Extensive property, concept

The most important new concept to come from thermodynamics is entropy. Like volume, internal energy and mole number it is an extensive property of a system and together with these, and other variables it defines an elegant self-consistent theory. However, there is one important difference entropy is the only one of the extensive thermodynamic functions that has no obvious physical interpretation. It is only through statistical integration of the mechanical behaviour of microsystems that a property of the average macrosystem, that resembles the entropy function, emerges. 

The conservation laws are often based on a rather simple and intuitive concept. They state the rate of accumulation of an extensive property of a system is equal to the net (incoming minus outgoing) transport rate of the property across the surfaces that bound the system plus the net (creation minus destruction) rate of internal generation of the property... 

The most fruitful and extensively used concept along these lines is the concept of an ideal reactor. The simplest reactor, whose performance is governed by the so-called zero dimensional equation is a completely mixed reactor . The key assumption is that mixing in the reactor is complete, so that the properties of the... 

The mole concept, together with Avogadro s number, provides important connections among the extensive properties mass of substance, number of moles of substance, and number of molecules or ions. These are summarized as follows. 

Extensive properties of solutions are those that depend upon the quantity of material in the system with which we are dealing. These properties can be readily handled by considering the contribution of each component separately using the concept of partial molar properties. A partial molar property of a particular component is that portion of the total extensive property of... 

The system is defined by the fluid mass within the control volume at the initial time t. The values of the analogous extensive properties of the system and the fluid within control volume are thus equal at this time, tf sys(to) = cv to)-A short time later a portion of the system fluid may have exited from the control volume and some of the surrounding fluid may have entered the control volume. Then we seek to determine how the rate of change of [ sys within the system is related to the rate of change of [ cv within the control volume at any instant. Based on a physical understanding of the concepts of the system and control volume motion, the kinematic Reynolds transport theorem relating system concepts to control volume concepts can be derived by geometrical analysis. 

Intensive properties should not be directly correlated with an extensive property such as %. It is much more reasonable to scale the values of the % indices in an appropriate manner and convert them to a set of intensive indices to be used in developing correlations for intensive properties. Scaling is a familiar concept in polymer physics, and is used in many different contexts [3], The very simple manner in which we will use a version of scaling in this manuscript is one more context for the application of this very useful concept. 

The difference U - TS = F characterizes extensive property, which is called isochrone-isothermal potential. This concept was introduced in 1882 by Herman Ludwig Ferdinand von Helmholtz (1821-1894). As heat TS is considered associated energy, he called it free energy. Often this potential is called Helmholtz free energy. Therefore, under isochrone-iso-thermal conditions maximum useful work is the function of free energy, or Helmholtz energy, change ... 

In order to gain insight into the significance of a partial molar quantity as defined by Eq. 9.2.1, let us first apply the concept to the volume of an open single-phase system. Volume has the advantage for our example of being an extensive property that is easily visualized. Let the system be a binary mixture of water (substance A) and methanol (substance B), two liquids that mix in all proportions. The partial molar volume of the methanol, then, is the rate at which the system volume changes with the amount of methanol added to the mixture at constant temperature and pressure Fb = dV/dn )T,p,riA-... 

To extract infomiation from the wavefimction about properties other than the probability density, additional postulates are needed. All of these rely upon the mathematical concepts of operators, eigenvalues and eigenfiinctions. An extensive discussion of these important elements of the fomialism of quantum mechanics is precluded by space limitations. For fiirther details, the reader is referred to the reading list supplied at the end of this chapter. In quantum mechanics, the classical notions of position, momentum, energy etc are replaced by mathematical operators that act upon the wavefunction to provide infomiation about the system. The third postulate relates to certain properties of these operators ... 

The concept of two-state systems occupies a central role in quantum mechanics [16,26]. As discussed extensively by Feynmann et al. [16], benzene and ammonia are examples of simple two-state systems Their properties are best described by assuming that the wave function that represents them is a combination of two base states. In the cases of ammonia and benzene, the two base states are equivalent. The two base states necessarily give rise to two independent states, which we named twin states [27,28]. One of them is the ground state, the other an excited states. The twin states are the ones observed experimentally. 

Extension of the appHcations of polymethine dyes has required special spectral and other characteristics. As a rule, the search for and synthesis of promising new compounds having desired properties imply the preliminary estimation of their most important parameters on the basis of elaborated theoretical conceptions. Thus, an effective way of governing electron properties consists of the variation of molecular topology of polymethines. 

The most striking feature of the earth, and one lacking from the neighboring planets, is the extensive hydrosphere. Water is the solvent and transport medium, participant, and catalyst in nearly all chemical reactions occurring in the environment. It is a necessary condition for life and represents a necessary resource for humans. It is an extraordinarily complex substance. Stmctural models of Hquid water depend on concepts of the electronic stmcture of the water molecule and the stmcture of ice. Hydrogen bonding between H2O molecules has an effect on almost every physical property of Hquid water. 

In this situation computer simulation is useful, since the conditions of the simulation can be chosen such that full equihbrium is established, and one can test the theoretical concepts more stringently than by experiment. Also, it is possible to deal with ideal and perfectly flat surfaces, very suitable for testing the general mechanisms alluded to above, and to disregard in a first step all the complications that real substrate surfaces have (corrugation on the atomistic scale, roughness on the mesoscopic scale, surface steps, adsorbed impurities, etc.). Of course, it may be desirable to add such complications at a later stage, but this will not be considered here. In fact, computer simulations, i.e., molecular dynamics (MD) and Monte Carlo (MC) calculations, have been extensively used to study both static and dynamic properties [11] in particular, structural properties at interfaces have been considered in detail [12]. 

The literature on catalytic hydrogenation is very extensive, and it is tempting to think that after all this effort there must now exist some sort of cosmic concept that would allow one to select an appropriate catalyst from fundamentals or from detailed knowledge of catalyst functioning. For the synthetic chemist, this approach to catalyst selection bears little fruit. A more reliable, quick, and useful approach to catalyst selection is to treat the catalyst simply as if it were an organic reagent showing characteristic properties in its catalytic behavior toward each functionality. For this purpose, the catalyst is considered to be only the primary catalytic metal present. Support and... 

The properties of barrier layers, oxides in particular, and the kinetic characteristics of diffusion-controlled reactions have been extensively investigated, notably in the field of metal oxidation [31,38]. The concepts developed in these studies are undoubtedly capable of modification and application to kinetic studies of reactions between solids where the rate is determined by reactant diffusion across a barrier layer. 

The counterflow configuration has been extensively utilized to provide benchmark experimental data for the study of stretched flame phenomena and the modeling of turbulent flames through the concept of laminar flamelets. Global flame properties of a fuel/oxidizer mixture obtained using this configuration, such as laminar flame speed and extinction stretch rate, have also been widely used as target responses for the development, validation, and optimization of a detailed reaction mechanism. In particular, extinction stretch rate represents a kinetics-affected phenomenon and characterizes the interaction between a characteristic flame time and a characteristic flow time. Furthermore, the study of extinction phenomena is of fundamental and practical importance in the field of combustion, and is closely related to the areas of safety, fire suppression, and control of combustion processes. 

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