The special case of equation (A2.1.27) when T and p are constant (dJ= 0, dp = 0) is called the Gibbs-Duhem equation, so equation (A2.1.27) is sometimes called the generalized Gibbs-Duhem equation . [Pg.345]

In the special case when a = 0, any symmetric 2-D tensor field can be represented as [Pg.134]

In the special case when a = 0 these measurements can be named as longitudinal, transversally longitudinal, and transverse measurement, respectively. These potentials can be reconstructed directly using the inverse Radon transform (5). [Pg.135]

For the special case of a bubble-point calculation (incipient vaporization), a is 0 (also Q = 0) and Equation (7-13) becomes [Pg.114]

Note that in this special case, the heat absorbed directly measures a state fiinction. One still has to consider how this constant-volume heat is measured, perhaps by an electric heater , but then is this not really work Conventionally, however, if work is restricted to pressure-volume work, any remaining contribution to the energy transfers can be called heat . [Pg.345]

Equation 11-3 is a special case of a more general relationship that is the basic equation of capillarity and was given in 1805 by Young [1] and by Laplace [2]. In general, it is necessary to invoke two radii of curvature to describe a curved surface these are equal for a sphere, but not necessarily otherwise. A small section of an arbitrarily curved surface is shown in Fig. II-3. The two radii of curvature, R and / 2

Rigid linear molecules are a special case in which an extended MS group, rather than the MS group, is isomorphic to the point group of the equilibrium structure see chapter 17 of [1]. [Pg.182]

A monolayer can be regarded as a special case in which the potential is a square well however, the potential well may take other forms. Of particular interest now is the case of multilayer adsorption, and a reasonable assumption is that the principal interaction between the solid and the adsorbate is of the dispersion type, so that for a plane solid surface the potential should decrease with the inverse cube of the distance (see Section VI-3A). To avoid having an infinite potential at the surface, the potential function may be written [Pg.627]

Equation (A2.1.21) includes, as a special case, the statement dS > 0 for adiabatic processes (for which Dq = 0) and, a fortiori, the same statement about processes that may occur in an isolated system (Dq = T)w = 0). If the universe is an isolated system (an assumption that, however plausible, is not yet subject to experimental verification), the first and second laws lead to the famous statement of Clausius The energy of the universe is constant the entropy of the universe tends always toward a maximum. [Pg.341]

Ss ) Pp are simultaneously zero for this special case, this point is at x = 1/2 and [Pg.627]

Only two of the many possible special cases need be considered. Thus if the products and reactants are weakly adsorbed, [Pg.727]

Although the exact equations of state are known only in special cases, there are several usefid approximations collectively described as mean-field theories. The most widely known is van der Waals equation [2] [Pg.443]

In order to specify fhe size of fhe sysfem, af leasf one of fhese variables ought to be extensive (one that is proportional to the size of the system, like n or the total volume V). In the special case of several phases in equilibrium several extensive properties, e.g. n and Vfor two phases, may be required to detennine the relative amounts of the two phases. The rest of the variables can be intensive (independent of the size of the system) like T,p, the molar volume V = V/n,or the density p. For multicomponent systems, additional variables, e.g. several ns, are needed to specify composifion. [Pg.322]

The final scattering angle 0 is defined rising 0 = 0(t = oo). There will be a correspondence between b and 0 that will tend to look like what is shown in figure A3.11.5 for a repulsive potential (liere given for the special case of a hard sphere potential). [Pg.995]

The volume fraction of water (S J and the saturation exponent n can be considered as expressing the increased difficulty experienced by an electrical current passing through a partially oil filled sample. (Note is only a special case of C, when a reservoir [Pg.148]

Flalf a century later Van Konynenburg and Scott (1970, 1980) [3] used the van der Waals equation to derive detailed phase diagrams for two-component systems with various parameters. Unlike van Laar they did not restrict their treatment to the geometric mean for a g, and for the special case of b = hgg = h g (equalsized molecules), they defined two reduced variables. [Pg.623]

Maxwell s equation are the basis for the calculation of electromagnetic fields. An exact solution of these equations can be given only in special cases, so that numerical approximations are used. If the problem is two-dimensional, a considerable reduction of the computation expenditure can be obtained by the introduction of the magnetic vector potential A =VxB. With the assumption that all field variables are sinusoidal, the time dependence [Pg.312]

Separation of mixtures of condensable and non-condensable components. If a fluid mixture contains both condensable and noncondensable components, then a partial condensation followed by a simple phase separator often can give a food separation. This is essentially a single-stage distillation operation. It is a special case that deserves attention in some detail later. [Pg.75]

If a surface reaction is bimolecular in species A and B, the assumption is that the rate is proportional to 5a x 5b- We now proceed to apply this interpretation to a few special cases. [Pg.724]

One serious issue is the detemihiation of the exchange energy per particle, e, or the corresponding exchange potential, V The exact expression for either of these quantities is miknown, save for special cases. If one [Pg.95]

For a long time the official specifications for diesel fuel set only a mciximum viscosity of 9.5 mm /s at 20°C. Henceforth, a range of 2.5 mm /s minimum to 4.5 mm /s maximum has been set no longer for 20°C but at 40°C which seems to be more representative of injection pump operation. Except for special cases such as very low temperature very fluid diesel fuel and very heavy products, meeting the viscosity standards is not a major problem in refining. [Pg.214]

© 2019 chempedia.info