Heat capacity behavior

Since Tg is determined by a change in expansion behavior, there will be an associated shift in heat capacity behavior the expansion of a material is a result of an increase in the mean atomic vibration amplitude between atoms, and this vibration... 

Heimburg, T., Mirzaev, S.Z., and Kaatze, U. Heat capacity behavior in the critical region of the ionic binary mixture ethylammonium nitrate - n-octanol. Phys. Rev. E, 2000, 62, p. 4963-76. 

The crystal field interaction has pronounced effects on the heat capacity behavior of the system. At very low temperatures, ions occupy the lowest crystal field states. With increasing temperature, excitation within the crystal field spectrum takes place resulting in a significant contribution to the heat capacity (38). This contribution is given by the expression... 

The heat capacity behavior of PrNi2 confirms that it becomes a Van Vleck paramagnet at low temperatures (65). It exhibits no X-type thermal anomaly expected if there is magnetic ordering only a Schottky-type heat capacity excess is observed. This is a consequence of the thermal population of the higher crystal field states. 

This was originally interpreted as arising from cooperative antiferromagnetic ordering however, later studies of heat capacity behavior of this compound failed to show a X-type anomaly in the neighborhood of 13 K, indicating that the maximum in X did... 

Arrhenius equation for the rate constant of any process where the condition kT is often involved and (2) in H-bonded solvents, OH vibrations are coupled with librations and intermolecular modes giving a wide manifold of states within which activation can arise—cf. the known heat-capacity behavior of H (aq). 

From 90.5 to 298.15 K, the selected values of heat capacity are generally those determined by Pecharsky et al. (1996), as given by Pecharsky (2006), because of the very high purity of the metal used. However, in the region of the Neel transition, Pecharsky et al. determined insufficient measurements to allow characterization of the heat capacity behavior and therefore the power law equations of Jayasuriya et al. (1985b) were used in the range of 179-181 K and joined smoothly with the measurements of Pecharsky et al. (1996) either side of this range. Above 280 K, the latter measurements show scatter but a heat capacity value of 26.56 0.12 J/(mol K) at 298.15 K was calculated. 

There were many experimental proofs of the BCS model. In one proof, N. E. Phillips (1959) compared the heat capacity of aluminum in the superconducting and nonsuperconducting phase at low temperature. In the latter case, superconductivity was destroyed by a strong magnetic field. Phillips found the expected heat capacity behavior as a function of temperature for the nonsuperconducting phase. In the superconducting phase, the heat capacity increased very rapidly from zero and reached a value much higher than normal, as the temperature approached the critical temperature from below. This behavior is typical for the Bose-Einstein condensation and depends on the rapid increase of the entropy as T approaches Tc from below. 

From the above considerations, it should be clear that running an adiabatic scanning calorimeter in the constant heating (or cooling) modes makes it possible to determine latent heats when present and distinguish between first-order and second-order phase transitions. On the basis of Cp = P/t, it is also possible to obtain information on the pretransi-tional heat capacity behavior, provided one is able to collect sufficiently detailed and ac-... 

Further experiments on two layer films clearly show a sharp anomaly in the heat capacity behavior, suggesting that the SmBhex-SmA transition is not well described by the theory of defect-mediated... 

The variation of Cp for crystalline thiazole between 145 and 175°K reveals a marked inflection that has been attributed to a gain in molecular freedom within the crystal lattice. The heat capacity of the liquid phase varies nearly linearly with temperature to 310°K, at which temperature it rises more rapidly. This thermal behavior, which is not uncommon for nitrogen compounds, has been attributed to weak intermolecular association. The remarkable agreement of the third-law ideal-gas entropy at... 

Gaseous helium is commonly used as the working fluid ia closed-cycle cryogenic refrigerators because of chemical iaertness, nearly ideal behavior at all but the lowest temperatures, high heat capacity per unit mass, low viscosity, and high thermal conductivity. 

SolubiHty parameters of 19.3, 16.2, and 16.2 (f /cm ) (7.9 (cal/cm ) ) have been determined for polyoxetane, po1y(3,3-dimethyl oxetane), and poly(3,3-diethyloxetane), respectively, by measuring solution viscosities (302). Heat capacities have been determined for POX and compared to those of other polyethers and polyethylene (303,304). The thermal decomposition behavior of poly[3,3-bis(ethoxymethyl)oxetane] has been examined (305). 

Vinyl acetate is a colorless, flammable Hquid having an initially pleasant odor which quickly becomes sharp and irritating. Table 1 Hsts the physical properties of the monomer. Information on properties, safety, and handling of vinyl acetate has been pubUshed (5—9). The vapor pressure, heat of vaporization, vapor heat capacity, Hquid heat capacity, Hquid density, vapor viscosity, Hquid viscosity, surface tension, vapor thermal conductivity, and Hquid thermal conductivity profile over temperature ranges have also been pubHshed (10). Table 2 (11) Hsts the solubiHty information for vinyl acetate. Unlike monomers such as styrene, vinyl acetate has a significant level of solubiHty in water which contributes to unique polymerization behavior. Vinyl acetate forms azeotropic mixtures (Table 3) (12). 

From this equation, the temperature dependence of is known, and vice versa (21). The ideal-gas state at a pressure of 101.3 kPa (1 atm) is often regarded as a standard state, for which the heat capacities are denoted by CP and Real gases rarely depart significantly from ideaHty at near-ambient pressures (3) therefore, and usually represent good estimates of the heat capacities of real gases at low to moderate, eg, up to several hundred kPa, pressures. Otherwise thermodynamic excess functions are used to correct for deviations from ideal behavior when such situations occur (3). 

Time constants. Where there is a capacity and a throughput, the measurement device will exhibit a time constant. For example, any temperature measurement device has a thermal capacity (mass times heat capacity) and a heat flow term (heat transfer coefficient and area). Both the temperature measurement device and its associated thermowell will exhibit behavior typical of time constants. 

The behavior of the internal energy, heat capacity, Euler characteristic, and its variance ( x ) x) ) the microemulsion-lamellar transition is shown in Fig. 12. Both U and (x) jump at the transition, and the heat capacity, and (x ) - (x) have a peak at the transition. The relative jump in the Euler characteristic is larger than the one in the internal energy. Also, the relative height of the peak in x ) - x) is bigger than in the heat capacity. Conclude both quantities x) and x ) - can be used to locate the phase transition in systems with internal surfaces. 

FIG. 12 The behavior of the internal energy U (per site), heat capacity Cy (per site), the average Euler characteristic (x) and its variance (x") — (x) close to the transition line and at the transition to the lamellar phase for/o = 0. The changes are small at the transition and the transition is very weakly first-order. The weakness of the transition is related to the proliferation of the wormhole passages, which make the lamellar phase locally very similar to the microemulsion phase (Fig. 13). Note also that the values of the energy and heat capacity are not very much different from their values (i.e., 0.5 per site) in the Gaussian approximation of the model [47]. (After Ref. 49.)... 

A wide variety of physical properties are important in the evaluation of ionic liquids (ILs) for potential use in industrial processes. These include pure component properties such as density, isothermal compressibility, volume expansivity, viscosity, heat capacity, and thermal conductivity. However, a wide variety of mixture properties are also important, the most vital of these being the phase behavior of ionic liquids with other compounds. Knowledge of the phase behavior of ionic liquids with gases, liquids, and solids is necessary to assess the feasibility of their use for reactions, separations, and materials processing. Even from the limited data currently available, it is clear that the cation, the substituents on the cation, and the anion can be chosen to enhance or suppress the solubility of ionic liquids in other compounds and the solubility of other compounds in the ionic liquids. For instance, an increase in allcyl chain length decreases the mutual solubility with water, but some anions ([BFJ , for example) can increase mutual solubility with water (compared to [PFg] , for instance) [1-3]. While many mixture properties and many types of phase behavior are important, we focus here on the solubility of gases in room temperature IFs. 

The form of equations (8.11) and (8.12) turns out to be general for properties near a critical point. In the vicinity of this point, the value of many thermodynamic properties at T becomes proportional to some power of (Tc - T). The exponents which appear in equations such as (8.11) and (8.12) are referred to as critical exponents. The exponent 6 = 0.32 0.01 describes the temperature behavior of molar volume and density as well as other properties, while other properties such as heat capacity and isothermal compressibility are described by other critical exponents. A significant scientific achievement of the 20th century was the observation of the nonanalytic behavior of thermodynamic properties near the critical point and the recognition that the various critical exponents are related to one another ... 

Actually, the temperature does not change as heat is added to change the solid to gas at the equilibrium sublimation temperature. Hence, the heat capacity becomes infinite at this temperature, and the dotted line shown in Figure 8.12 should extend vertically to infinity. The compressibility and coefficient of expansion would show a similar behavior. 

Figure 10.14 Graph showing the limiting behavior at low temperatures of the heat capacity of (a), krypton, a nonconductor, and (b). copper, a conductor. The straight line in (a) follows the prediction of the Debye low-temperature heat capacity equation. In (b), the heat capacity of the conduction electrons displaces the Debye straight line so that it does not go to zero at 0 K.

A sample of nitrogen gas of volume 20.0 L at 5.00 kPa is heated from 20.°C to 400.°C at constant volume. What is the change in the entropy of the nitrogen The molar heat capacity of nitrogen at constant volume, CVm, is 20.81 J-K -mol . Assume ideal behavior. 

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... 

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