Critical temperature, determination

The critical temperature determined in the usual manner by observation of the disappearance of the meniscus, was found to be 372° C. The ratio between the boiling-point and the critical temperature on the absolute scale was found to be normal. ... 

As mentioned earlier, Lacher (12) reproduced the experimental behaviour of the Pd - H system by making proper allowance for the attractive interaction of defects. At any temperature below a certain critical temperature, determined by the magnitude of the defect interaction energy, increase in pressure of hydrogen increases the... 

Figure 25 displays the effects of thermal composition fluctuations on the inverse susceptibility S(0) for a (PEE PDMS) mixture (sample 10 in Table 2) versus 1/T for different diblock concentrations below the Lifshitz line [48]. The critical temperatures determined from S Ho) = 0 decrease with increasing diblock content in a similar way as shown for the (PB PS) blend (Fig. 23). The = 4.3% sample behaves as a pure blend At high temperatures S (0)...

Critical Temperature The critical temperature of a compound is the temperature above which a hquid phase cannot be formed, no matter what the pressure on the system. The critical temperature is important in determining the phase boundaries of any compound and is a required input parameter for most phase equilibrium thermal property or volumetric property calculations using analytic equations of state or the theorem of corresponding states. Critical temperatures are predicted by various empirical methods according to the type of compound or mixture being considered. 

Various methods are available for estimation of the normal boiling point of organic compounds. Lyman et al. review and give calcula-tional procedures for the methods of Meissner, Miller, and Lydersen/ Forman-Thodos. A more recent method that has been determined to be more accurate is the method of Pailhes, which reqmres one experimental vapor pressure point and Lydersen group contributions for critical temperature and critical pressure (Table 2-385). 

The regression constants A, B, and D are determined from the nonlinear regression of available data, while C is usually taken as the critical temperature. The hquid density decreases approximately linearly from the triple point to the normal boiling point and then nonhnearly to the critical density (the reciprocal of the critical volume). A few compounds such as water cannot be fit with this equation over the entire range of temperature. Liquid density data to be regressed should be at atmospheric pressure up to the normal boihng point, above which saturated liquid data should be used. Constants for 1500 compounds are given in the DIPPR compilation. 

Figure 1 determines the foregoing temperature effect and is easier to use than the equation or a nomograph proposed by Kharbanda for this relation. The results are fairly accurate, provided the temperatures for which the surface tensions are considered are not close to the critical temperature of the material in question. Best results are obtained for nonpolar compounds. 

The nucleate region is the one of interest in most plant design as previously described for plain tube boiling. The critical temperature difference curves have been determined experimentally for a reasonable number of fluids and should be used whenever possible. 

Check to determine that the maximum flux, Q/A, and critical temperature difference. Ah, are not exceeded. 

Fig. 3.18. Temperature dependence of the critical length determined experimentally and theoretically...

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. 

A third empirical criterion is based on the effect of temperature on the amount adsorbed. For physical adsorption the amount of gas adsorbed always decreases monotonically as the temperature is increased. Significant amounts of physical adsorption should not occur at temperatures in excess of the normal boiling point at the operating pressure. Appreciable chemisorption can occur at temperatures above the boiling point and even above the critical temperature of the material. Because chemisorption can be an activated process that takes place at a slow rate, it may be difficult to determine the amount of chemisorption corresponding to true equilibrium. Moreover, the process may not be reversible. It is also possible for two or more types of chemisorption or for chemical and physical adsorption to occur simultaneously on the same surface. These facts make it difficult to generalize with regard to the effect of temperature on the amount adsorbed. Different behavior will be observed for different adsorbent-adsorbate systems. 

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