Heat capacity estimation

More accurate heat capacity estimation formulas for various types of gases and liquids are given in Chapter 5 of Reid. Prausnitz, and Poling (see footnote 4), and several correlations are presented by Gold and Ogle. ... 

Heat capacity estimated by comparison to the other zirconium halides and titanium halides. Entropy estimated from additive constants. 

Gardas RL, Coutinho JAP (2008) A group contribution method for heat capacity estimation of ionic liquids. Ind Eng Chem Res 47 5751-5757... 

Morad, N.A., Mustafa Kamal, A.A., Panau, F. and Yew, T.W. (2000) Lipid specific heat capacity estimation for fatty acids, triacylglycerols, and vegetable oils based on their fatty acid composition. J. Am. Oil Chem. Soc., 77, 1001-1005. 

When the excess surface heat capacity estimated by Sorai et al. between 80 and 130 K was assumed to remain constant up to 300 K values of C° ,(Ni(OH)2, cr,... 

Heat capacity estimates may be made using DTA. In the ideal system, with identical reference and sample materials, the true baseline of the instrument is obtained. Using a reference and sample of different heat capacities, the baseline will not be the same and an estimate of the heat capacity of an unknown may be obtained by comparing the baseline shift with that for a sample of known heat capacity. A shift in the baseline is almost always observed after a DTA peak because of change in heat capacity of the sample. In addition, some reactions such as the glass transition of polymers yield virtually no DTA peak, but there is a rather sharp shift in the baseline after the transition temperature. 

Table 7.5 lists the heat capacities, estimated in a range temperature between 300 and 1500 K. With respect to DFT values, we note a good agreement for the heat capacities, varying between 0.02 and 2.85 cal mof K compared to GA. A deviation of 2.85 cal mol K can be considered insignificant compared to ca. 100 cal mof K ... 

Above 23 K and up to 80 K, the heat capacity values of Parkinson et al. (1951) (2-160 K) were preferred but above this temperamre begin to deviate higher such that they could not extrapolate to values of heat capacity selected in the room temperature region. Therefore, the three values of heat capacity estimated by Hultgren et al. (1973) at 150, 200, and 250 K were accepted together with the selected value at 298.15 K and with an interpolation between 80 and 150 K based on values of specific heat and their derivatives at these two temperatures. From 2 to 30 K, the measurements of Parkinson et al. (1951) tend from 21% low to converge to the selected values, but above 80 K, the trend is to a maximum of 8% high. 

Glasser L, Jenkins HBD (2012) Single-ion heat capacities, Cp(298)ion, of solids with a novel route to heat-capacity estimation of complex anions. Inorg Chem 51 6360-6366... 

Rycerz L, Gaune-Escard M (2002) Thermodynamics of SmCl3 and TmCl3 experimental enthalpy of fusion and heat capacity. Estimation of thermodynamic functions up to 1300 K. Z Naturforsch 57a 79-84 Thermodynamics of EUCI3 experimental cuithalpy of fusion and heat capacity and estimation of thermodynamic functions up to 1300 K (2002) Z Naturforsch 57a 215-220... 

Cp n molar heat capacity estimated by Neumann-Kopp s theory... 

The value of at zero temperature can be estimated from the electron density ( equation Al.3.26). Typical values of the Femii energy range from about 1.6 eV for Cs to 14.1 eV for Be. In temis of temperature (Jp = p//r), the range is approxunately 2000-16,000 K. As a consequence, the Femii energy is a very weak ftuiction of temperature under ambient conditions. The electronic contribution to the heat capacity, C, can be detemiined from... 

Investigations to find such additive constituent properties of molecules go back to the 1920s and 1930s with work by Fajans [6] and others. In the 1940s and 1950s lhe focus had shifted to the estimation of thermodynamic properties of molecules such as heat of formation, AHf, entropy S°, and heat capacity, C°. 

Residue Hea.tup. Equations 27—30 can be used to estimate the time for residue heatup, by replacing the Hquid properties, such as density and heat capacity, with residue properties, and considering the now smaller particle in evaluating the expressions for ( ), and T. In the denominator of T, 0is replaced by and is replaced by T the ignition temperature of the residue. 

Heat Capacity. The mean heat capacity (0—900°C) at constant pressure, 6, in J/(kg- " C), can be estimated in vitreous silica using the following expression, where / is temperature in °C. 

Phonon transport is the main conduction mechanism below 300°C. Compositional effects are significant because the mean free phonon path is limited by the random glass stmcture. Estimates of the mean free phonon path in vitreous siUca, made using elastic wave velocity, heat capacity, and thermal conductivity data, generate a value of 520 pm, which is on the order of the dimensions of the SiO tetrahedron (151). Radiative conduction mechanisms can be significant at higher temperatures. 

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). 

A relatively simple example of a group contribution technique is the method for estimating Hquid and soHd heat capacities (159). This method is a modification of Kopp s rule (160,161) which was originally proposed in 1864. Kopp s rule states that, at room temperature, the heat capacity of a soHd compound is approximately equal to a stoichiometric summation of the heat capacities of its atoms (elements). The Hurst-Harrison modified equation is as follows ... 

Heat Capacity. The multiple property estimation methods for constant pressure ideal-gas heat capacities cover a broad range of organic compounds (188,216,217). Joback s method (188) is the easiest to use however, usage of all these methods has been recommended only over the range 280—1100 K (7). An accurate method for ideal-gas heat capacities (constant pressure), limited to hydrocarbons, has been presented (218) that involves a fit of seven variables, and includes steric, ring, branching, alkene, and even allene corrections. 

Constant volume heat capacities for Hquid organic compounds were estimated with a four parameter fit (219). A 1.3% average absolute error for 31 selected species was reported. A group contribution method for heat capacities of pure soHds andHquids based on elemental composition has also been provided (159). 

Example 15 Estimate Solid Heat Capacity of Dinenzothiophene.. . ... 

Example 16 Estimate Liquid Heat Capacity of 2-Butanol. 

Heat Capacity, C° Heat capacity is defined as the amount of energy required to change the temperature of a unit mass or mole one degree typical units are J/kg-K or J/kmol-K. There are many sources of ideal gas heat capacities in the hterature e.g., Daubert et al.,"" Daubert and Danner,JANAF thermochemical tables,TRC thermodynamic tables,and Stull et al. If C" values are not in the preceding sources, there are several estimation techniques that require only the molecular structure. The methods of Thinh et al. and Benson et al. " are the most accurate but are also somewhat complicated to use. The equation of Harrison and Seaton " for C" between 300 and 1500 K is almost as accurate and easy to use ... 

Example Q Using Eq. 2-48 to estimate the ideal gas heat capacity of acetone (C HgO) at 600 K ... 

There are no reliable prediction methods for solid heat capacity as a function of temperature. However, the atomic element contribution method of Hurst and Harrison,which is a modification of Kopp s Rule, provides estimations at 298.15 K and is easy to use ... 

Example 15 Estimate solid heat capacity of dibenzothiophene, Ci2HsS. The required atomic element contributions from Table 2-393 are C = 10.89, H = 7.56, and S = 12.36. Substituting in Eq. (2-63) ... 

There are a number of reliable estimating techniques for obtaining pure-component hq uid heat capacity as a function of tem )erature, including Ruzicka and Dolmalsld, Tarakad and Danner, " and Lee and Kesler. These methods are somewhat compheated. The relatively single atomic group contribution approach of Chueh and Swanson for liquid heat capacity at 29.3.15 K is presented here ... 

Example 16 Estimate the liquid heat capacity at 293.15 K of 2-hiitanol. The atomic groups are ... 

TABLE 2-393 Atomic Element Contributions to Estimate Solid Heat Capacity at 298.15 K... 

TABLE 2-394 Atomic Group Contributions to Estimate Liquid Heat Capacity at 293.15 K... 

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