Characteristic variables

The effect of synthesis gas composition on conversion, catalyst life, carbon black formation, etc. was determined in numerous tests. Characteristic variables in the synthesis gas composition are the H2/CO ratio, residual C02 content, and content of trace components in the form of higher hydrocarbons and catalyst poisons. 

Combination of several variables that characterize a chemical-technological process into a single or a few characteristic variables... 

We assume that n objects have been measured for m characteristics (variables), and that the objects originate from k different groups. Suppose that the groups consist of... 

N cuum technology mass spectrometer partial pressure gauges, definitions, characteristic variables, operating conditions 11/86... 

E Nondestructive testing - determination of characteristic variables for mass spectrometer leak detectors ... 

Coordination MOs are delocalized in space — three-dimensional CuCl C0CI2 (crystal) There are no distinct characteristics variable coordination number and magnetic moment, strong mutual influence of ligands... 

Figure 5. The correlations of the no teeth parameter with the other teeth characteristics show the interdependent nature of the untransformed plant characteristic variables. [Used by permission of Geological Society of America, from Forest et al. (1999), Geol. Soc. Am. Bull., Vol. Ill, Fig. 7, p. 506.]...

By choosing characteristic variables for temperatures, velocities and lengths we can reduce the dimensionality even further. The temperature is scaled based on the maximum gradient, the length with the gap thickness and screw channel depth and the velocity with the barrel x-velocity,... 

Mathematical modeling of systems for which characteristic variables are time-dependent only and not space-dependent is done by ordinary differential equations (ODEs). The situation is found in a nearly well-mixed batch reactor. There one may find differences in temperature or concentrations from one site to another due to imperfect mixing. When space changes are not important to the model, the process variables can be approximated by means of lumped parameter models (LPMs). When the... 

The identification of phenomena that explain the behavior of a studied system depends on the analysis of their kinetic data. Normally, this kinetic analysis is performed using characteristic variables calculated from the experimental data. The specific rates and the yield coefficients are the common values used in this task. When cell concentration data are available, cell growth and death rates, as well as cell viability, are the best kinetic variables to characterize the population physiological state. In the absence of this information - as can occur, for example, with immobilized cells - the treatment must be based on substrate consumption or on metabolites production (Miller and Reddy, 1998). 

Obviously, the energy functions of free energy F and free enthalpy G play the role of thermodynamic potentials for an irreversible process to occur in isothermal systems at constant volume and constant pressure, respectively. In general, the energy functions of F, and G can be used as the thermodynamic potentials to indicate the direction of an irreversible processes to occur under the condition that their respective characteristic variables remain constant. 

The affinity of irreversible processes, as mentioned above, is related to the thermodynamic potentials U, H, F, and G under the conditions that their respective characteristic variables are kept constant. From Eqs. 3.30, 3.31, 3.32, and 3.33, we obtain the partial differentials of... 

This equation 5.20, called the Gibbs-Duhem equation, is unique among a variety of the thermodynamic equations of state in that the characteristic variables are all intensive quantities, each multiplied by its conjugate extensive quantity. 

Free Radical Cure UV Adhesives. As with any adhesive, formulation variables are critical to the processing and performance characteristics. Variables such as oligomer selection, modifiers and additives, monomer structure, molecular weight, and glass transition temperature directly affect application and performance properties. 

This partial differential equation can be approximated by an ordinary one by creating a new characteristic variable that is, t = f - r/ G — x/u. Appl5dng the initial condition for this problem, the characteristic can be shown to be a constant t = -r(JG. Making this variable transformation, the new characteristic population balance becomes... 

Position of the sampie vessei. Although the position of the sample container with respect to the transducer is not a characteristic variable of US application, it determines the amount of energy that is received by the sample. This variable, exclusive of ultrasonic baths, should be optimized in both DUSAL and CUSAL methods. When only one sample is leached, the precision is not affected provided the sample vessel is always in the same position — cavitational effects can be maximal or not in this situation, however. If several samples are simultaneously treated, then the precision is probably affected because the irradiation profile is not uniform throughout the bath. One example is the DUSAL of cadmium and lead from foods, where the iodine method was used to locate the best position for cavitational effects [5]. This requires the use of mapping techniques. 

The phosphotungstate salts cannot be used for equivalent weight determinations, for their characteristically variable composition leads to inconsistent titration results. However, treatment of the salts with aqueous sodium hydroxide led to recovery of the free bases in reproducible amounts. These results show that one-fifth of the high molecular weight asphaltenes and one-third of the preasphaltenes are precipitated as phosphotungstate salts. Considerably less of the unfractionated H-coal vacuum-still bottoms and none of the low molecular weight asphaltenes and oils and resins were separated in this manner. 

An equation of this sort which connects the pressure, the volume, and the temperature of a body with one another is called an equation of condition. The state of a body is determined uniquely when the values of any two of these quantities are given for example, p and v, or p and T, or V and T. We may call the three quantities p, v, and T the characteristic variables of the body, or the variables of condition. 

In order to precisely quantify the positions of the energy barriers, a description of molecular coordinates is required. The experimental variables, force and extension, at which an energy barrier is overcome, show large fluctuations due to the stochastic nature of the process, which is caused by the thermal energy ksT. Furthermore, force and extension depend on experimental parameters such as pulling speed, temperature, or properties of the solvent. In contrast, the contour length is the characteristic variable for the positions of energy barriers. 

While the decision matrix shown in Table 2 suggests a rather simple testing approach, in reality, adherence to the SE concept requires that it be applied to a multitude of characteristic variables including chemical SE, biological SE, SE of potential exposure routes, and the SE of possible overall safe use. 

The fundamental thermodynamic properties that arise in connection with the first and second laws of thermodynamics are internal energy and entropy. These properties together with the two laws for which they are essential apply to all types of systems. However, different types of systems are characterized by different sets of measurable coordinates or variables. The type of system most commonly encountered in chemical technology is one for which the primary characteristic variables are temperature T, pressure P, molar volume V, and composition, not all of which are necessarily independent. Such systems are usually made up of fluids (liquid or gas) and are called PVT systems. 

When the free energy A is given as a function of its characteristic variables, viz., T and V, it is possible to calculate all thermodynamic properties of the system. We list, for instance, the... 

We are interested in the case in which p2 > P, where the system is potentially unstable. Although we have established the principle of nondimensionalizing as a way of identifying dimensionless parameters, in the present case it is not clear what choice to make for any of the characteristic variables, and so we proceed in this case with the dimensional equations and boundary conditions. 

The selection of sites for monitoring must take into account the three-dimensional nature of the groundwater body, flow characteristics, variability of land use, ground-water vulnerability and the potential receptors. All these should have been identified in file conceptual model. An effective network of monitoring sites will be one that is able to detect tlie impacts from pressures and the evolution in groundwater quality along flow paths within the groundwater body. 

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