Writing the

We can now consider the most convenient form for writing the liquid-phase fugacity of component i. First we consider a condensable component and write... 

As discussed in Chapter 2, for noncondensable components, the unsymmetric convention is used to normalize activity coefficients. For a noncondensable component i in a multicomponent mixture, we write the fugacity in the liquid phase... 

A group of eminent specialists was placed in charge of writing the series, with those involved being listed at the beginning of each relevant volume. We would like to thank all of them for their dynamic and even enthusiastic approach to this project. 

Maintenance costs account for a large fraction of the total operating expenditure (opex) of a project. Because of the bath tub curve mentioned above, maintenance costs typically increase as the facilities age just when the production and hence revenues enter into decline. The measurement and control of opex often becomes a key issue during the producing lifetime of the field as discussed in Section 14.0. However, the problem should be anticipated when writing the FDP. 

Finally, we write the boundary conditions in terms of the stress functions... 

Writing the electromagnetic field in terms of transverse electric (TE) and transverse magnetic (TM) components, the electric field has the form ... 

The problem of film flow is formulated on the assumption that the film thickness h is much smaller than the length 1 (in our case h/1 10 ). In Cartesian coordinates with transversal axis y and longitudinal one z we can write the equation for a film flow as follows ... 

Finally, we can write the signal S( x,y,t) received at time t and for the scanning position (x, y) (the x-axis being in the plane of incidence while the y-axis being normal to it) as an integral over the surface of the defect... 

The exact treatment of capillary rise must take into account the deviation of the meniscus from sphericity, that is, the curvature must correspond to the AP = Ap gy at each point on the meniscus, where y is the elevation of that point above the flat liquid surface. The formal statement of the condition is obtained by writing the Young-Laplace equation for a general point (x, y) on the meniscus, with R and R2 replaced by the expressions from analytical geometry given in... 

Capillary waves may be generated mechanically by means of an oscillating bar, and for this case one writes the solutions to Eqs. IV-25 and IV-26 in the form... 

The surface excess per square centimeter F is just n/E, where n is the moles adsorbed per gram and E is the specific surface area. By means of the Gibbs equation (111-80), one can write the relationship... 

The effect is to write the adsorption free energy or, approximately, the energy of adsoiption Q as a sum of electrostatic and chemical contributions. A review is provided by Ref. 156. 

The radioautographic work suggests another model illustrated in Fig. XII-11. The load is supported over area A, with metal contacts of shear strength s over a portion of the area ctA and film-film contacts of shear strength Sf over the rest of the area. In analogy to Eq. XII-9, one can write the total frictional force, F as... 

The nitrogen adsorption isotherm is determined for a finely divided, nonporous solid. It is found that at = 0.5, P/P is 0.05 at 77 K, gnd P/F is 0.2 at 90 K. Calculate the isosteric heat of adsorption, and AS and AC for adsorption at 77 K. Write the statement of the process to which your calculated quantities correspond. Explain whether the state of the adsorbed N2 appears to be more nearly gaslike or liquidlike. The normal boiling point of N2 is 77 K, and its heat of vaporization is 1.35 kcal/mol. 

An illustrative example is provided by investigating the possible momenta for a single particle travelling in the v-direction, p First, one writes the equation that defines the eigenvalue condition... 

For this simple Hamiltonian, let us write the many-body wavefunction as... 

One can quantify the pseudopotential by writing the total crystalline potential for an elemental solid as... 

Wlien we apply pemiiitations (or other syimnetry operations) successively (this is conmionly referred to as multiplying the operations so that (31) is the product of (123) and (12)), we write the operation to be applied first to the right hi the manner done for general quaiitum mechanical operators. Pemiiitations do not necessarily commute. For example. 

We use the nuclear pennutation operations (123) and (12) to show what happens when we apply two operations in succession. We write the successive effect of these two pennutations as (remember that we are using the N-convention see (equation A 1.4.14))... 

By definition, a synnnetry operation R connnutes with the molecular Hamiltonian //and so we can write the operator equation ... 

These limitations lead to electron spin multiplicity restrictions and to differing nuclear spin statistical weights for the rotational levels. Writing the electronic wavefunction as the product of an orbital fiinction and a spin fiinction there are restrictions on how these functions can be combined. The restrictions are imposed by the fact that the complete function has to be of synnnetry... 

Moreover, we will write the density matrix for the system as... 

To arrive at a dynamical interpretation of this diagram it is instructive to write the fomuila for the dominant tenn inP - explicitly ... 

The equation is more conventionally written expressing the variable n/V as the inverse of the molar volume, l/v, although nJVis just the molar concentration c, and one could equally well write the equation as... 

The value of the standard free energy AG depends on the choice of reference state, as does the equilibrium constant. Thus it would be safer to write the equilibrium constant K for a gaseous reaction as... 

Considering, for simplicity, only electrostatic interactions, one may write the solute-solvent interaction temi of the Hamiltonian for a solute molecule surrounded by S solvent molecules as... 

For a bimolecular reaction, this situation is easily illustrated by simply writing the reaction as a sequence of two steps... 

The generalization of the treatment of the previous section to the detennination of a wavepacket for the Hamiltonian in equation (A3.11.1) is accomplished by writing the solution as follows ... 

We call this a partial M/ave expansion. To detennine tire coefficients one matches asymptotic solutions to the radial Scln-ddinger equation with the corresponding partial wave expansion of equation (A3.11.106). It is customary to write the asymptotic radial Scln-ddinger equation solution as... 

If we write the time-dependent Sclnodinger equation as 5i i/(T = -(i/li)f7i i, then, after replacing the time derivative by a central difference, we obtain... 

This solution is appropriate for the regime of a weak driving field E(t). If we now treat the material as a collection of non-hiteracting oscillators, we may write the induced polarization as a sum of the individual... 

We may then write the amplitude for the hannonically varying polarization as proportional to the corresponding quantity for the driving field, E(oi) ... 

We then write the solution of equation B1.5.7 as a power series expansion hi temis of the strength X of the perturbation ... 

In analogy to equation Bl.5.3. we can write the steady-state solution to equation B 1.5.10 for tlie SFIG process as... 

Nuclear spin relaxation is caused by fluctuating interactions involving nuclear spins. We write the corresponding Hamiltonians (which act as perturbations to the static or time-averaged Hamiltonian, detemiming the energy level structure) in tenns of a scalar contraction of spherical tensors ... 

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