Upper critical temperature

The Te-S system is peculiar it is a simple eutectic-type diagram and shows (like an island completely surrounded by the single-phase field of the liquid) a small oval insolubility region situated between —37 and 41.5 at.% S and between two critical temperatures (upper Tc = 740°C and lower Tc = 690°C). This behaviour (often observed for instance in organic systems) among the different pairs of elements has been described only for Te-S. 

Upper critical end point, or critical temperature,upper layer. ... 

It should be noted that the modern view is that all partially miscible liquids should have both a lower and upper critical solution temperature so that all such systems really belong to one class. A closed solubility curve is not obtain in all cases because the physical conditions under normal pressure prevent this. Thus with liquids possessing a lower C.S.T., the critical temperature (the critical point for the liquid vapour system for each component, the maximum temperature at which liquefaction is possible) may be reached before the consolute temperature. Similarly for liquids with an upper C.S.T., one or both of the liquids may freeze before the lower C.S.T. is attained. 

Fig. 3.24 Test of the tensile strength hysteresis of hysteresis (Everett and Burgess ). TjT, is plotted against — Tq/Po where is the critical temperature and p.. the critical pressure, of the bulk adsorptive Tq is the tensile strength calculated from the lower closure point of the hysteresis loop. C), benzene O. xenon , 2-2 dimethyl benzene . nitrogen , 2,2,4-trimethylpentane , carbon dioxide 4 n-hexane. The lowest line was calculated from the van der Waals equation, the middle line from the van der Waals equation as modified by Guggenheim, and the upper line from the Berthelot equation. (Courtesy Everett.)...

Fig. 5. Lower and upper critical tielines in a quaternary system at different temperatures and a plot of the critical end point salinities vs temperature, illustrating lower critical endline, upper critical endline, optimal line, and tricritical poiat for four-dimensional amphiphile—oil—water—electrolyte-temperature...

Normalizing. In this operation, steel is heated above its upper critical temperature (A ) and cooled in air. The purpose of this treatment is to refine the hot-roUed stmcture (often quite inhomogeneous), depending on the finishing temperature, and to obtain a carbide size and distribution that is more favorable for carbide solution on subsequent heat treatment than the eadier as-roUed stmcture. 

The usual practice is to normalize at 50—80°C above the upper critical temperature. For some alloy steels, however, considerably higher temperatures may be used. Heating may be carried out in any type of furnace that permits uniform heating and good temperature control. 

As can be seen in the table above, the upper two results for heat transfer coefficients hp between particle and gas are about 10% apart. The lower three results for wall heat transfer coefficients, h in packed beds have a somewhat wider range among themselves. The two groups are not very different if errors internal to the groups are considered. Since the heat transfer area of the particles is many times larger than that at the wall, the critical temperature difference will be at the wall. The significance of this will be shown later in the discussion of thermal sensitivity and stability. 

The boiling point is limited by the critical temperature at the upper end, beyond which it cannot exist as a liquid, and by the triple point at the lower end, which is at the freezing temperature. Between these two limits, if the liquid is at a pressure higher than its boiling pressure, it will remain a liquid and will be subcooled below the saturation condition, while if the temperature is higher than saturation, it will be a gas and superheated. If both liquid and vapour are at rest in the same enclosure, and no other volatile substance is present, the condition must lie on the saturation line. 

As shown in Fig. 21, in this case, the entire system is composed of an open vessel with a flat bottom, containing a thin layer of liquid. Steady heat conduction from the flat bottom to the upper hquid/air interface is maintained by heating the bottom constantly. Then as the temperature of the heat plate is increased, after the critical temperature is passed, the liquid suddenly starts to move to form steady convection cells. Therefore in this case, the critical temperature is assumed to be a bifurcation point. The important point is the existence of the standard state defined by the nonzero heat flux without any fluctuations. Below the critical temperature, even though some disturbances cause the liquid to fluctuate, the fluctuations receive only small energy from the heat flux, so that they cannot develop, and continuously decay to zero. Above the critical temperature, on the other hand, the energy received by the fluctuations increases steeply, so that they grow with time this is the origin of the convection cell. From this example, it can be said that the pattern formation requires both a certain nonzero flux and complementary fluctuations of physical quantities. 

Reciprocals of the critical temperatures, i.e., the maxima in curves such as those in Fig. 121, are plotted in Fig. 122 against the function l/x +l/2x, which is very nearly 1/x when x is large. The upper line represents polystyrene in cyclohexane and the lower one polyisobutylene in diisobutyl ketone. Both are accurately linear within experimental error. This is typical of polymer-solvent systems exhibiting limited miscibility. The intercepts represent 0. Values obtained in this manner agree within experimental error (<1°) with those derived from osmotic measurements, taking 0 to be the temperature at which A2 is zero (see Chap. XII). Precipitation measurements carried out on a series of fractions offer a relatively simple method for accurate determination of this critical temperature, which occupies an important role in the treatment of various polymer solution properties. 

In both Figures 2.6 and 2.7 there is a temperature range in which phase separation does not occur. In Figure 2.6, this temperature (7uc) is the maximum temperature at which two phases form, also known as the upper critical temperature. This maximum point occurs because the greater thermal motion in the system results in complete miscibility of the phases. In Figure 2.7, this temperature (ThC) is the minimum temperature at which phase separation is observed, or... 

Figure 3,10 Solvus and spinodal decomposition fields in regular (B) and subregular (D) mixtures. Gibbs free energy of mixing curves are plotted at various T conditions in upper part of figure (A and C, respectively). The critical temperature of unmixing (or consolute temperature ) is the highest T at which unmixing takes place and, in a regular mixture (B), is reached at the point of symmetry.

The instance we have considered here, that of a polymer in a poor solvent, results in an upper critical solution temperature (UCST) as shown in Figure 2.33. This occurs due to (a) decreased attractive forces between like molecules at higher temperatures and (b) increased solubility. For some systems, however, a decrease in solubility can occur, and the corresponding critical temperature is located at the minimum of the miscibility curve, resulting in a lower critical solution temperature (LCST). This situation is illustrated in Figure 2.34. 

The nucleate type of boiling is far more common than any other type. This form usually occurs in commercial evaporators, still pots, and similar boiling equipment. Much attention has been given to nucleate boiling and a good many data are available. Because the critical temperature difference is the upper limit to nucleate boiling, it too has received notice. The number of data for it is far from ample, because of the burnout difficulty discussed in Sec. IID. 

Near a critical temperature, however, solubility often decreases with rising temperature, so that there may actually be no CST at all—for example, see the systems of aniline with methane, ethane, or propane (Table I). One phase reaches its critical temperature below the CST. A few such critical temperatures of the upper layer are listed—e.g., for carbon dioxide, ethane, and ethyl ether (Table I). 

The upper limit of the vapor-pressure line is the critical point, indicated by point C. The temperature and pressure represented by this point are called the critical temperature, TC) and the critical pressure, pc. 

CONSOLUTF TEMPERATURE. The upper convolute temperature for two partially miscible liquids is the critical temperature above which the two liquids are miscible in all proportions. In some systems where the mutual solubility decreases with increasing temperature over a certain temperature range, the lower convolute temperature corresponds to the critical temperature below which the two liquids are miscible in all proportions. Some systems such as mclhylclhyl ketone and water have both upper and lower consolute temperatures. 

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