Quantity, extensive

Quantities extensive, 54 intensive, 54 molar, 54 physical, 52 specific, 54... 

HCt (pH-2), unreacted chlorine amyl-phenol, sulfur monochlonde and sulfur dioxide in trace quantities, extensive aeration... 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

As in Section III-2A, it is convenient to suppose the two bulk phases, a and /3, to be uniform up to an arbitrary dividing plane S, as illustrated in Fig. Ill-10. We restrict ourselves to plane surfaces so that C and C2 are zero, and the condition of equilibrium does not impose any particular location for S. As before, one computes the various extensive quantities on this basis and compares them with the values for the system as a whole. Any excess or deficiency is then attributed to the surface region. 

Generally speaking, intermolecular forces act over a short range. Were this not the case, the specific energy of a portion of matter would depend on its size quantities such as molar enthalpies of formation would be extensive variables On the other hand, the cumulative effects of these forces between macroscopic bodies extend over a rather long range and the discussion of such situations constitutes the chief subject of this chapter. 

Both (E) and Cy are extensive quantities and proportional to N or the system size. The root mean square fluctuation m energy is therefore proportional to A7 -, and the relative fluctuation in energy is... 

By virtue of their simple stnicture, some properties of continuum models can be solved analytically in a mean field approxunation. The phase behaviour interfacial properties and the wetting properties have been explored. The effect of fluctuations is hrvestigated in Monte Carlo simulations as well as non-equilibrium phenomena (e.g., phase separation kinetics). Extensions of this one-order-parameter model are described in the review by Gompper and Schick [76]. A very interesting feature of tiiese models is that effective quantities of the interface—like the interfacial tension and the bending moduli—can be expressed as a fiinctional of the order parameter profiles across an interface [78]. These quantities can then be used as input for an even more coarse-grained description. 

The quantum phase factor is the exponential of an imaginary quantity (i times the phase), which multiplies into a wave function. Historically, a natural extension of this was proposed in the fonn of a gauge transformation, which both multiplies into and admixes different components of a multicomponent wave function [103]. The resulting gauge theories have become an essential tool of quantum field theories and provide (as already noted in the discussion of the YM field) the modem rationale of basic forces between elementary particles [67-70]. It has already been noted that gauge theories have also made notable impact on molecular properties, especially under conditions that the electronic... 

Local spin density functional theory (LSDFT) is an extension of regular DFT in the same way that restricted and unrestricted Hartree-Fock extensions were developed to deal with systems containing unpaired electrons. In this theory both the electron density and the spin density are fundamental quantities with the net spin density being the difference between the density of up-spin and down-spin electrons ... 

Place 84 g. of iron filings and 340 ml. of water in a 1 - 5 or 2-litre bolt-head flask equipped with a mechanical stirrer. Heat the mixture to boiling, stir mechanically, and add the sodium m-nitrobenzenesulphonate in small portions during 1 hour. After each addition the mixture foams extensively a wet cloth should be applied to the neck of the flask if the mixture tends to froth over the sides. Replace from time to time the water which has evaporated so that the volume is approximately constant. When all the sodium salt has been introduced, boU the mixture for 20 minutes. Place a small drop of the suspension upon filter paper and observe the colour of the spot it should be a pale brown but not deep brown or deep yellow. If it is not appreciably coloured, add anhydrous sodium carbonate cautiously, stirring the mixture, until red litmus paper is turned blue and a test drop upon filter paper is not blackened by sodium sulphide solution. Filter at the pump and wash well with hot water. Concentrate the filtrate to about 200 ml., acidify with concentrated hydrochloric acid to Congo red, and allow to cool. Filter off the metanilic acid and dry upon filter paper. A further small quantity may be obtained by concentrating the mother liquid. The yield is 55 g. 

Large quantities of zinc are used to produce die castings, which are used extensively by the automotive, electrical, and hardware industries. An alloy called Prestal(R), consisting of 78 percent zinc and 22 percent aluminum, is reported to be almost as strong as steel and as easy to mold as plastic. The alloy said to be so moldable that it can be molded into form using inexpensive ceramics or cement die casts. 

By far of greatest importance is the isotope Pu2sy with a half-life of 24,100 years, produced in extensive quantities in nuclear reactors from natural uranium 23su(n, gamma) —> 239U—(beta) —> 239Np—(beta) —> 239pu. Fifteen isotopes of plutonium are known. 

At first glance, the contents of Chap. 9 read like a catchall for unrelated topics. In it we examine the intrinsic viscosity of polymer solutions, the diffusion coefficient, the sedimentation coefficient, sedimentation equilibrium, and gel permeation chromatography. While all of these techniques can be related in one way or another to the molecular weight of the polymer, the more fundamental unifying principle which connects these topics is their common dependence on the spatial extension of the molecules. The radius of gyration is the parameter of interest in this context, and the intrinsic viscosity in particular can be interpreted to give a value for this important quantity. The experimental techniques discussed in Chap. 9 have been used extensively in the study of biopolymers. 

Sandstone. Sandstone wheels were once quarried extensively for farm and industrial use, and special grades of stone for precision honing, sharpening, and lapping are a small but important portion of today s abrasive industry. Production of honing and sharpening stones from deposits of dense, fine grain sandstone in Arkansas account for 76% of the value (about 2 million in 1987) and 88% of the total quantity of such stones in the United States (4). 

Although acetic acid and water are not beheved to form an azeotrope, acetic acid is hard to separate from aqueous mixtures. Because a number of common hydrocarbons such as heptane or isooctane form azeotropes with formic acid, one of these hydrocarbons can be added to the reactor oxidate permitting separation of formic acid. Water is decanted in a separator from the condensate. Much greater quantities of formic acid are produced from naphtha than from butane, hence formic acid recovery is more extensive in such plants. Through judicious recycling of the less desirable oxygenates, nearly all major impurities can be oxidized to acetic acid. Final acetic acid purification follows much the same treatments as are used in acetaldehyde oxidation. Acid quahty equivalent to the best analytical grade can be produced in tank car quantities without difficulties. 

Microchemical or ultramicrochemical techniques are used extensively ia chemical studies of actinide elements (16). If extremely small volumes are used, microgram or lesser quantities of material can give relatively high concentrations in solution. Balances of sufficient sensitivity have been developed for quantitative measurements with these minute quantities of material. Since the amounts of material involved are too small to be seen with the unaided eye, the actual chemical work is usually done on the mechanical stage of a microscope, where all of the essential apparatus is in view. Compounds prepared on such a small scale are often identified by x-ray crystallographic methods. 

Although the compounds were isolated in quantities of only a few milligrams per kilogram of cmde plant leaves, extensive work on a variety of animal tumor systems led to eventual clinical use of these bases, first alone and later in conjunction with other materials, in the treatment of Hodgkin s disease and acute lymphoblastic leukemia. Their main effect appears to be binding tightly to tubuHn, the basic component of microtubules found in eukaryotic cells, thus interfering with its polymerization and hence the formation of microtubules required for tumor proliferation (82). 

Other sources of energy worth noting are the extensive wind farms, solar projects, and related emerging unconventional technologies. These renewable resources provide only small quantities of energy to the U.S. economy as of this writing. 

Health nd Safety Factors. The toxicological and safety properties of xanthan gum have been extensively investigated (82). On the basis of these studies, the EDA issued a food additive order in 1969 that allowed the use of xanthan gum in food products without specific quantity limitations. 

---