Heat capacity of transition

Entropies and Heat Capacities of Transition State Structnres... 

The entropies and heat capacities of transition state structures are calculated and reported in this section. S°gg and Cp iT) are obtained with the SMCPS program for which the imaginary... 

BD Hanson, M Mahnig, LE Toth. Low temperature heat capacities of transition metal borides. Z Naturforsch 26a 739, 1971. 

Many substances exist in two or more solid allotropic fomis. At 0 K, the themiodynamically stable fomi is of course the one of lowest energy, but in many cases it is possible to make themiodynamic measurements on another (metastable) fomi down to very low temperatures. Using the measured entropy of transition at equilibrium, the measured heat capacities of both fomis and equation (A2.1.73) to extrapolate to 0 K, one can obtain the entropy of transition at 0 K. Within experimental... 

The heat capacity of thiazole was determined by adiabatic calorimetry from 5 to 340 K by Goursot and Westrum (295,296). A glass-type transition occurs between 145 and 175°K. Melting occurs at 239.53°K (-33-62°C) with an enthalpy increment of 2292 cal mole and an entropy increment of 9-57 cal mole °K . Table 1-44 summarizes the variations as a function of temperature of the most important thermodynamic properties of thiazole molar heat capacity Cp, standard entropy S°, and Gibbs function - G°-H" )IT. 

The notion of concurrent SnI and Sn2 reactions has been invoked to account for kinetic observations in the presence of an added nucleophile and for heat capacities of activation,but the hypothesis is not strongly supported. Interpretations of borderline reactions in terms of one mechanism rather than two have been more widely accepted. Winstein et al. have proposed a classification of mechanisms according to the covalent participation by the solvent in the transition state of the rate-determining step. If such covalent interaction occurs, the reaction is assigned to the nucleophilic (N) class if covalent interaction is absent, the reaction is in the limiting (Lim) class. At their extremes these categories become equivalent to Sn and Sn , respectively, but the dividing line between Sn and Sn does not coincide with that between N and Lim. For example, a mass-law effect, which is evidence of an intermediate and therefore of the SnI mechanism, can be observed for some isopropyl compounds, but these appear to be in the N class in aqueous media. 

As indicated earlier, when phase transitions occur, AS for the phase transition must be included in the Third Law calculation of the entropy. For example, Figure 4.4 summarizes the heat capacity of Nt as a function of temperature, up... 

Figure 4.4 Heat capacity of N as a function of temperature. A solid phase transition occurs at 35.62 K, the melting temperature is 63.15 K, and the normal boiling temperature is 77.33 K.

Figure 4.8 Heat capacity of glycerol as a function of temperature. The solid line indicates Cp,m for the liquid and glassy phase. The dashed line represents Cp m for the solid. The dotted line at the melting temperature of 291.05 K. indicates the change in heat capacity upon melting. A glass transition occurs in the supercooled liquid at approximately 185 K. The heat capacities of the solid and the glass approach one another as the temperature is lowered they are almost identical below 140 K.

The interpretation of AC is that it is the difference in the standard molar heat capacities of the transition state and the reactants. Values of AC for the solvolysis of neutral molecules lie in the range 0 to -400 J mol-1 K l. The need for high-precision determinations of k (and 77) is emphasized by these values. 

Wunderlich, B. and Baur, H. Heat Capacities of Linear High Polymers. Vol. 7, pp. 151-368. Wunderlich, B. and Grebowic2, JThermotropic Mesophases and Mesophase Transitions of Linear, Flexible Macromolecules. Vol. 60/61, pp. 1-60. 

The heat capacity function for the solid phase Is from Fink (4. Fink points out that although (U,Pu)02 UO2, and ThC>2 have solid-solid phase transitions, the available data (4) make It impossible to determine the existence of a similar phase transition for Pu02 If additional high-temperature measurements indicate the presence of a solid-solid phase transition, the heat capacity of Pu02 between the phase transition and 2701 K may be significantly higher. 

A thermogram from a differential scanning calorimeter. The peak indicates a phase change in the sample, and the difference in base line before and after the phase transition is due to the difference in heat capacities of the two phases. 

The discovery of a transition which we identify with this has been reported by Simon, Mendelssohn, and Ruhemann,16 who measured the heat capacity of hydrogen with nA = 1/2 down to 3°K. They found that the heat capacity, after following the Debye curve down to about 11°K, rose at lower temperatures, having the value 0.4 cal/deg., 25 times that of the Debye function, at 3°K. The observed entropy of transition down to 3°K, at which the transition is not completed, was found to be about 0.5 E.U. That predicted by Eq. (15) for the transition is 2.47 E.U. 

The semiconducting properties of the compounds of the SbSI type (see Table XXVIII) were predicted by Mooser and Pearson in 1958 228). They were first confirmed for SbSI, for which photoconductivity was found in 1960 243). The breakthrough was the observation of fer-roelectricity in this material 117) and other SbSI type compounds 244 see Table XXIX), in addition to phase transitions 184), nonlinear optical behavior 156), piezoelectric behavior 44), and electromechanical 183) and other properties. These photoconductors exhibit abnormally large temperature-coefficients for their band gaps they are strongly piezoelectric. Some are ferroelectric (see Table XXIX). They have anomalous electrooptic and optomechanical properties, namely, elongation or contraction under illumination. As already mentioned, these fields cannot be treated in any detail in this review for those interested in ferroelectricity, review articles 224, 352) are mentioned. The heat capacity of SbSI has been measured from - 180 to -l- 40°C and, from these data, the excess entropy of the ferro-paraelectric transition... 

In order to compute the heat capacity of the ripplons on top of the structural transitions, we will need to consider the (classical) density of the inelastic states in more detail than in the previous section. The density of states (e) = was derived earlier taking as the reference state the generic... 

Heat capacity measurements at the glass transition temperature, Tg, are based on the same differential concept. The weight fraction of amorphous phase is calculated as the ratio of changes of heat capacity of the semi-crystalline sample ACp(S) over the change in heat capacity of the melt (ACp(m)) at the glass transition. For a two-phase system, the degree of crystallinity is given as ... 

One such property, as has been demonstrated (see [26]), is the change in partial heat capacity of the copolymer solution upon the heat-induced conformational transition of macromolecules. Such a change was detected by high-sensitivity differential scanning calorimetry (HS-DCS). The DSC data for the NVCl/NVIAz-copolymers synthesized at initial comonomer ratios of 85 15 and 90 10 (mole/mole) are given as thermograms in Fig. 4. 

The temperature dependence of reaction enthalpies can be determined from the heat capacity of the reactants and products. When a substance is heated from T to T2 at a particular pressurep, assuming no phase transition is taking place, its molar enthalpy change from AHm (T]) to AHm (T2) is... 

Figure 1.6 Heat capacity of rhombic and monoclinic sulfur [4,5] and the derived entropy of transition between the two polymorphs.

Thermodynamic representation of transitions often represents a challenge. First-order phase transitions are more easily handled numerically than second-order transitions. The enthalpy and entropy of first-order phase transitions can be calculated at any temperature using the heat capacity of the two phases and the enthalpy and entropy of transition at the equilibrium transition temperature. Small pre-tran-sitional contributions to the heat capacity, often observed experimentally, are most often not included in the polynomial representations since the contribution to the... 

Figure 8.24 Heat capacity of C03O4 [23-25]. The insert shows the magnetic order-disorder transition at around 30 K [24] in detail.

Figure 8.27 Heat capacity of some glass-forming liquids close to their glass transition temperatures ZnCl2 [45], GeSe2 [46], and a selected titanosilicate [47], aluminosilicate [48] and borosilicate [49] system.

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