Specific heat peaks

Scientific awareness of a low-temperature transition in magnetite began in 1929 with the observation of a A-type anomaly in the specific heat at about 120 K. The anomaly was typical of an order-disorder transition, but it was well below the magnetic-ordering temperature Tc = 850 In 1931, Okamura observed an abrupt semiconductor-semiconductor transition near 120 K. The transition exhibits no thermal hysteresis, but the transition temperature is sensitive to the oxygen stoichiometry. More recent specific-heat measurements show the presence of two resolvable specific-heat peaks at the transition temperature the lower-temperature peak near 110 K appears to be due to a spin reorientation. 

This trend Is more easily seen In Figures 6-8. Specific heat curves of PVC annealed at 1, 31.6, and 1000 hours at the various annealing temperatures are Illustrated. In the 1 hour figure, the specific heat peak Increased from 65-80 C. However, at 85 C the magnitude of the peak suddenly decreased and became much broader. 

A comparison of the volume and enthalpy data substantiates this hypothesis. The second step of volume reduction is clearly related to the development of the specific heat peaks above Tg. The overshoots of enthalpy below the equilibrium value are moved from a lower temperature to a higher one if the Initial volume is decreased below a critical value. 

YbBiPt and Yo,5Ybo.sBiPt. This (complex) cubic (space group F43m) system has a remarkably high Sommerfeld constant of 8 J/(molK ) below 0.2 K. AC-susceptibility points towards some form of magnetic order around 0.4 K and specific heat peaks near that temperature as well (Fisk et al. 1991). An Yb moment of 3/tb was deduced from susceptibility below lOK. 

The formation of the hydrogen superlattice in several LaD2+x compounds was clearly seen in the form of specific-heat peaks at 250-270 K (fig. 33) and also as breaks in the x-... 

The specific heat of water (see Fig. A3.9(b)) (as well as of other fluids, for example, for carbon dioxide, see Fig. A3.18 and Fig. A3.26 for helium) has a maximum value at the critical point. The exact temperature that corresponds to the specific heat peak above the critical pressure is known as the pseudocritical temperature (see also Figs. A3.23 and A3.24, and Table A3.2 for water and carbon dioxide). For water at pressures approximately above 300 MPa and for carbon dioxide at pressures above 30 MPa (see Fig. A3.24), a peak (here, it is better to say a hump ) in specific heat almost disappears therefore, the term such as a pseudocritical point no longer exists. The same applies to the pseudocritical line. 

Fig. 5.2(a)] result in a pseudo-transition which is represented by the first specific-heat peak in Fig. 5.1. The second less-pronounced peak in Fig. 5.1 around T 0.6 — 0.7 signals the melting into globular structures, whereas at still higher temperatures T 1.5 the well-known collapse peak indicates the dissolution into the random-coil phase. The distribution of the maximum values of the specific heat with respect to the maximum temperatures is shown in Fig. 5.3. Not surprisingly, the peaks belonging to the... 

The low temperature magnetic susceptibility of monoclinic, cubic, stoichiometric and substoichiometric gadolinium oxides have been measured in the range 1-6 K by Miller et al. (1971). Transformation temperatures and correlations with specific heat peaks in Gd metal containing appreciable amounts of oxygen are made. 

Figure C2.5.6. Thennodynamic functions computed for the sequence whose native state is shown in figure C2.5.7. (a) Specific heat (dotted curve) and derivative of the radius of gyration with respect to temperature dR /dT (broken curve) as a function of temperature. The collapse temperature Tg is detennined from the peak of and found to be 0.83. Tf, is very close to the temperature at which d (R )/d T becomes maximum (0.86). This illustrates...

The specific heat of polyethylene is higher than for most thermoplastics and is strongly dependent on temperature. Low-density materials have a value of about 2.3 J/g at room temperature and a value of 2.9 J/g at 120-140°C. A somewhat schematic representation is given in Figure 10.9. The peaks in these curves may... 

Fig. 3.9. Specific heat of FeCl2 4H20 drawn from data obtained by Friedberg et al. [35] and Raquet and Friedberg [36]. The peak near 1K is only partly shown, the highest value of the specific heat measured being... 

An example of magnetic contributions to the specific heat is reported in Fig. 3.9 that shows the specific heat of FeCl24H20, drawn from data of ref. [35,36]. Here the Schottky anomaly, having its maximum at 3K, could be clearly resolved from the lattice specific heat as well as from the sharp peak at 1K, which is due to a transition to antiferromagnetic order (lambda peak). 

Fig. 5.5. Per cent of remaining liquid 4He after pumping the bath down to the temperature T. Note the step around 2.2 K due to the transition to the superfluid phase with a peak in the specific heat... 

Experimental Methods In Differential thermal analysis (DTA) the sample and an inert reference substance, undergoing no thermal transition in the temperature range under study are heated at the same rate. The temperature difference between sample and reference is measured and plotted as a function of sample temperature. The temperature difference is finite only when heat is being evolved or absorbed because of exothermic or endothermic activity in the sample, or when the heat capacity of the sample changes abruptly. As the temperature difference is directly proportional to the heat capacity so the curves are similar to specific heat curves, but are inverted because, by convention, heat evolution is registered as an upward peak and heat absorption as a downward peak. 

If a temperature is desired at an equivalence ratio other than that listed, it is best obtained from a plot of T versus for the given values. The errors in extrapolating in this manner or from the graph are trivial, less than 1%. The reason for separate Figs 1.4 and 1.5 is that the values for = 1.0 and 4> = 1.1 overlap to a great extent. For Fig. 1.5, = 1.1 was chosen because the flame temperature for many fuels peaks not at the stoichiometric value, but between = 1.0 and 1.1 owing to lower mean specific heats of the richer products. The maximum temperature for acetylene-air peaks, for example, at a value of = 1.3 (see Table 1.2). 

C02 increases and the differences diminish. At the highest reaction enthalpies, the temperature for many fuels peaks not at the stoichiometric value, but, as stated, between

mean specific heats of the richer products. 

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