Heat capacity comparison

Sengers and coworkers (1999) have made calculations for the coexistence curve and the heat capacity of the real fluid SF and the real mixture 3-methylpentane + nitroethane and the agreement with experiment is excellent their comparison for the mixture [28] is shown in figure A2.5.28. 

A considerable variety of experimental methods has been applied to the problem of determining numerical values for barriers hindering internal rotation. One of the oldest and most successful has been the comparison of calculated and observed thermodynamic quantities such as heat capacity and entropy.27 Statistical mechanics provides the theoretical framework for the calculation of thermodynamic quantities of gaseous molecules when the mass, principal moments of inertia, and vibration frequencies are known, at least for molecules showing no internal rotation. The theory has been extended to many cases in which hindered internal rotation is... 

An even better example of this type of comparison is taken from measurements of Giauque1 of the heat capacity on phosphine PH3 shown in Figure 4.7.7 Cooling PH3 (g) causes it to condense to liquid at 185.41 K point... 

Figure 10.12 Comparison for diamond of the experimental Cr.m (circles) and the prediction of the Einstein heat capacity equation with = 1400 K (solid line). The experimental results below T = 300 K are closely spaced in temperature, and not all are shown in the figure.

Figure 10.15 Comparison of the fit of the Debye heat capacity equation for several elements. Reproduced from K. S. Pitzer. Thermodynamics. McGraw-Hill, Inc., New York, 1995, p. 78. Reproduced with permission of the McGraw-Hill Companies.

The STM postulated tunneling matrix element distribution P(A) oc 1 /A implies a weakly (logarithmically) time-dependent heat capacity. This was pointed out early on by Anderson et al. [8], while the first specific estimate appeared soon afterwards [93]. The heat capacity did indeed turn out time dependent however, its experimental measures are indirect, and so a detailed comparison with theory is difficult. Reviews on the subject can be found in Nittke et al. [99] and Pohl [95]. Here we discuss the A distribution dictated by the present theory, in the semiclassical limit, and evaluate the resulting time dependence of the specific heat. While this limit is adequate at long times, quantum effects are important at short times (this concerns the heat condictivity as well). The latter are discussed in Section VA. 

Here we will report measurements on the heat capacity of two NTD Ge 34B wafers, one non-metallized (only doped and annealed) and the other metallized (by B+ implantation and Au deposition). The comparison of data obtained from the non-metallized NTD Ge wafer and from the wafer with electrical contacts revealed an excess heat capacity, which can be attributed to the implantation process with B ions [44],... 

Quantitative estimates of E are obtained the same way as for the collision theory, from measurements, or from quantum mechanical calculations, or by comparison with known systems. Quantitative estimates of the A factor require the use of statistical mechanics, the subject that provides the link between thermodynamic properties, such as heat capacities and entropy, and molecular properties (bond lengths, vibrational frequencies, etc.). The transition state theory was originally formulated using statistical mechanics. The following treatment of this advanced subject indicates how such estimates of rate constants are made. For more detailed discussion, see Steinfeld et al. (1989). 

Table 8.3 Comparison of Debye temperatures derived from heat capacity data and from elastic properties.

Table 8. Comparison of internal energies and heat capacities for BNS and R potentials from Monte-Carlo simulation 72>...

Although the parameters in equation 6.58 were varied over a wide range, the heat capacities per unit volume and the thermal conductivities of the liquids were almost constant, as they are for most organic liquids, and the dimensions of the surface and of the tube were not varied. Nevertheless, for the purposes of comparison with other results, it is useful to work in terms of dimensionless groups. 

Giauque, whose name has already been mentioned in connection with the discovery of the oxygen isotopes, calculated Third Law entropies with the use of the low temperature heat capacities that he measured he also applied statistical mechanics to calculate entropies for comparison with Third Law entropies. Very soon after the discovery of deuterium Urey made statistical mechanical calculations of isotope effects on equilibrium constants, in principle quite similar to the calculations described in Chapter IV. J. Kirkwood s development showing that quantum mechanical statistical mechanics goes over into classical statistical mechanics in the limit of high temperature dates to the 1930s. Kirkwood also developed the quantum corrections to the classical mechanical approximation. 

Figure 2. Comparison of DSC thermograms for native and glutaraldehyde (GA)-crosslinked / -D-glucosidase at pH 5.0 in lOmM NaCl. In order to facilitate comparison of the peaks, the differential heat capacity values plotted for the native enzyme are the actual values multiplied by a fector of 0.571.

Table 3.5 Comparison of simple additivity of oxide constituents (column II) and exchange method of Helgeson et al. (1978) (column I), as methods of estimating heat capacity for crystalline components. Experimental values are shown for comparison in column III. Lower part of table adopted exchange reactions (for which it is assumed that ACp reaction = 0). Data in J/(mole X K) (adapted from Helgeson et ah, 1978).

The thermodynamic constants of THF polymerization have been investigated by a number of authors. A variety of experimental techniques have been utilized including determinations of conversion to polymer, combustion, heat capacities eind vapor pressure. Comparison of our results with some previously published data shows that our results are within the range of the values reported (Table 3). 

Aminomethylpyridine (picolylamine) is an important ligand in respect to spin cross-over, [Fe(2-pic)3]Cl2 being the key compound." Fleat capacity measurements on [Fe(2-pic)3]Cl2 EtOH gave values of 6.14kJmol and 50.59 JK moC for the spin eross-over entropy the determined entropy was analyzed into a spin contribution of 13.38, an ethanol orientational effeet of 8.97, and a vibrational contribution of 28.24 JK mol. " This compound exhibits weak cooperativity in the solid state." The heat capacity of [Fe(2-pic)3]Cl2 MeOH is consistent with very weak cooperativity." [Fe(2-pic)3]Br2 EtOH shows a lattice expansion significantly different from that expected in comparison with earlier-established behavior of [Fe(2-pic)3]Cl2 EtOH." ... 

Fig. 9 Comparison of heat capacities for ST016 and ST018-95. Inset shows enlarged plot of C/T versus T near 100 K...

Fig. 7.7 A comparison of the theoretical and experimental 4d and 5d electronic heat capacities. The theoretical values were obtained directly from eqn (7.28) and Fig. 7.6, neglecting any changes in the density of states due to bandwidth variation within the 4d and 5d series.

We now show that equations analogous to Eq. (34) follow for the enthalpy and entropy of mixing, AHM and ASM, but that, in contrast to the chemical potentials, the partial molar enthalpies and entropies for the components differ from those for the species. Finally we show that the equation for the constant pressure relative heat capacity is of a slightly more complicated form than Eq. (34). Equation (34) and its analogs for and ASM are necessary for comparison of model predicted quantities with experiment. From basic thermodynamic equations we have... 

Some physical properties of water are shown in Table 7.2. Water has higher melting and boiling temperatures, surface tension, dielectric constant, heat capacity, thermal conductivity and heats of phase transition than similar molecules (Table 7.3). Water has a lower density than would be expected from comparison with the above molecules and has the unusual property of expansion on solidification. The thermal conductivity of ice is approximately four times greater than that of water at the same temperature and is high compared with other non-metallic solids. Likewise, the thermal dif-fusivity of ice is about nine times greater than that of water. 

LC-PB-MS has been investigated as a potential confirmatory method for the determination of malachite green in incurred catfish tissue (81) and of cephapirin, furosemide, and methylene blue in milk, kidney, and muscle tissue, respectively (82). Results showed that the mobile-phase composition, nebulization-de-solvation, and source temperature all play an important role in the sensitivity of the method. The sensitivity increases with decreasing heat capacity of the mobile phase in the order methanol acetonitrile isopropanol water and with decreasing flow rate. A comparison of the PB with the thermospray interface showed that less structural information was provided by the latter, whereas the sensitivity was generally lower with the thermospray interface. 

Table 6.1 Comparison of the mean molar heat capacities for carbon dioxide and hydrogen, and carbon monoxide and water...

The values of (H2 — Hj ) for rounded molalities at 298.15° K were obtained from the plots of (H2 — H >) against ra1/2. The smooth curve was drawn through all the experimental points the average deviation from the smoothed curve was 15 calth mol-1 for 50 mass percent monoglyme. These values are presented in Table XIV and are higher than those found for hydrochloric acid in the same mixed solvents (1). The values of (H2 — H%) in aqueous medium at 298.15° K are given for direct comparison. The relative partial molal heat capacity (Cp — Cp) was calculated by the following formula ... 

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