Evaluating the Work Term

It is customary to separate the work term, IV, into flow work and other work, tVs- The term H i. often referred to as the shaft work, could be produced from such things as a stirrer in a CSTR or a turbine in a PFR. Flosv work is work that is necessary to get the mass into and out of the system. For example, when shear stresses are absent, we write 

Let s look at the units of the flow work term, which is 

We see that the units for flow work are consistent with the other terms in Equation (8-2), i.e., J/s. 

In most instances, the flow work term is combined with those terms in the energy balance that represent the energy exchange by mass flow across the system boundaries. Substituting Equation (8-4) into (8-3) and grouping terms, we have 

The energy Ej is the sum of the internal energy ((/(), the kinetic energy (h, /2), the potential energy (gZj), and any other energies, such as electric or 

In almost all chemical reactor situations, the kinetic, potential, and other energy terms are negligible in comparison with the enthalpy, heat transfer, and work terms, and hence will be omitted that is. 

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The nonconvective energy flux across the boundary is composed of two terms a heat flux and a work term. The work term in turn is composed of two terms useful work deflvered outside the fluid, and work done by the fluid inside the control volume B on fluid outside the control volume B, the so-called flow work. The latter may be evaluated by imagining a differential surface moving with the fluid which at time 2ero coincides with a differential element of the surface, S. During the time dt the differential surface sweeps out a volume V cosdSdt and does work on the fluid outside at a rate of PV cos dS. The total flow work done on the fluid outside B by the fluid inside B is... 

The work term IF is restricted to the mechanical work deflvered to the outside via normal and shear forces acting on the boundary. Electrochemical work, ie, by electrolysis of the fluid, is excluded. Evaluation of the integral requires knowledge of the equation of state and the thermodynamic history of the fluid... 

The improvement of the quality of a design is seen as the primary need of industry, but to facilitate this we need appropriate methods for predicting quality and evaluating the long-term quality of an engineer s design (Morup, 1993 Russell and Taylor, 1995 Shah, 1998 Taguchi et al., 1989). However, there is relatively little work... 

The first term is due to the irreversible expansion from V, to Vj, and the second term to the isentropic expansion from Vj to Vj. Adamczyk does not actually say how p3 should be chosen. A reasonable choice for seems to be the initial-peak shock overpressure, as calculated from Eq. (6.3.22). The equation presented above can be compared to the results of Guirao et al. (1979). They numerically evaluated the work done by the expanding contact surface. When the difference between... 

In order to fully evaluate Eq. (17), expressions involving the outer-sphere reorganization term A,q, as well as the work terms, were also established [5],... 

The extent to which steric effects adversely affect the attainment of such intimate ion-pair structures would be reflected in an increase in the work term and concomitant diminution of the inner-sphere rate. This qualitative conclusion accords with the reactivity trend in Figure 16. However, Marcus theory does not provide a quantitative basis for evaluating the variation in the work term of such ion pairs. To obtain the latter we now turn to the Mulliken theory of charge transfer in which the energetics of ion-pair formation evolve directly, and provide quantitative informa-... 

Evaluation of the Work Term from Charge Transfer Spectral Data. The intermolecular interaction leading to the precursor complex in Scheme IV is reminiscent of the electron donor-acceptor or EDA complexes formed between electron donors and acceptors (21). The latter is characterized by the presence of a new absorption band in the electronic spectrum. According to the Mulliken charge transfer (CT) theory for weak EDA complexes, the absorption maximum hv rp corresponds to the vertical (Franck-Condon) transition from the neutral ground state to the polar excited state (22). 

Figure 19, Variation of the work term Awp evaluated for various charge-transfer...

Plan. Evaluate Angas gaseous products- gaseous reactants The sign of the work term is opposite that of Awgas since w = -PAY = -AngasRT at constant P and T. 

The advantages of the fluctuation theory are that it does not require that clusters be spheres, they need not have sharply defined bounding surfaces, nor is an equilibrium between phases assumed. The disadvantage is a practical one how can the work term (defined later) be evaluated ... 

An alternate approach is to evaluate the unknown terms of Equation 3.30, (8S, q")1. Several expressions can be found in the literature, where the original solutions were presented by DeRis [16] and Tarifa et al. [20], The following expression was obtained from the work by Femandez-Pello [21] ... 

The last term in Eq. (2.17) that has to be considered is the work term. This work is done by the fluid on the control volume by virtue of the forces exerted by the flowing fluid on the surface of the control volume. These forces arise due to the normal pressure and due to the previously discussed shearing stresses on its surface. The way in which this work is done and die way in which the work term is evaluated are perhaps most easily seen by considering the control volume to be moving through the fluid which is at rest. 

Notice that in Eq. (1.16.4) there is now no explicit reference to any heat flow from or to the surroundings. Rather, emphasis is placed on the work term 3W, which can always be either measured or calculated by the methodology of Section 1.7. In fact, we will presently show how the calculation of 3W under a variety of constraints permits one to evaluate certain thermodynamic functions of state that are of general interest. Also, we show how one can ascertain whether physical system are at equilibrium or not. Namely,... 

Both pseudo-rate constants may then be evaluated from a suitable description of the work terms Wr(x) and Wp(x) necessary to bring the reactant centers or those of the products, respectively, from infinity to a distance x. When the work terms are negligible, straightforward integration of Eqs. (50) and (51) yields... 

As discussed in the introduction, many current-distrihution problems are not described by a simple, convection-diffusion equation or by Laplace s equations. Alavyoon era/. provided an example in which the coupled concentration and potential fields were solved throughout the entire computational domain, along with natural convection flow fields. The equations were solved by evaluating the nonlinear terms at the previous time step. Gu etal. provided an additional study that coupled charge and mass transfer to natural convection. This work is related to... 

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