Non-ideality factor

Mixtures of an ionic and a non-ionic surfactant are quite similar to those considered above, because the contribution of the DEL to the surface pressure for an ionic surfactant can be treated approximately as a non-ideality factor. If the solution of individual ionic surfactants and their mixtures are studied at a fixed ionic strength (which is usually accomplished by addition of an indifferent electrolyte), then the surface pressure of a mixed solution, similarly to nonionic surfactants, is calculated from the data obtained for individual solutions according to Eq. (3.41). 

The last thing that I want to say about competition is that it might be rewarding to consider models of it that take into account some of the non-ideal factors that frequently complicate growth of microorganisms. By non-ideal factors I mean such things as the occurrence of maintenance, variability of biomass yield, time lag of metabolic process rates in response to changes in... 

Taking into consideration all of these non-ideal factors, the practical high-gain noise figure of an SOA is given by... 

Matrix of non-ideality factor (in terms of activity coefficient y), dimensionless... 

However, in real devices ideal behaviour is rarely observed since losses occur and so a non-ideality factor, y, which accounts for the transport mechanism of the dark current, is introduced ... 

The simplest type of solutions which exhibit non-randomness are those in which the non-randomness is attributable solely to geometric factors, i.e. it does not come from non-ideal energetic effects, which are assumed equal to zero. This is the model of an athermal solution, for which... 

Since non-ideal gases do not obey the ideal gas law (i.e., PV = nRT), corrections for nonideality must be made using an equation of state such as the Van der Waals or Redlich-Kwong equations. This process involves complex analytical expressions. Another method for a nonideal gas situation is the use of the compressibility factor Z, where Z equals PV/nRT. Of the analytical methods available for calculation of Z, the most compact one is obtained from the Redlich-Kwong equation of state. The working equations are listed below ... 

K = Specific heat ratio, at inlet conditions given for some substances in Table 1. Note Published values of K at 15 °C and one atmosphere may be used. If K is unknown, a conservative value of K = 1.001 may be used, in which case the factor C = 315. Note that a correction for non-ideal gases may be necessary. 

For a high-pressure non-ideal gas behavior, the term (TqTi/TtIo) is replaced by (ZqTqTi/ZTtIq), where Z is the compressiblity factor. To change to another key reactant B, then... 

Equilibrium Basic Consideration, 1 Ideal Systems, 2 K-Factor Hydrocarbon Equilibrium Charts, 4 Non-Ideal Systems, 5 Example 8-1 Raoult s Law, 14 Binary System Material Balance Constant Molal Overflow Tray to Tray,... 

For a non-ideal gas, equation 2.15 is modified by including a compressibility factor Z which is a function of both temperature and pressure ... 

The actual stage can be a mixing vessel, as in a mixer-settler used for solvent extraction applications, or a plate of a distillation or gas absorption column. In order to allow for non-ideal conditions in which the compositions of the two exit streams do not achieve full equilibrium, an actual number of stages can be related to the number of theoretical stages, via the use of a stage-efficiency factor. 

Here w is a weighting factor. Asr (s) is the absorption factor (in this case for symmetrical absorption), Hz (5) and In consider the non-ideal character of the two-phase topology (cf. p. 124, Fig. 8.10) by consideration of a smooth phase transition zone and density fluctuations inside the phases. 

This should come as no surprise, since the physical behavior of materials is non-linear and unpredictable, especially when materials are formulated or in combination. Two examples will suffice high temperature ceramic superconductors and insulators above their critical temperatures or at non-ideal stoichiometries composite structures may show several times the strength or impact resistance than would be expected from their component materials. Materials discovery will always require a good deal of trial and error, factors that may be mitigated by techniques that permit the simultaneous synthesis of large numbers of materials, followed by rapid or parallel screening for desired properties. 

A gas that obeys these five postulates is an ideal gas. However, just as there are no ideal students, there are no ideal gases only gases that approach ideal behavior. We know that real gas particles do occupy a certain finite volume, and we know that there are interactions between real gas particles. These factors cause real gases to deviate a little from the ideal behavior of the Kinetic Molecular Theory. But a non-polar gas at a low pressure and high temperature would come pretty close to ideal behavior. Later in this chapter, we ll show how to modify our equations to account for non-ideal behavior. 

Results from a series of Odyssey simulations of non-ideal gases are shown in Figure 6. The compression factor PV/nRT is plotted as a function of the pressure for two systems. The first system is a mixture of hydrogen and helium (T-120 K 90 and 10 molecules, respectively) as it might be encountered in the atmosphere of Jupiter. The second system is pure gaseous ammonia (7 298 K 50 molecules). 

While an ideal-gas law serves very well under many circumstances, there are also circumstances in which non-ideal behavior can be significant. A compressibility factor Z is an often-used measure of the extent of nonideality,... 

The enhancement factor contains three terms supercritical phase, ideal behaviour of the pure component 2 in the vapour phase at the sublimation pressure, and the Poynting factor that describes the influence of the pressure on the fugacity of pure solid 2. 

Many attempts have been made to develop PVT relations for detonation products of condensed expls. These product gases, even in the absence of any condensed phase products, are very far from ideal. Thus most EOS for detonation products have included correction factors to account for non-ideality. Most product EOS are semi-empirical because they have to be adjusted to fit expti data. Usually the Abel equation, pv=nRT+atp, is used as a starting point. In the original Abel equation a is a constant covolume, but a constant a does not agree with observation. Therefore various attempts have been made to modify the Abel equation by inclusion of a = a(v) or a = a(p) and so on. The various attempts at obtaining a true EOS are summarized in Vol 4, D268-L to D298-R. Below we will briefly describe a new EOS which was developed recently... 

Although very simple, the criteria used to obtain characteristic parameters of surface-confined molecules correspond to an ideal behavior in line with the premises presented in Sect. 6.4.1. Unfortunately, it is difficult to meet these criteria and several contributing factors need to be considered in order to explain the non-idealities observed in these redox systems. One of the most common deviations from the ideal criteria is that related to the width of the voltammetric signals, which are typically broader than the values predicted by the ideal model (i.e., W1 /2 90 mV for reversible systems see Eq. (6.162)). Some possible reasons for this experimental evidence are ... 

---