Quantity lower range value

One should not adhere to the mistaken notion that the analysis of subsection (a) can be used in the upper range of xA values and that the analysis of subsection (b) for the same solution can then be used in the lower range. The two approaches are based on different standard states (i.e. P versus P, as discussed earlier) and therefore are not interchangeable or interrelated. Further, one must stay with one scheme or the other to obtain internally consistent results. It is just more convenient to apply methodology (b) if one is interested primarily in the thermodynamic characterization of solutes in dilute solution, and methodology (a) if one wishes to analyze the properties of solvents. This discussion again points to the fact (see also subsection (e) below) that it is only the differences in the chemical potential themselves that are unique in value all other quantities must be determined self-consistently. 

See algebra. 2. The range between the limits within which a quantity is measured. It is expressed by stating the lower and upper range values. 

The summary given in Fig. 13.25 indicates that the thermodynamic interaction between polymer and solvent plays an important role in governing growth from dilute solution. A better solvent, with a lower xi value, will expand the coil and reduce intramolecular segmental interaction. In contrast, the coil will contract in a poorer solvent and intramolecular interactions will become enhanced. The relation between the nominal concentration and the effective concentration, the quantity needed for nucleation theory, will also be affected by the nature of the solvent. There has not been very much attention paid to this important aspect of the problem. Studies with poorer solvents, in the lower molecular weight range, could be illuminating. The influence of cilia is minimal under these circumstances so that the role of solvent could be assessed independently. The source of the chain units that form the nucleus, i.e. from either within a molecule or between molecules, or proportional between them, needs to be elucidated. 

Thin hardwood plywood in the range of 4.5—6.0 mm (3/16—1 /4 in.) was normally a three-ply constmction with a thin, medium-quaHty back ply, a thicker lower value core, and another thin, high quaHty decorative face veneer. These panels were used as wall paneling, door facings, or for fumiture/cabinet appHcations requiring thin panels. Currently, only relatively small quantities of these types of panels are produced in the United States. 

Furthermore, accidental vapor cloud explosions are anything but detonations of the full amount of available fuel. Therefore, practical values for TNT equivalencies of vapor cloud explosions are much lower than the theoretical upper limit. Reported values for TNT equivalency, deduced from the damage observed in many vapor cloud explosion incidents, range from a fraction of one percent up to some tens of percent (Gugan 1978 and Pritchard 1989). For most major vapor cloud explosion incidents, however, TNT equivalencies have been deduced to range from 1% to 10%, based on the heat of combustion of the full quantity of fuel released. Apparently, only a small part of the total available combustion energy is generally involved in actual explosive combustion. 

Inventory ranges are indicators to make different businesses comparable. Commodity businesses of high volumes can be compared using the quantity-based inventory range. Specialty businesses with lower volumes of higher value with regard to commodity businesses can be compared with commodity inventory ranges, if sales and inventory values are considered. 

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