Heat capacity calorimetric properties

There are various methods of the glass transition temperature evaluation based on temperature dependence of polymer physical properties in the interval of glass transition 1) specific volume of polymer at slow cooling (dilatometric method) 2) heat capacity (calorimetric method),3) refraction index (refractometric method) 4) mechanical properties 5) electrical properties (temperature dependence of electric conductivity) or maximum of dielectric loss 6) NMR ° 7) electronic paramagnetic resonance, etc. 

Both the Einstein and Debye theories show a clear relationship between apparently unrelated properties heat capacity and elastic properties. The Einstein temperature for copper is 244 K and corresponds to a vibrational frequency of 32 THz. Assuming that the elastic properties are due to the sum of the forces acting between two atoms this frequency can be calculated from the Young s modulus of copper, E = 13 x 1010 N m-2. The force constant K is obtained by dividing E by the number of atoms in a plane per m2 and by the distance between two neighbouring planes of atoms. K thus obtained is 14.4 N m-1 and the Einstein frequency, obtained using the mass of a copper atom into account, 18 THz, is in reasonable agreement with that deduced from the calorimetric Einstein temperature. 

Johnson et al. [143] used low-temperature adiabatic calorimetry and high-temperature drop calorimetry to obtain the heat capacity of both forms of mordenite as a function of the temperature. These results and the results of the reaction-solution calorimetric studies discussed herein, enabled the tabulation of the thermodynamic properties (C°, S°, Af H°, and Af G°) of mordenite from 0 K to 500 K and dehydrated mordenite from 0 K to 900 K. 

Calorimetric measurements, when combined with the normally available room temperature thermodynamic properties, give values for free energy, enthalpy, heat capacity and even volume at high temperatures. 

Thermal conductivity data are even more difficult to obtain. In the case of calorimetric data of heat capacity and heats of dissociation, the measurements though still reasonably challenging are aided by significant improvements in commercial calorimeters that can operate at high pressures. Thermal property data are presented in Section 6.3.2. 

Calorimetric (DSC) measurements yield thermodynamic properties of duplex melting in these oligonucleotides independent of any assumptions concerning the model of melting, such as a cooperative all-or-none process versus a noncooperative, multiple-stage melting process. Comparison of calorimetric enthalpies with van t Hoff enthalpies obtained either from the manipulation of heat capacity curves outlined in equations (16.19) to (16.22), or from optical or NMR measurements [equations (16.14) to (16.17)] allows conclusions to be drawn concerning the size of the cooperative unit. If the two... 

Another important event contributing to the progress in this field was the development of reaction microcalorimetry, which has permitted direct measurement of heat effects involved with the transfer of hydrophobic substances from a nonpolar environment to water. These processes have been thought to mimic the unfolding of compact protein, structures. Prior to the development of direct calorimetric techniques, all information on the interaction of a hydrophobic substance with water was obtained from equilibrium studies. However, the results were limited in accuracy, particularly those properties that are obtained by consecutive temperature differentiation of the solubility, for example, the change in heat capacity. 

The following properties belong to the calorimetric category (1) specific and molar heat capacities, (2) latent heats of crystallization or fusion. It will be shown that both groups of properties can be calculated as additive molar quantities. Furthermore, starting from these properties the molar entropy and enthalpy of polymers can be estimated. 

Heat capacity and derived properties at and below 298.15 K are taken from the calorimetric data (16 - 380 K) of Purukawa and Saba (4). The entropy is based on S (16 K) - 0.004 cal K" mol . Above 298.15 K the adopted C data are based on Ishihara and West s (5) merging of enthalpy data of Ditmar and Douglas (6) (323 - 1173 K) and Ishihara and West (5) (1182 - 2137) with the C data of Purukawa and Saba (4). Values above 2137 K are our extrapolation. Ishihara and West report a sharp rise in enthalpy data above 2030 K, apparently associated with premelting phenomena. Data in this region was Ignored by Ishihara and West during their treatment. 

The heat capacity quantifies the amount of thermal energy absorbed by a material upon heating, or released by it upon cooling. The heat capacity can be used to calculate all of the other thermodynamic properties, such as the enthalpy, entropy and Gibbs free energy, as functions of the temperature and pressure. The thermodynamic properties are often called calorimetric properties because they are usually measured by calorimetry [1-6]. 

Gardner, W. L., Mitchell, R. E., and Cobble, J. W., 1969, The thermodynamic properties of high-temperature aqueous solutions. XI. Calorimetric determination of the stemdeird partial molar heat capacity and entropy of sodium chloride solutions from 100 to 200"C. J. Phys. Chem., 73 2025-32. 

Obviously, the experimental description of the device should also contain information such as 1) the purpose of the instmment (combustion, heat of mixing, heat capacity, sublimation, etc.) 2) the principles and design of the calorimeter proper, including the ranges of temperature and pressure in which measurements can be performed 3) the measured quantity and measuring device 4) the static and dynamic properties of the calorimeter the calibration mode and the methods of measurement and determination of heat effects 5) the operational characteristics of the calorimetric device, the sensitivity noise level, the method of calibration, the accuracy, etc. 6) a description of the experimental procedure used in the calibration and the actual measurements. 

The relationship above leads directly to the standard calorimetric methods for determining the heat of a process either temperature is held constant by appropriate compensation for the heat effect, and the required compensation power is measured, or a temperature change is determined and used to calculate a corresponding value for exchanged heat. A precondition for the latter approach is accurate knowledge of the heat capacity as well as the heat transport properties of the measurement system. 

Thermodynamic properties of lactic acids and lactide, including entropy of fusion (A5), heat of formation (AHf), and heat capacity Cp), have been determined calorimetrically. Table 2.7 summarizes some of the thermodynamic data at... 

The tables may be used to calculate barrier heights in cases where appropriate spectroscopic data are not available, but where experimental values of heat capacity or entropy are known at one or more temperatures. The calorimetrically determined value of the barrier height may then be used in conjunction with the tables to calculate internal rotation contributions to thermodynamic properties over an extended temperature range. Examples of this procedure include calculations for ethane," propene, acetaldehyde, buta-1,2-diene, acetic acid, hexafluoro-ethane, 3-methylthiophen, and 2-methylthiophen. Where spectroscopic values of the barrier height have subsequently been determined, satisfactory agreement has been obtained with the earlier calorimetric values. The agreement between calorimetric (8.16 kJ mol ) and subsequent micro-wave [(8.28 0.07) kJ mol ] values of the barrier height in propene... 

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