Systems, ideal

For systems with mutual miscibility in the solid phase - so-called solid solutions - Eq. (8.9) has to be used instead Eq. (8.10). In the case of ideal systems (y, = 1) the concentrations and of the liquidus and solidus line in the whole concentration range can directly be determined from the melting temperatures Tmj and the enthalpies of fusion Ahm.i of the compounds involved. For compounds 1 and 2 of a binary system the following expressions are obtained  

Calculate the SLE data of the system anthracene (l)-phenanthrene (2), assuming that both the liquid and the solid phase behave ideally. 

In this example the calculation is performed for a temperature of 430 K. Using Eq. (8.16) one obtains 

Using this value for Xi directly the mole fraction in the liquid phase can be calculated  

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The cost of shaftwork required to run a refrigeration system can be estimated approximately as a multiple of the shaftwork required for an ideal system. The performance of an ideal system is given by... 

A2.2.4.6 APPLICATION TO IDEAL SYSTEMS BLACK BODY RADIATION... 

Figure A2.2.3. Planck spectral density fimction as a fimction of the dimensionless frequency /)oi/(/rj 7). A2.2.4.7 APPLICATION TO IDEAL SYSTEMS ELASTIC WAVES IN A SOLID...

This is an example of a classical non-ideal system for which the PF can be deduced exactly [13]. Consider N hard rods of length [Pg.459]

Clusters are intennediates bridging the properties of the atoms and the bulk. They can be viewed as novel molecules, but different from ordinary molecules, in that they can have various compositions and multiple shapes. Bare clusters are usually quite reactive and unstable against aggregation and have to be studied in vacuum or inert matrices. Interest in clusters comes from a wide range of fields. Clusters are used as models to investigate surface and bulk properties [2]. Since most catalysts are dispersed metal particles [3], isolated clusters provide ideal systems to understand catalytic mechanisms. The versatility of their shapes and compositions make clusters novel molecular systems to extend our concept of chemical bonding, stmcture and dynamics. Stable clusters or passivated clusters can be used as building blocks for new materials or new electronic devices [4] and this aspect has now led to a whole new direction of research into nanoparticles and quantum dots (see chapter C2.17). As the size of electronic devices approaches ever smaller dimensions [5], the new chemical and physical properties of clusters will be relevant to the future of the electronics industry. 

The full quantum mechanical study of nuclear dynamics in molecules has received considerable attention in recent years. An important example of such developments is the work carried out on the prototypical systems H3 [1-5] and its isotopic variant HD2 [5-8], Li3 [9-12], Na3 [13,14], and HO2 [15-18], In particular, for the alkali metal trimers, the possibility of a conical intersection between the two lowest doublet potential energy surfaces introduces a complication that makes their theoretical study fairly challenging. Thus, alkali metal trimers have recently emerged as ideal systems to study molecular vibronic dynamics, especially the so-called geometric phase (GP) effect [13,19,20] (often referred to as the molecular Aharonov-Bohm effect [19] or Berry s phase effect [21]) for further discussion on this topic see [22-25], and references cited therein. The same features also turn out to be present in the case of HO2, and their exact treatment assumes even further complexity [18],... 

However, in the study of thermodynamics and transport phenomena, the behavior of ideal gases and gas mixtures has historically provided a norm against which their more unruly brethren could be measured, and a signpost to the systematic treatment of departures from ideality. In view of the complexity of transport phenomena in multicomponent mixtures a thorough understanding of the behavior of ideal mixtures is certainly a prerequisite for any progress in understanding non-ideal systems. 

For example, a thiazole-cyclohexane solution at 25 C is less viscous than the ideal system, and the deviation from ideality can be explained assuming that in solution there is a breakage between the existing association of the thiazole molecules in pure state (157). 

Terminal activity coefficients, 7°, are noted in Figure 3. These are often called infinite dilution coefficients and for some systems are given in Table 1. The hexane—heptane mixture is included as an example of an ideal system. As the molecular species become more dissimilar they are prone to repel each other, tend toward liquid immiscihility, and have large positive activity coefficients, as in the case of hexane—water. 

Theoretically based correlations (or semitheoretical extensions of them), rooted in thermodynamics or other fundamentals are ordinarily preferred. However, rigorous theoretical understanding of real systems is far from complete, and purely empirical correlations typically have strict limits on apphcabihty. Many correlations result from curve-fitting the desired parameter to an appropriate independent variable. Some fitting exercises are rooted in theory, eg, Antoine s equation for vapor pressure others can be described as being semitheoretical. These distinctions usually do not refer to adherence to the observations of natural systems, but rather to the agreement in form to mathematical models of idealized systems. The advent of readily available computers has revolutionized the development and use of correlation techniques (see Chemometrics Computer technology Dimensional analysis). 

HBA + HBA HBA-I-NB HBD-1-HBD HBD-I-NB NB + NB Ideal, quasi-ideal systems always positive or no deviations azeotropes, if any, minimum-boihng No H-bonding involved... 

This expression can be used to describe both pore and solid diffusion so long as the driving force is expressed in terms of the appropriate concentrations. Although the driving force should be more correctly expressed in terms of chemical potentials, Eq. (16-63) provides a qualitatively and quantitatively correct representation of adsorption systems so long as the diffusivity is allowed to be a function of the adsorbate concentration. The diffusivity will be constant only for a thermodynamically ideal system, which is only an adequate approximation for a limited number of adsorption systems. 

Commercial computer services are available to do rigorous distillation calculations. Perhaps the licensor will provide copies of rigorous computer runs to validate his balances. Alternately, the operating company can make such runs. For highly non-ideal systems, literature data for binary pairs may have to be sought. In some cases, laboratory equilibrium data may have to be obtained in-house or contracted out to one of several organizations or universities that are in this business. 

Fluid bed processes have been subject to many problems and uncertainties in development and scale up from bench-scale reactors. The fluidization behavior of each process seems different and very often does not meet expectations based on experience with earlier plants. With hindsight fluid cat cracking seems to be an ideal system from the point of view of easy operation and straightforward scale up. 

The f, fg, f, and fp are determined for the pure gas at the pressure of the mixture and depend on the pressure and the temperature. In gaseous mixtures, the quantity Kp as defined by Equation 2-38 is used. Eor an ideal gas reaetion mixture, Kf = Kp. Eor a non-ideal system. Equation 2-39 ean be used to ealeulate Kp from the measured equilibrium eompositions Ky using Equation 2-42. The eomposition... 

Introduction to Reactor Design Fundamentals for Ideal Systems... 

Introduction to Reactor Design Fundamentals for Ideal Systems 267 Substituting Equation 5-10 into Equation 5-7 gives... 

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