large system into a set of smaller, overlapping subsystems S)t , a = 1,2,.., Nsuh- Ultimately, the goal is to obtain electronic information for each subsystem separately, then combine this information in such a way as to achieve an accurate description of the overall system. Since the density matrix P fully characterizes electronic structure, the focus of D C is to estimate P by assembling contributions P from each subsystem 9I . With P available, energies, gradients, and other properties may be computed just as they would in a conventional semiempirical MO calculation. 

The carrier-phonon interaction decreases with the lowering of temperature, since the emission and absorption of phonons by carriers is proportional to the number of final states available to carriers and phonons. At sufficiently low temperatures, the interaction between the two subsystems can be so weak that there is no thermal equilibrium between them, and the energy is distributed among electrons more rapidly than it is distributed to the lattice, resulting in a different temperature for electron and phonon subsystems, giving rise to the so-called electron-phonon decoupling . 

In contrast to the subsystem representation, the adiabatic basis depends on the environmental coordinates. As such, one obtains a physically intuitive description in terms of classical trajectories along Born-Oppenheimer surfaces. A variety of systems have been studied using QCL dynamics in this basis. These include the reaction rate and the kinetic isotope effect of proton transfer in a polar condensed phase solvent and a cluster [29-33], vibrational energy relaxation of a hydrogen bonded complex in a polar liquid [34], photodissociation of F2 [35], dynamical analysis of vibrational frequency shifts in a Xe fluid [36], and the spin-boson model [37,38], which is of particular importance as exact quantum results are available for comparison. 

Three flow sheets with consistent assumptions, and using commercially available equipment where possible, were developed. The flow sheets and mass and energy balances were used to generate sized equipment lists. Estimated costs for unit operations are based on industry databases for materials and labour, and on the estimates of technical experts from associated research and development programmes. Installation costs, including labour and field bulk materials, were estimated on a subsystem basis. 

In this case, as shown in Figure 4, the subsystems are stoichiometry, material balance, energy balance, chemical kinetics, and interphase mass transfer. The mass transfer phenomena can be subdivided into (1) phase equilibrium which defines the driving force and (2) the transport model. In a general problem, chemical kinetics may be subdivided into (1) the rate process and (2) the chemical equilibrium. The next step is to develop models to describe the subsystems. Except for chemical kinetics, generally applicable mathematical equations based on fundamental principles of physics and chemistry are available for describing the subsystems. 

Essential relations describing each subsystem are overall equations for mass balance, for energy balance, for performance, and for costing in terms of performance. Presently available cost trends (17) in terms of capacity parameters (e.g. area, mass rate, power,. ..) are suitable costing equations to start with. They may be implemented to include the influence of variables such as pressure, temperature or efficiency whenever sufficient data are available. 

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