Work terms

If the surface is to be in mechanical equilibrium, the two work terms as given must be equal, and on equating them and substituting in the expressions for dx and dy, the final result obtained is... 

A consistent sign convention has been applied to the pressure-volume work term A positive dV corresponds to an expanded system, and work is done by the system to push back the surrounding atmosphere. 

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... 

Thus, an analysis of the lost work, made by calculation of the fraction that each individual lost-work term represents of the total lost work, is the same as an analysis of the rate of entropy generation, made by expressing each individual entropy-generation term as a fraclion of the sum of all entropy-generation terms. 

A work analysis gives each of the individual work terms on the right as a fraction of W. 

There are two work terms to consider when a nucleus forms from the liquid. Equations (6.1) and (6.2) show that work of the type AH (T, - T)/T, is available to help the nucleus form. If AH is expressed as the latent heat given out when unit volume of the solid forms, then the total available energy is (4/3)ot AH (T, - T)/T, . But this is offset by the work 4 rr ysL needed to create the solid-liquid interface around the crystal. The net work needed to form the crystal is then... 

If the work term W( is expanded to breakdown shaft work done to or from the system and the work done by the system, then... 

The enthalpy term h includes both internal energy and flow work terms. Since dw=0 between compressor stations, the equation becomes ... 

Ti = Temperature of the gas at the point of origin, °F W = Thermodynamic flow work term... 

If the heat transferred from the control volume is not used externally to create work, but is simply lost to the atmosphere in which further entropy is created, then Equj can be said to be equal to /quj, a lost work term, due to external irreversibility. Another form of Eq. (2.23) is thus... 

Kotas [3] has drawn a distinction between the environmental state, called the dead state by Haywood [1], in which reactants and products (each at po. To) are in restricted thermal and mechanical equilibrium with the environment and the truly or completely dead state , in which they are also in chemical equilibrium, with partial pressures (/)j) the same as those of the atmosphere. Kotas defines the chemical exergy as the sum of the maximum work obtained from the reaction with components atpo. To, [—AGo], and work extraction and delivery terms. The delivery work term is Yk k kJo ln(fo/pt), where Pii is a partial pressure, and is positive. The extraction work is also Yk kRkTo n(po/Pk) but is negative. 

In general, we shall not subsequently consider these extraction and delivery work terms here, but use [ —AGq] as an approximation to the maximum work output obtainable from a chemical reaction, since the work extraction and delivery quantities are usually small. Their relative importance is discussed in detail by Horlock et al. [4]. 

For the steam plant, the condenser pressure, the turbine and pump efficiencies are also specified there is also a single phase of water/steam heating, with no reheating. The feed pump work term for the relatively low pressure steam cycle is ignored, so that /ij, = /i. For the HRSG two temperature differences are prescribed ... 

This is essentially the approach adopted by Ruffi [9] in a comprehensive set of calculations, but he assumed that the economiser entry water temperature 7b is raised above the condenser temperature by feed heating, which was specified for all his calculations. The T,s diagram is shown in Fig. 7.6 the feed pump work terms are neglected so that h.j, = hy and h. = /ib. 

An important issue in the thermodynamics of confined fluids concerns their symmetry which is lower than that of a corresponding homogeneous bulk phase because of the presence of the substrate and its inherent atomic structure [52]. The substrate may also be nonplanar (see Sec. IV C) or may consist of more than one chemical species so that it is heterogeneous on a nanoscopic length scale (see Sec. VB 3). The reduced symmetry of the confined phase led us to replace the usual compressional-work term —Pbuik F in the bulk analogue of Eq. (2) by individual stresses and strains. The appearance of shear contributions also reflects the reduced symmetry of confined phases. 

PV work term = -RT since 1 mole of gas is lost in the reactions. 

Work interchange between a system and its surroundings can take on any of a variety of forms including mechanical shaft work, electrical work, magnetic work, surface tension, etc. For many applications, the only work involved is that of compression or expansion against the surroundings, in which case the work term in Equation 2-102 becomes... 

Since the surface energy term will usually be negligible by comparison with the plastic work term in the stress corrosion of ductile materials, it may be neglected. The remaining terms may be derived from fracture mechanics and conventional electrochemical conditions and, for the various boundary conditions indicated by West result in... 

Substitution into Eq. (10-83), still ignoring the work terms, gives... 

When R is CH3 the process is called methyl transfer. For such reactions, the work terms and are assumed to be very small compared to AG° and can be neglected, so that the Marcus equation simplifies to... 

Here, E is the total energy of the system, Ej is the energy per mole of component i, F is the volumetric flow rate, C is the molar concentration and S is the number of components (reactants and inerts). The work term can be separated into flow work and other work Ws, according to... 

Gibbs energy of electron transfer (AGe ) and the work terms for precursor formation (Wp) and successor dissociation (ws),... 

In subsequent works, Marcus developed his theory further in a series of papers providing expressions for the work terms, the reorganization energy and the macroscopic ET rate constants [3 6]. Assuming a sharp liquid-liquid boundary, the solution of the mean molar volume of reactants yields an expression for of the form... 

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 flat interface model employed by Marcus does not seem to be in agreement with the rough picture obtained from molecular dynamics simulations [19,21,64-66]. Benjamin examined the main assumptions of work terms [Eq. (19)] and the reorganization energy [Eq. (18)] by MD simulations of the water-DCE junction [8,19]. It was found that the electric field induced by both liquids underestimates the effect of water molecules and overestimates the effect of DCE molecules in the case of the continuum approach. However, the total field as a function of the charge of the reactants is consistent in both analyses. In conclusion, the continuum model remains as a good approximation despite the crude description of the liquid-liquid boundary. 

According to Marcus theory [69-71], in the absence of work terms, the Gibbs free energy of activation for an ET reaction is given by ... 

Electrical, and the mechanical forms of energy, are included in the work term in an energy balance. Electrical energy will only be significant in energy balances on electrochemical processes. 

In chemical processes, the kinetic and potential energy terms are usually small compared with the heat and work terms, and can normally be neglected. 

For many processes the work term will be zero, or negligibly small, and equation 3.7 reduces to the simple heat balance equation ... 

The work term in an energy balance is unlikely to be significant unless a gas is expanded or compressed as part of the process. To compute the pressure work term ... 

In most circumstances of interest to the designer of chemical reactors, the kinetic and potential energy effects are negligible as is the shaft work term. Under these circumstances,... 

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