Ideal state

Peclet number independent of Reynolds number also means that turbulent diffusion or dispersion is directly proportional to the fluid velocity. In general, reactors that are simple in construction, (tubular reactors and adiabatic reactors) approach their ideal condition much better in commercial size then on laboratory scale. On small scale and corresponding low flows, they are handicapped by significant temperature and concentration gradients that are not even well defined. In contrast, recycle reactors and CSTRs come much closer to their ideal state in laboratory sizes than in large equipment. The energy requirement for recycle reaci ors grows with the square of the volume. This limits increases in size or applicable recycle ratios. 

Comparing Eqs. (8-95) and (8-97) shows that the quantity m X is a measure of solution acidity in excess of the ideal state this gives rise to the term excess acidity method for the X acidity function approach. We also have, from Eqs. (8-87) and (8-88),... 

Many gases deviate from the ideal state when pressures and/or temperatures are greater than 100-500 psia and 100°F. Some deviations yield a compressihility factor, Z, less than 1.0, and others give values greater than 1.0. 

The practice of corrosion inhibition requires that the inhibitive species should have easy access to the metal surface. Surfaces should therefore be clean and not contaminated by oil, grease, corrosion products, water hardness scales, etc. Furthermore, care should be taken to avoid the presence of deposited solid particles, e.g. stones, swarf, building materials, etc. This ideal state of affairs is often difficult to achieve but there are many cases where less than adequate consideration has been given to the preparation of systems to receive inhibitive treatment. Acid treatments, notably with 3-5% citric acid, with or without associated detergent washes, are often recommended and adopted for cleaning systems prior to inhibition. However, it is not always appreciated that these treatments will not remove particulate material particularly when, as is often the case, the material is insoluble in acids. 

It has often been supposed that at very high temperatures all gases would behave normally, i.e., would approach a limiting ideal state. As a matter of fact the deviations appear to be influenced by the density of the gas, and disappear at infinitely small densities whatever the temperature may be. Thus a saturated vapour at very low temperatures may behave like a permanent gas, on account of its very small density. 

As shown in Fig. 10-13, there is also a flux of O2 produced during net photosynthesis from the ocean to the atmosphere and an export flux of particulate and dissolved organic matter out of the euphotic zone. For a steady-state system, new production should equal the flux of O2 to the atmosphere and the export of organic carbon (Eppley and Peterson, 1979) (when all are expressed in the same units, e.g., moles of carbon). Such an ideal state probably rarely exists because the euphotic zone is a dynamic place. Unfortunately, there have been no studies where all three fluxes were measured at the same time. Part of the difficulty is that each flux needs to be integrated over different time scales. The oxygen flux approach has been applied in the subarctic north Pacific (Emerson et al, 1991) and subtropical Pacific (Emerson et al, 1995, 1997) and Atlantic (Jenkins and Goldman, 1985). The organic carbon export approach has... 

The changeover to thermodynamic activities is equivalent to a change of variables in mathematical equations. The relation between parameters and a. is unambiguous only when a definite value has been selected for the constant p. For solutes this constant is selected so that in highly dilute solutions where the system p approaches an ideal state, the activity will coincide with the concenttation (lim... 

The degree of departure of a system from the ideal state can be described by another parameter, the activity coefficient, which is defined as the ratio of activity to concentration ... 

In electrolyte solutions, nonideality of the system is much more pronounced than in solutions with uncharged species. This can be seen in particular from the fact that electrolyte solutions start to depart from an ideal state at lower concentrations. Hence, activities are always used in the thermodynamic equations for these solutions. It is in isolated instances only, when these equations are combined with other equations involving the number of ions per unit volume (e.g., equations for the balance of charges), that concentrations must be used and some error thus is introduced. 

The departure of a system from the ideal state is due to interaction forces between the individual particles contained in the system. The dependence of chemical potential of a species on its concentration can be written as... 

Steady-state reactors with non-ideal flow pattern. In fact, all reactors presented as reactors with ideal flow patterns show some non-idealities as already mentioned above. The deviation from the ideal state for multiphase reactors arises from the presence of phases with very different physical properties. 

The ideal state heat capacity of ethylene is given by the equation ... 

The dependence of gas specific heats on temperature was discussed in Chapter 3, Section 3.5. For a gas in the ideal state the specific heat capacity at constant pressure is given by ... 

For the vapour phase, the deviation of the specific enthalpy from the ideal state can be illustrated using the Redlich-Kwong equation, written in the form ... 

As this work has been claimed as Hermetic, I have classed it as an alchemical text. "The New Atlantis, 1627, is essentially a utopia, in which Bacon outlines an ideal state. It has sometimes been interpreted as an elaborate allegory with hermetic (and even Rosicrucian) undertones. This text was prepared by Kirk Crady from scanner output provided by Internet Wiretap"... 

Andreae, Johann Valentin.Christianopolis an ideal state of the seventeenth century translated with historical introduction by F.E. Held. Translated by Felix Emil Held. New York OUP, 1916. 287p. 

When solution is infinitely dilute, i.e. in the ideal state, rate constant in solution (ks)0 will be given by... 

The examples in section 3.1.2 of calculations using stability constants involve concentrations of M, L, and ML . Rigorously, a stability constant, as any thermodynamic equilibrium constant should be defined in terms of standard state conditions (see section 2.4). When the system has the properties of the standard state conditions, the concentrations of the different species are equal to their activities. However, the standard state conditions relate to the ideal states described in Chapter 2, which can almost never be realized experimentally for solutions of electrolytes, particularly with water as the solvent. For any conditions other than those of the standard state, the activities and concentrations are related by the activity coefficients as described in Chapter 2, and especially... 

However, in doing so one tests two theories the network formation theory and the rubber elasticity theory and there are at present deeper uncertainties in the latter than in the former. Many attempts to analyze the validity of the rubber elasticity theories were in the past based on the assumption of ideality of networks prepared usually by endllnklng. The ideal state can be approached but never reached experimentally and small deviations may have a considerable effect on the concentration of elastically active chains (EANC) and thus on the equilibrium modulus. The main issue of the rubber elasticity studies is to find which theory fits the experimental data best. This problem goes far beyond the network... 

Note 1 In some respects, a polymer solution in the theta state resembles an ideal solution and the theta state may he referred to as a pseudo-ideal state. However, a solution in the theta state must not be identified with an ideal solution. 

Note 2 Both phases are assumed to have properties identical with those of their ideal states, with no influence of interfaces. 

There are only three broad structural categories into which most of the reported oxide superconductors can be classified i.e., sodium chloride, perovskite, and spinel. It is interesting to note that these three structures possess cubic symmetry in their most idealized state. A detailed discussion of the research performed on oxide compounds derived from these three structures will be presented in Section 2.0 below. But before we continue with the general study of superconductivity in other materials, an overview of the oxide work is given in chronological fashion (to 1975) in the following Section. 

Eyring also stated (Ref 3> p 98, as quoted in Ref 4, p 201) that release of energy by lateral expansion of the products permits stabilization of one of the sub-ideal states in the shock front. Of the hydro-dynamic equations only that of continuity, expressing the constancy of mass velocity, is perturbed by the expansion... 

Owing to its single composition and pure covalent bonding, diamond is a standard solid material, and takes the role of the most appropriate sample in explaining the effects upon structure-sensitive properties when the structure of solid material deviates from the ideal state. 

The set of equations (3.7-3.9) shows that the sign and magnitude of the second virial coefficient provides information on how the behaviour of the macromolecular solution deviates from that of the thermodynamically ideal state, thus reflecting the nature and intensity of the inter-molecular pair interactions (both biopolymer-biopolymer and biopolymer-solvent) (Prigogine and Defay, 1954 Tanford, 1961 Ogston 1962 ... 

The numbers succeeding the asterisk show that equilibrium was in all probability then attained. The dotted curve, Fig. 8, shows the probable state which would occur if the reactions balanced as in the ideal state indicated in Fig. 7. Indeed, if the temp, exceeds 490°, the final state is the same whatever be the initial products. The space between the two lines represents a system below 490° in what P. Duhem calls un etat de faux equilibre. The region where there is no reaction and where... 

The reversibility of the reaction was noted by D. Heercn and T. Schlosing,2 who found that the conversion of sodium chloride into the hydro-carbonate stops with a two-thirds or four-fifths conversion and J. A. Bradburn was able to reverse the reaction completely by blowing air through the mother liquid containing the sodium hydrocarbonate when the ammonium carbonate formed by the action of ammonium chloride on sodium hydrocarbonate was carried away in a stream of air. An excess of ammonium hydrocarbonate is required to counteract the reversal of the reaction by the action of -the ammonium chloride on the sodium hydrocarbonate. E. Solvay stated that he was able to decompose the sodium chloride completely, but he later must have noticed that his yields fell short of this ideal state. 

So far, in connection with the formation and decomposition of compounds, we have only considered the implications of potential energy and temperature, but a complication does occur when, as often happens, the reaction velocity between two substances is so small that the ideal state is not reached. In order to increase the velocity of the reaction, the temperature of the system must be raised. The fact that mercury and oxygen do not react at —100°G, but do react rapidly at 200°C, is not because HgO is not stable at low temperatures, but because the reaction velocity is then so low that chemical combination cannot be observed. 

The traditional method of dealing with irreversible processes is, of course, the use of the Boltzmann integro-differential equation and its various extensions. But this method leads to two serious difficulties. The first is that Boltzmann s equation is neither provable nor even meaningful except in the context of molecular encounters, i.e., under the assumption that the intermolecular forces are of such short range in comparison with molecular distances that a molecule spends only a negligible fraction of its time within the influence of others. This drastically restricts the field of applicability, confining the treatment to gases close to the ideal state. But even then the equation can only be established on the basis of an essential assumption of molecular probabilistic independence ( micromolecular chaos ).3... 

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