Heat capacity contributions

The electronic contribution is generally only a relatively small part of the total heat capacity in solids. In a few compounds like PrfOHE with excited electronic states just a few wavenumbers above the ground state, the Schottky anomaly occurs at such a low temperature that other contributions to the total heat capacity are still small, and hence, the Schottky anomaly shows up. Even in compounds like Eu(OH)i where the excited electronic states are only several hundred wavenumbers above the ground state, the Schottky maximum occurs at temperatures where the total heat capacity curve is dominated by the vibrational modes of the solid, and a peak is not apparent in the measured heat capacity. In compounds where the electronic and lattice heat capacity contributions can be separated, calorimetric measurements of the heat capacity can provide a useful check on the accuracy of spectroscopic measurements of electronic energy levels. 

In Table 12.1, the contributions to the heat capacity Csp of the addendum are shown specific heat data references are reported in ref. [20], A factor 1/3 was attributed to the heat capacity contribution of the elements linking the crystal to the frame [15], Note that the electron heat capacity of the NTD Ge 31 sensor was derived from the electron... 

The heat capacity of the copper envelope and capillaries was subtracted from the heat capacity of the Torlon sample, whereas the other heat capacity contributions were neglected. 

Kieffer has estimated the heat capacity of a large number of minerals from readily available data [8], The model, which may be used for many kinds of materials, consists of three parts. There are three acoustic branches whose maximum cut-off frequencies are determined from speed of sound data or from elastic constants. The corresponding heat capacity contributions are calculated using a modified Debye model where dispersion is taken into account. High-frequency optic modes are determined from specific localized internal vibrations (Si-O, C-0 and O-H stretches in different groups of atoms) as observed by IR and Raman spectroscopy. The heat capacity contributions are here calculated using the Einstein model. The remaining modes are ascribed to an optic continuum, where the density of states is constant in an interval from vl to vp and where the frequency limits Vy and Vp are estimated from Raman and IR spectra. 

Heat capacity contributions of electronic origin Electronic and magnetic heat capacity... 

RADICALC Bozzelli, J. W. and Ritter, E. R. Chemical and Physical Processes in Combustion, p. 453. The Combustion Institute, Pittsburgh, PA, 1993. A computer code to calculate entropy and heat capacity contributions to transition states and radical species from changes in vibrational frequencies, barriers, moments of inertia, and internal rotations. 

Let hs = heat capacity of the particles per unit volume of the bed, fmn = fraction of this heat capacity contributed by the m, nth kind of particle,... 

In Figure 4, A gives a graph of the contribution due to three torsional Debye modes with 6 = 200° K., while B represents the heat capacity contribution of three hindered rotational degrees of freedom with ... 

The points in Figure 4 are the corresponding experimental values for H/Pd = 0.5 in palladium black in the temperature region 10° to 180° K. These points were calculated on the basis of PdH4 by adding the experimental heat capacity of one palladium atom to the experimental heat capacity contribution of four hydrogen atoms in Pd2H (palladium black) (8). 

A computer code to calculate entropy and heat capacity contributions to transition states and radical species from changes in vibrational frequencies, barriers, moments of inertia, and internal rotations. 

Finally, significant advances in the techniques of both thermal and thermochemical measurements have come to fruition in the last decade, notably aneroid rotating-bomb calorimetry and automatic adiabatic shield control, so that enhanced calorimetric precision is possible, and the tedium is greatly reduced by high speed digital computation. Non-calorimetric experimental approaches as well as theoretical ones, e.g., calculation of electronic heat capacity contributions to di- and trivalent lanthanides by Dennison and Gschneidner (33), are also adding to definitive thermodynamic functions. 

Other estimated values that have been reported include 200 cm ( ) and 37 cm (5 ). The inactive torsional frequency is treated as a hindered Internal rotation. We use an estimated potential barrier of 8.0 kcal mol ( ) to calculate heat capacity contributions for hindered rotation from the table of Pitzer and Brewer (9). Contributions below 201 K could not be obtained by... 

As S° and Cp for H+ are taken as zero at all temperatures, the negative ion values will show the rapid changes. The -(G°-H29g)/RT function has the advantage that the heat capacity contributions are canceled out to a large extent and an analytical function for -(G°-H2qg)/RT can be quite simple even if the heat capacity is behaving in a complex manner. 

We would like to find the contribution of the surface heat capacity to the total lattice heat capacity at a given temperature for a particle of a given size. Because the surface heat capacity is proportional to the surface area and the bulk term is proportional to the volume, the surface/volume ratio will clearly play an important role in determining the magnitude of the contribution of the surface heat capacity to the total heat capacity. The ratio of the bulk- and surface-heat-capacity tenns indicates both the temperature range and the thickness of the specimen for which the surface-heat-capacity contribution will become detectable. The ratio fora cube with sides of length L is approximately given by... 

Estimate the surface-heat-capacity contribution to the total heat capacity of a nickel cube with a side length of 100 A. 

There are no measurements of the heat capacity of ThD2(cr) or ThT2(cr), but Flotow et al. [1984FLO/HAS] have estimated the following values by modelling the heat capacity contributions from the lattice vibrations, represented by an Einstein function, conduction electrons and acoustic modes. This method had been shown to be valid for the deuterides of uranium, yttrium and zirconium. 

Also plotted in Fig. 1.2 is the experimental heat capacity of the liquid (at omi-stant pressure) In simple cases, such as polyethylene, the heat capacity of the liquid state could be understood by introducing a heat capacity contribution for the excess volume (hole theory) and by assuming that the torsional skeletal vibration can be treated as a hindered rotator A more general treatment makes use of a separation of the partition function into the vibrational part (approximated for heat capacity by the spectrum of the solid), a conformational part (approximated by the usual conformational statistics) and an external or configurational part. 

Figure 6 Second harmonic of the heat capacity contribution.

For dilute aqueous solutions of inorganic salts, a rough estimate of the specific heat capacity can be made by ignoring the heat capacity contribution of the dissolved substance, i.e. 

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