Reversible work

Figure III-l depicts a hypothetical system consisting of some liquid that fills a box having a sliding cover the material of the cover is such that the interfacial tension between it and the liquid is zero. If the cover is slid back so as to uncover an amount of surface dJl, the work required to do so will he ydSl. This is reversible work at constant pressure and temperature and thus gives the increase in free energy of the system (see Section XVII-12 for a more detailed discussion of the thermodynamics of surfaces).

A number of more or less equivalent derivations of the electrocapillary Eq. V-49 have been given, and these have been reviewed by Grahame [113]. Lippmann based his derivation on the supposition that the interface was analogous to a parallel-plate condenser, so that the reversible work dG, associated with changes in area and in charge, was given by... 

Shuttleworth [26] (see also Ref. 27) gives a relation between surface free energy and stretching tension as follows. For an anisotropic solid, if the area is increased in two directions by dAi and dA2, as illustrated in Fig. VII-1, then the total increase in free energy is given by the reversible work against the surface stresses, that is. 

The force F which has to be applied to a molecular lever requires accurate knowledge of its position x if reversible work is to be perfonned. Specifying the positional accuracy as Ax, the uncertainty principle gives the energy requirement as... 

To compute tire work fVdone by the system, equation (C2.14.33) is integrated over the appropriate x interval. The first tenn on tire right-hand side yields tire reversible work IV and tire second tenn yields -A x I]. F. - F., for... 

Subtractive dye precursors (couplers) that could be immobilized in each of the silver containing layers were sought, so that dye formation in all layers could proceed simultaneously rather than successively. The first of these to be commercialized were in Agfacolor Neue and Ansco Color films, introduced soon after Kodachrome film. These reversal working films contained colorless couplers that were immobilized (ballasted) by the attachment of long paraffinic chains. The addition of sulfonic or carboxyUc acid groups provided the necessary hydrophilicity to make them dispersible as micelles in aqueous gelatin. 

As shown by Eq. (6) the PME is the reversible work done by the average force. It is possible to express relative values of the PME between different solute configurations X i and X2 using Eq. (6) and the reversible work theorem [4] ... 

G() is related to the reversible work of adhesion obtained using contact angle measurements, but in general is greater than W. This is because once an interface is formed and the adhesive solidifies, strain energy is required to mechanically disrupt the interface. This strain energy arises because of the physical connection between the attachment sites between the adhesive and the substrate and the connectivity between this interface and the adhesive bulk. 

W. quantifies the specific, discrete interactions that exist between a wetting liquid and a substrate. These interactions may be Van der Waals, acid-base, or covalent. The reversible work of adhesion is the product of the areal density of these interaction sites (or attachment points) and the energy per attachment point ... 

Eqs. 1-5 hold whether failure is interfacial or cohesive within the adhesive. Furthermore, Eq. 5 shows that the reversible work of adhesion directly controls the fracture energy of an adhesive joint, even if failure occurs far from the interface. This is demonstrated in Table 5, which shows the static toughness of a series of wedge test specimens with a range of adherend surface treatments. All of these samples failed cohesively within the resin, yet show a range of static toughness values of over 600%. 

For an open circuit (non-cyclic) gas turbine plant (Fig. 1.3) a different criterion of performance is sometimes used—the rational efficiency (tjr). This is defined as the ratio of the actual work output to the maximum (reversible) work output that can be achieved between the reactants, each at pressure (po) and temperature (To) of the environment, and products each at the same po. Tq. Thus... 

The maximum (reversible) work obtained from the inner control volume CV is therefore equal to... 

Under this new arrangement, Eq. (2.15) for the reversible work delivered from CV would become... 

The (maximum) reversible work in steady flow between reactants at an entry state Rq(Po, Tq) and products at a leaving state Pq(po, Tq) is... 

The thermal efficiency, the work output as a fraction of the fuel exergy (the maximum reversible work), is shown as no. 1 in the figure and is 0.368. The internal irreversibility terms, are shown as nos. 2, 3, and 4 in the diagram, for the combustion... 

This expression shows that the maximum possible useful work (i.e., reversible work) that can be obtained from any process occurring at constant temperature and pressure is a function of the initial and final states only and is independent of the path. The combination of properties U + PV - TS or H - TS occurs so frequently in thermodynamic analysis that it is given a special name and symbol, F, the free energy (sometimes called the Gibbs Free Energy). Using this definition, Equation 2-143 is written... 

Thus, in an isothermal reversible process, dA equals the reversible work. Note that <5vr in equation (3.92) is the total work. It includes pressure-volume work and any other forms, if present."1... 

If the process is conducted reversibly, dQ = TdS where S is the entropy of the elastic body. Substitution of this expression for dQ in Eq. (5) will require dW to represent the element of reversible work. In order to comply with this requirement, the coefficients P and / in Eq. (6) must be assigned their equilibrium values. In particular, / will henceforth represent the equilibrium tension for a given state of the system, which may be specified variously by aS, F, and L, by T, F, and L, or by T, P, and L. Then... 

Mills G, Jonsson H, Schenter GK. 1995. Reversible work transition state theory application to dissociative adsorption of hydrogen. Surf Sci 324 305-337. 

Fig. 3. Current efficiency for hydrogen separation. Calculated overall energy efficiency vs. current density of hydrogen purification for conditions of Table 1 including reversible work O excluding reversible work.

The equality is valid if the control parameter is changed reversibly, i.e., if the system is in equilibrium at all times during the transformation. Equivalently, this result can be stated as the maximum work theorem [34] the amount of work delivered by a system during a transformation from a specific initial to a specific final state is always smaller than the free energy difference between the initial and final states. The work is maximum and equal to the free energy difference for a reversible process, hence the term reversible work for the equilibrium free energy. 

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