Extensive factors

An extensity factor—the total amount of surface area of filler per unit volume in contact with the elastomer. 

Another categorization of factors is based on their dependence on the size of a system. The value of an intensive factor is not a function of the size of the system. The value of an extensive factor is a function of the size of the system. 

The mass of a system, on the other hand, does depend on the size of the system and is therefore an extensive factor. Other examples of extensive factors are volume and heat content. 

List five extensive factors. List five intensive factors. How can the extensive factor mass be converted to the intensive factor density ... 

Klerman GL, DiMascio A, Weissman MM, et al Treatment of depression by drugs and psychotherapy. Am J Psychiatry 131 186-191, 1984 Kleven MS, Seiden LS D-, L- and DL-fenfluramine cause long-lasting depletions of serotonin in rat brain. Brain Res 505 351-353, 1989 Kligman D, Marshak D Purification and characterization of a neurite extension factor from bovine brain. Proc Natl Acad Sci U S A 82 7136-7139, 1985 Klimek V, Maj J Repeated administration of antidepressants enhances agonist affinity for mesolimbic D2 receptors. J Pharm Pharmacol 41 555-558, 1989 Klinkhamer P, Szelies B, Heiss WD Effect of phosphatidylserine on cerebral glucose metabolism in Alzheimer s disease. Dementia 1 197-201, 1990... 

Each term on the right-hand side is a product of an intensive factor (one that does not depend on the amount of matter in this system) and an extensive factor (one that does depend on the amount of matter in the system). Thus,... 

Keeping the intensive factors (T, p, y, d< >, i) constant, let the extensive factors be increased from their differential values to their absolute values for the system concerned, S, V, A, One now has for the energy of the system... 

Thus, the apparent change of state is equivalent to merely selecting two samples of the same state. In this way, one can see that the intensities (i.e., the shared Ty P of the coexisting phases) are the appropriate descriptors of the special state (condition) of the two-phase system, without regard to the arbitrarily chosen amounts of each phase (which are described rather trivially by extensive factors). It is essentially irrelevant for thermodynamic purposes whether we choose a thimble-full, a liter container, or an entire geyser pool of water to characterize this special state of the two-phase system. 

Equation (1.75) is a mathematical statement of the second law of thermodynamics for reversible processes. The introduction of the integrating factor for Sq causes the thermal energy to be split into an extensive factor. S and an intensive factor T. Introducing Eq. (1.75) into Eq. (1.56) yields the combined first and second laws... 

Kligman D, Marshak DR (1985) Puiificadon and characteiizadon of a neuiite extension factor from bovine brain. Proc Natl Acad Sci USA 82 7136-7139. 

A. E. Hirschler (Sun Oil Co., Marcus Hook, Pa. 19061) I should like to make a comment relating to your statement that activity is not a simple function of acidity. This statement appears to contain the implicit assumption that all acid sites able to protonate pyridine would have the same catalytic activity. Actually, one might expect an intensity factor (acid strength) to be operative in acid catalysis as well as an extensive factor, and the apparent lack of correlation you observed may result from an influence of acid strength on catalytic activity. Pyridine adsorption data alone do not completely define Bronsted acidity. One may need also some measure of acid strength. Acidity measurement with Hr indicators, such as we and others have reported, may supply useful information relative to acid strength as well as number of acid sites. 

Structure and Acidity of Zeolites. - Hall and cowoikers have expressed the total acidity of zeolites in terms of an extensive factor, representing the total number of acid sites in the zeolite, and an intensive factor, representative of the strength of the individual sites In a structurally pure H-zeolite, the nature of the acid site is easy to conceptualize, consisting of the bridging hydroxyl group between two tetrahedra, one centered on aluminum and the other on a silicon, viz. 

The purpose of this article is to review recent work concerning the characterization of the acid sites in zeolites, concentrating on the use of various techniques which can give detailed information concerning both the intensive and the extensive factors of acidity in zeolites. Due to the large number of papers being published in the area of zeolite catalysis, this review will certainly not be all-inclusive and the available literature will have greatly expanded by the time of publication. 

The role of any technique used for characterizing acidity is to give a quantitative measurement of the number of acid sites (extensive factor) and their strength (intensive factor). In addition, it should ideally be able to differentiate between Brpnsted and Lewis types of acid sites. Of the techniques most commonly used for this purpose, few are able to characterize the acid sites accurately and quantitatively. Thus, in most instances a combination of characterization techniques become necessary. 

Figure i Idealized TPD pattern for characterizing acid sites by desorption of a simple base like ammonia. Temperature at maximum gives Information on the Intensive factor area under the curves gives quantitative Information on the extensive factor. 

Calorimetry has not been used as extensively as other techniques and thus is perhaps not quite as acceptable to the research community as a reliable technique for characterizing acidity. Its ability to provide a quantitative measurement of the extensive factor, however, makes this technique quite powerful for the study of acid catalysts. 

NMR spectroscopy has shown much promise as a technique for characterizing acid sites. In theory, it should enable the direct characterization of both the intensive and extensive factors of acidity in zeolites. The current limitations of the techniques have to do with the instrumentation not allowing for sufficient resolution for complete analysis of the proton sites. New NMR instrumentation is currently being developed that should allow for more complex experiments with higher accuracy. 

To obtain a uniform distance between particles (the extensity factor)... 

In general, energy or work is the product of an intensive factor and an extensive factor. Intensive factors are those properties that are independent of the size of the system, such as temperature, pressure, odour and density. An extensive factor on the other hand is one which depends on the size of the system, such as mass, volume and internal energy. 

An easy way to deteremine whether a factor is intensive or extensive is to divide the system into two equal parts with a partition. Each part will have the same value of intensive factors as the original system, but half the value of the extensive factors. Mechanical energy = force x distance,... 

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