Critical temperature for the

For the phase separation problem, the maximum and minima in Fig. 8.2b and the inflection points between them must also merge into a common point at the critical temperature for the two-phase region. This is the mathematical criterion for the smoothing out of wiggles, as the critical point was described above. 

From literature sources, find the critical temperatures for the gaseous hydrocarbons methane, ethane, propane, and butane. Explain the trends observed. 

Calculations of the composition (112/ns) of symmetric nuclear matter (np = nn, no Coulomb interaction) are shown in Fig. 3 [7], At low densities, the contribution of bound states becomes dominant at low temperatures. At fixed temperature, the contribution of the correlated density 112 is first increasing with increasing density according to the mass action law, but above the Mott line it is sharply decreasing, so that near nuclear matter density (ns = ntot = 0.17 fm-3) the contribution of the correlated density almost vanishes. Also, the critical temperature for the pairing transition is shown. 

Casein is soluble at high concentrations of Ca2+ (0.4 M) at temperatures below 18°C, but above 18°C /9-casein is very insoluble, even in the presence of low concentrations of Ca2 + (4 mM). Ca-precipitated /9-casein redissolves readily on cooling to below 18°C. About 20°C is also the critical temperature for the temperature-dependent polymerization of /9-casein and the two phenomena may be related. 

Similar behavior is reported for tetralin and naphthalene, where single phases with water are seen in the 300-340°C range. In these cases the critical temperatures for the two organics are greater than that of water. Thus the critical temperature of water is lowered by the addition of aromatics like those in coal and coal products. 

As seen from Fig. 6 at 305°C the values of partial molar enthalpy for different runs of hydrogen desorption have a large deviation probably because of a proximity to critical temperature, thus it is difficult to determine the phase boundaries. The critical temperature for the existence of ZrMn2 hydride phase estimated by different authors is 277-327 °C [8] and 318°C [15], The plot of the AHdes. -C could be divided into three parts the hydrogen a-solid solution region (0pi transition (0.6p2 transition (1.0[Pg.353]

A model-independent conclusion The general behaviour of the in-plane paraconductivity is not affected, even up to T°, by doping. The SCF effects in L l eSr CuCU thin films seem to be not related to the pseudogap. t From the comparison of the measured paraconductivity with the ex-ended GGL approach i) The measured l c is a good mean-held critical temperature for the GGL approach, ii) Both the relaxation time of the SCF and the reduced temperature, e°, where the SCF vanish, are doping-independent and they take values close to those of BCS superconductors. This last result demands further studies. 

The mixing rules for the hard convex body part of the GvdW-EOS are given by theory [7]. The most significant parameter for the attractive part of the GvdW-EOS is the critical temperature. For the mixture, this is calculated for an equivalent substance as in the previous paper [2] ... 

The critical temperature for the thermal rearrangement of 3a under various conditions (in the melt,96 in quinoline20 or naphthalene17) appears to be in the vicinity of 180°. The 3-methoxy derivative (70) isomerizes readily with lithium iodide (in methyl ethyl ketone at 64°).17,96 When ethyl iodide is added to this reaction, i r-methylsaccharin (8) and iV-ethylsaccharin (22) are formed together.96 Lithium iodide catalysis is particularly useful in rearranging nucleoside derivatives, e.g., 71.17 The 3-benzyloxy derivative (73) reacts with debenzylation.17 Even more complex systems like derivatives of steroid alcohols17,20 are isomerized on heating in reasonable yields. When the optically active 3-(2-(cZ)octyloxy)benz[d]isothiazole-l, 1-dioxide was thermally re-... 

T. Kotoyori, Critical Temperatures for the Thermal Explosion of Liquids, Combust. Flame, 95, 307-312 (1993). 

The procedure to calculate the critical temperature for the spontaneous ignition or Tc for a gas-permeable oxidatively-heating substance, having some one of the several specific shapes above referred to as well as an arbitrary size, placed in the atmosphere under isothermal conditions, by applying the reduced form of the F-K equation, in the same manner as performed for a powdery chemical of the TD type, is introduced in Chapters 7 and 8. Principles and experimental procedures which are common to both powdery chemicals of the TD type and gas-permeable oxidatively-heating substances are, however, explained in the present chapter. 

Many research reports have appeared hitherto regarding various aspects of the thermal decomposition reaction or the combustion of woods or woody materials. However, instances in each of which the value of the critical temperature for the spontaneous ignition or for a bulky sawdust heap was actually measured have been only a few so far. In this regard, the works performed by Gross et al. [66], Akita [67], Anthony et al. [68], John [69] and Schliemann [70] are thought to be quite precious. 

In this connection, as commented in a footnote given under Table 24 in Section 9.5, it has been reported by J. Isler that the critical temperature for the thermal explosion of nitrocellulose powder (13.4 % N) formed into a cylinder, 1,1 cm ill diameter, 1,3 in specific gravity, and placed in the atmosphere under isothermal, but open, conditions, is 145 "C [75], This temperature value, 145 C, is far higher than 76" 77 °C, i.e., the value of SADT calculated herein for guncotton or collodion cotton, having an arbitrary shape and an arbitrary size, confined in an arbitrary closed container of the corresponding shape and size, and placed in the atmosphere under isothermal conditions (refer to the superscript, given in Table 24). 

T. Kotoyori, Critical Temperatures for the Self-Heating of Eight High Explosives of the True Autocatalytic Decomposition Type, Proceedings of the 11 Symposium on Chemical Problems Connected with the Stability of Explosives, Bastad, Sweden, 1998, Sektionen for Detonik och Forbranning, Sundbyberg, Sweden, 221-239 (2000). 

The term r/ refers to the critical temperature for the pure phase (Xb = 0), and the result demonstrates that Tc(Xb) is proportional to xf rather than to, as is the case when concentrations of solute are high. The resulting profile of the variation of the critical temperature with composition actually is concave up and represents an inverse plateau. When solutes are not randomly distributed but present as clusters, Salje (1995) argues that the proportionality of Tc goes as xf. This profile is concave downward and more closely resembles the plateau effects measured experimentally. 

The critical temperatures for the monoclinic to triclinic transition decrease with increasing Sr content (Fig. 28). As with the transition sequence, the room-temperature critical composition xsr varies with the degree of Al-Si order. Experimental data (Bruno... 

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