Isothermal, definition

Reservoir fluids (oil, water, gas) and the rock matrix are contained under high temperatures and pressures they are compressed relative to their densities at standard temperature and pressure. Any reduction in pressure on the fluids or rock will result in an increase in the volume, according to the definition of compressibility. As discussed in Section 5.2, isothermal conditions are assumed in the reservoir. Isothermal compressibility is defined as ... 

The preceding derivation, being based on a definite mechanical picture, is easy to follow intuitively kinetic derivations of an equilibrium relationship suffer from a common disadvantage, namely, that they usually assume more than is necessary. It is quite possible to obtain the Langmuir equation (as well as other adsorption isotherm equations) from examination of the statistical thermodynamics of the two states involved. 

Type I isotherms are characterized by a plateau which is nearly or quite horizontal, and which may cut the p/p° = 1 axis sharply or may show a tail as saturation pressure is approached (Fig. 4.1). The incidence of hysteresis varies many Type I isotherms exhibit no hysteresis at all (Fig. 4.1), others display a definite loop, and in others there is hysteresis which may or may not persist to the lowest pressures ( low-pressure hysteresis ) (Fig. 4.2). Type 1 isotherms are quite common, and are no longer restricted, as seemed at one time to be the case, to charcoals. Many solids, if suitably prepared, will yield Type 1 isotherms the xerogcls of silica, titania, alumina... 

The phenomenological definition for the change in entropy associated with the isothermal, reversible absorption of an element of heat dq is... 

In the course of the study, we found that a family of monosaccharides exhibited a definite adsoi ption selectivity (Langmuir s isotherm adsoi ption constant), reflecting their molecular stmctures. 

Where activated carbon is a potential treatment technology, the first evaluation step is generally to run simple isotherms to determine feasibility. Isotherms are based on batch treatment where impurities reach equilibrium on available carbon surface. While such tests provide an indication of the maximum amount of impurity a GAC can adsorb, it cannot give definite scale up data for a GAC operation due to several factors ... 

Thus, from an investigation of the compressibility of a gas we can deduce the values of its critical constants. We observe that, according to van der Waals theory, liquid and gas are really two distant states on the same isotherm, and having therefore the same characteristic equation. Another theory supposes that each state has its own characteristic equation, with definite constants, which however vary with the temperature, so that both equations continuously coalesce at the critical point. The correlation of the liquid and gaseous states effected by van der Waals theory is, however, rightly regarded as one of the greatest achievements of molecular theory. 

We shall now prove that P, for fixed values of 7r and the temperature, is definite for a given solution. For this purpose we have first of all to show that the dilution or concentration of the solution can be effected isothermally and reversibly. If the above apparatus is constructed of some good conductor of heat, placed in a large constant-temperature reservoir, and if all processes are carried out very slowly, the isothermal condition is satisfied. Further, suppose the end pistons fixed, and then apply to the septum an additional small pressure SP towards the solution. There will be a slight motion of the septum, through a small volume SV, and work... 

Again, if we consider the initial substances in the state of liquids or solids, these will have a definite vapour pressure, and the free energy changes, i.e., the maximum work of an isothermal reaction between the condensed forms, may be calculated by supposing the requisite amounts drawn off in the form of saturated vapours, these expanded or compressed to the concentrations in the equilibrium box, passed into the latter, and the products then abstracted from the box, expanded to the concentrations of the saturated vapours, and finally condensed on the solids or liquids. Since the changes of volume of the condensed phases are negligibly small, the maximum work is again ... 

We have seen how to calculate q for the isochoric and isobaric processes. We indicated in Chapter 1 that q = 0 for an adiabatic process (by definition). For an isothermal process, the calculation of q requires the application of other thermodynamic equations. For example, q can be obtained from equation (2.3) if AC and w can be calculated. The result is... 

Effective core potential, 269 Effective double layer characterization of, 189 isotherm, 306, 315 kinetic expressions, 316 observations of with STM, 259 stability of, 225, 351, 503 Effectiveness factor of promotion computation of, 505 definition of, 505 Electrocatalysis... 

Electrode etymology of, 2 potential of, 123 work function of, 138,203, 340 Electron acceptor adsorbate chemical potential of, 208 definition of, 24 isotherm, 309 Electron donor adsorbate chemical potential of, 208 definition of, 24 isotherm, 309... 

The yield of a gas-solid heterogeneous reaction depends not on the total time that molecules spend in the reactor but on the time that they spend on the catalyst surface. The contact time distribution provides a standardized measure of times spent in the absorbed state. A functional definition is provided by the following equation applicable to a first-order, heterogeneous reaction in an isothermal reactor ... 

On the other hand, as shown in Figure 4, the isotherm of Cs2.2 (72 m g"l) was of Type I [27], where most of the adsorption took place at the very low pressure region, indicating that these salts have only micropores (according to the lUPAC definition, the pore diameter is less than 20 A) [28]. Cs2.1 also gave the Type I... 

Note from the definition is follows that the pH of the isotherm intersection point in Fig. 2.13 represents the isopotential pHf of the Metrohm EA121 combined electrode.)... 

Vocabulary of Terms Used in Reactor Design. There are several terms that will be used extensively throughout the remainder of this text that deserve definition or comment. The concepts involved include steady-state and transient operation, heterogeneous and homogeneous reaction systems, adiabatic and isothermal operation, mean residence time, contacting and holding time, and space time and space velocity. Each of these concepts will be discussed in turn. 

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