Thermodynamic limitations

Resolution, like the separation factor, differs for each specific component pair and therefore fails as a global criterion of separation. For analytical separations, more universal criteria have evolved, such as plate height, number of plates, rate of generation of plates, and peak capacity (Chapter 5). While these indices differ somewhat from one component to another, they effectively establish a ballpark figure of merit for different systems and different conditions of operation. 

While separation processes must generate selective increases and decreases in the mole fraction of components, the absolute concentration levels differ enormously. Separation at such different levels of purity may be referred to by specific terms enrichment, concentration, and purification [21,22]. Rony has proposed that enrichment be used when the mole fraction of the desired component remains under 0.1, concentration when it stays below 0.9, and purification when the mole fraction is above 0.9 [22]. TTiese levels, while arbitrary, help illustrate the variability of concentration levels employed in preparative separations. 

Analytical separations generally deal with highly dilute solutions. Important components are sometimes found in the parts per billion range or lower, which is sufficient to produce the desired information with highly sensitive detection. 

It seems enigmatic that we often struggle so hard to achieve desired separations when the basic concept of moving one component away from another is inherently so simple. Much of the difficulty arises because separation flies in the face of the second law of thermodynamics. Entropy is gained in mixing, not in separation. Therefore it is the process of mixing that occurs spontaneously. To combat this and achieve separation, one must apply and manipulate external work and heat and allow dilution in a 

The inherent difficulties of separation can be largely explained in terms of two closely related processes. The second law of thermodynamics tells us that both processes are accompanied by an increase in entropy, making them spontaneous. Both act to hinder separation. First we have 

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Due to such large numbers, it is usefiil to consider the limiting case of the thermodynamic limit, which is defined as... 

This behaviour is characteristic of thennodynamic fluctuations. This behaviour also implies the equivalence of various ensembles in the thermodynamic limit. Specifically, as A —> oo tire energy fluctuations vanish, the partition of energy between the system and the reservoir becomes uniquely defined and the thennodynamic properties m microcanonical and canonical ensembles become identical. 

Other Technologies. As important as dehydrogenation of ethylbenzene is in the production of styrene, it suffers from two theoretical disadvantages it is endothermic and is limited by thermodynamic equiHbrium. The endothermicity requites heat input at high temperature, which is difficult. The thermodynamic limitation necessitates the separation of the unreacted ethylbenzene from styrene, which are close-boiling compounds. The obvious solution is to effect the reaction oxidatively ... 

Dehydrogenation of /i-Butane. Dehydrogenation of / -butane [106-97-8] via the Houdry process is carried out under partial vacuum, 35—75 kPa (5—11 psi), at about 535—650°C with a fixed-bed catalyst. The catalyst consists of aluminum oxide and chromium oxide as the principal components. The reaction is endothermic and the cycle life of the catalyst is about 10 minutes because of coke buildup. Several parallel reactors are needed in the plant to allow for continuous operation with catalyst regeneration. Thermodynamics limits the conversion to about 30—40% and the ultimate yield is 60—65 wt % (233). 

Energy Requirements The thermodynamic limit on energy is the ideal energy needed to move water from asahne solution to a pure phase. The theoretical minimum energy is given by ... 

Since there is no reason to suspect that ol Ix) exhibits any anomalies up to and, in the thermodynamic limit, at the yield point, is a finite... 

Very recently, considerable effort has been devoted to the simulation of the oscillatory behavior which has been observed experimentally in various surface reactions. So far, the most studied reaction is the catalytic oxidation of carbon monoxide, where it is well known that oscillations are coupled to reversible reconstructions of the surface via structure-sensitive sticking coefficients of the reactants. A careful evaluation of the simulation results is necessary in order to ensure that oscillations remain in the thermodynamic limit. The roles of surface diffusion of the reactants versus direct adsorption from the gas phase, at the onset of selforganization and synchronized behavior, is a topic which merits further investigation. 

A much more selective reaction is possible by using vapor-phase fluonnahon over a chromia" catalyst at 300 to 400 °C, but conversions are thermodynamically limited to 10-20% under acceptable operating conditions [fO 11 Despite this disadvantage, this process has been selected by ICI and Hoechst for their first plants... 

The inset illustrates the extrapolation of the simulation data to the thermodynamic limit according to mixed field finite size scaling for Na = 40 and Nb = 120. From Muller and Binder. ... 

The question of how to terminate the box is fundamental to all the calculations of interfacial energy in compounds, including the calculation of surface energies. It has been addressed previously for particular cases by Chetty and Martin [11,12]. These authors pointed out that a suitable termination is one which is on a symmetry plane of the crystal, or which follows symmetry planes if it is not parallel to the boundary. However, it may not always be possible to find a symmetry plane. I offer a solution here which is more general. It reconciles the atomistic picture with the thermodynamic limit. 

If all the heat absorbed were converted into work, the efficiency would be 1, or 100 percent. If none of the heat absorbed was converted into work, the efficiency would be 0. The first law of thermodynamics limits the efficiency of any heat engine to 1 but does not prevent an efficiency of 1. The efficiency of practical heat engines is always less than 1. For example, the efficiency of a large steam turbine in an electric power plant is about 0.5, which is considerably more efficient than the typical 0.35 efficiency of an auto engine. When two objects at different temperatures are m... 

Much of the potential for improvement in technical energy efficiencies in industrial processes depends on how closely such processes have approached their thermodynamic limit. There are two types of energy efficiency measures (1) more efficient use in existing equipment through improved operation, maintenance or retrofit of equipment and (2) use of more efficient new equipment by introducing more efficient processes and systems at the point of capital turnover or expansion of production. More efficient practices and new technologies exist for all industrial sectors. Table 2 outlines some examples of energy efficiency improvement techniques and practices. 

Infinite Systems The ultimate fate of infinite systems, in the infinite time limit, is quite different from their finite cousins. In particular, the fate of infinite systems does not depend on the initial density of cr = 1 sites. In the thermodynamic limit, there will always exist, with probability one, some convex cluster large enough to grow without limit. As f -4 oo, the system thus tends to p —r 1 for all nonzero initial densities. What was the critical density for finite systems, pc, now becomes a spinodal point separating an unstable phase for cr = 0 sites for p > pc from a metastable phase in which cr = 0 and cr = 1 sites coexist. For systems in the metastable phase, even the smallest perturbation can induce a cluster that will grow forever. 

Any computation, whether performed by a slide rule, computer workstation or brain, is inherently a physical process, and as such is subject to whatever laws and limitations apply to physical systems in general. It is a natural question to ask, then, whether there exists a fundamental thermodynamic limit to computation i.e. 

It is important to understand that critical behavior can only exist in the thermodynamic limit that is, only in the limit as the size of the system N —> = oo. Were we to examine the analytical behavior of any observables (internal energy, specific heat, etc) for a finite system, we would generally find no evidence of any phase transitions. Since, on physical grounds, we expect the free energy to be proportional to the size of the system, we can compute the free energy per site f H, T) (compare to equation 7.3)... 

Note that the critical behavior just described holds true strictly only in the thermodynamic limit i.c. only when the number of sites N oo. The above results are in fact obtained by extrapolating from finite system calculations. Kinzel... 

The recognition that there is no fundamental thermodynamic limitation to constructing fully reversible, energy dissipationless, computers both classical and quantum. 

The series of reactors and exchangers which methanates a raw syngas without pretreatment other than desulfurization is collectively termed bulk methanation. The chemical reactions which occur in bulk methana-tion, including both shift conversion and methanation, are moderated by the addition of steam which establishes the thermodynamic limits for these reactions and thereby controls operating temperatures. The flow sequence through bulk methanation is shown in Figure 1. 

Neglecting for simplicity the long-range character of the Coulomb force, the above summations yield (31) a bounded result (x) when extended to infinity. Bielectron integrals can thus be regarded as scaling like Nq", either in the thermodynamic limit (Nq °°), or (31) in the dissociation limit (aQ °°). 

Countercurrent flow has advantages in product and thermodynamically limited reactions. Catalytic packings (see Figure 9. Id) are commonly used in that mode of operation in catalytic distillation. Esterification (methyl acetate, ethyl acetate, and butyl acetate), acetalization, etherification (MTBE), and ester hydrolysis (methyl acetate) were implemented on an industrial scale. 

The chemical industry of the 20 century could not have developed to its present status on the basis of non-catalytic, stoichiometric reactions alone. Reactions can in general be controlled on the basis of temperature, concentration, pressure and contact time. Raising the temperature and pressure will enable stoichiometric reactions to proceed at a reasonable rate of production, but the reactors in which such conditions can be safely maintained become progressively more expensive and difficult to make. In addition, there are thermodynamic limitations to the conditions under which products can be formed, e.g. the conversion of N2 and H2 into ammonia is practically impossible above 600 °C. Nevertheless, higher temperatures are needed to break the very strong N=N bond in N2. Without catalysts, many reactions that are common in the chemical industry would not be possible, and many other processes would not be economical. 

Lueders T, B Pommerenke, MW Friedrich (2004) Stable-isotope probing of microorganisms thriving at thermodynamic limits syntrophic propionate oxidation in flooded soil. Appl Environ Microbiol 70 5778-5786. 

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