Standard entropy and heat capacity

An assumption of a higher uncertainty for the accepted value of C° (Ni2Si04, olivine, 298.15 K) was necessary to achieve the coincidence of the standard heat capacity value at 298.15 K obtained from the low temperature measurements [84ROB/HEM] and from the high temperature thermal heat capacity function selected by this review (see below). 

According to [84ROB/HEM] between 300 and 1300 K the heat capacities can be represented by the equation  

The standard molar entropy at 298.15 K for Ni2Si04-olivine as determined by calorimetric measurements by Robie et al. [84ROB/HEM] is  

This value was also selected by the present review. The entropy value calculated from the temperature dependence of the Gibbs energy of the reaction of nickel with silica and oxygen e.g., as estimated by [68CAM/ROE], [76MAH/PAN], was not accepted by this review. 

The enthalpy of formation of Ni2Si04 olivine from the component oxides was measured by solution calorimetry in a molten oxide solvent at (965 2) K by Navrotsky 

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Low-temperature heat capacity and standard entropy of the solid trihalides... 

The selected values for the heat capacity and standard entropy of gaseous zirconium at 298.15 K and atmospheric pressure are ... 

The measnrements of the heat capacity of a very pure sample of ThF4(cr) by Lohr et al. [1954LOH/OSB] provide the selected values of the heat capacity and standard entropy ... 

The heat capacity of thiazole was determined by adiabatic calorimetry from 5 to 340 K by Goursot and Westrum (295,296). A glass-type transition occurs between 145 and 175°K. Melting occurs at 239.53°K (-33-62°C) with an enthalpy increment of 2292 cal mole and an entropy increment of 9-57 cal mole °K . Table 1-44 summarizes the variations as a function of temperature of the most important thermodynamic properties of thiazole molar heat capacity Cp, standard entropy S°, and Gibbs function - G°-H" )IT. 

Heat Capacity and Standard Partial Molal Entropy... 

In addition to the intermolecular potential, there is an intramolecular portion of the Helmholtz free energy. Cheetah uses a polyatomic model to account for this portion including electronic, vibrational, and rotational states. Such a model can be expressed conveniently in terms of the heat of formation, standard entropy, and constant-pressure heat capacity of each species. 

All calculations will be done for the standard pressure of 1 bar and, unless otherwise noted, at T = 298.15 K for one mole of gas. Table 8.1 lists the calculated molecular partition function, thermal energy (energy in excess of the ground-state energy), heat capacity, and entropy. The individual contributions from translation, rotation, each of the six vibrational modes, and from the first excited electronic energy level are included. 

The Third Law of Thermodynamics postulates that the entropy of a perfect crystal is zero at 0 K. Given the heat capacity and the enthalpies of phase changes, Eq. (12-3) allows the calculation of the standard absolute entropy of a substance, S° = AS for the increase in temperature from 0 K to 298 K. Some absolute entropies for substances in thermodynamic standard states are listed in Table 12-1. 

Reference data on total energies of forms 19-23 optimized by means of different theoretical methods in the gas phase are given in Table 2. Various energetic characteristics of tetrazoles can be successfully estimated. The vertical adiabatic ionization potentials of both neutral tautomers 20 and 21 were calculated for a- and Tt-radical cations <2000CPL(330)212>. The standard molar thermodynamic functions (enthalpies, heat capacities, and entropies) of... 

Heats of formation, standard entropies and heat capacities... 

It is necessary to specify zero ionic strength here because Debye-HUckel adjustments for ionic strength depend on the temperature. Heat capacities and transformed heat capacities are discussed in an Appendix to this chapter. However, since there is not very much information in the literature on heat capacities of species or transformed heat capacities of reactants, the treatments described here are based on the assumption that heat capacities of species are equal to zero. When molar heat capacities of species can be taken as zero, both standard enthalpies of formation and standard entropies of formation of species are independent of temperature. When Af H° and Af 5° are independent of temperature, standard Gibbs energies of formation of species at zero ionic strength can be calculated using... 

This value is adopted since the heat capacity and entropy calculated from estimated molecular parameters can be expected to be quite accurate for a diatomic molecule. The additional uncertainty originating from the recalculation to the standard temperature is hence moderate in relation to the uncertainty in the reaction enthalpy. The result is included in Appendix E since it was calculated with non-TDB auxiliary data. 

We now specify the equation of state used to model detonation products. For the ideal gas portion of the Helmholtz free energy, we use a polyatomic model including electronic, vibrational, and rotational states. Such a model can be conveniently expressed in terms of the heat of formation, standard entropy, and constant pressure heat capacity of each species. The heat capacities of many product species have been calculated by a direct sum over experimental electronic, vibrational, and rotational states. These calculations were performed to extend the heat capacity model beyond the 6000K upper limit used in the JANAF thermochemical tables (J. Phys. Chem. Ref. Data, Vol. 14, Suppl. 1, 1985). Chebyshev polynomials, which accurately reproduce heat capacities, were generated. 

In this chapter the focus will be on K, the equilibrium constant, and the following thermodynamic quantities, U, the energy, H, the enthalpy, G, the free energy, S, the entropy, V, the volume, C the heat capacity, and /x, the chemical potential. The significance of standard changes in the values of these quantities. At/, A//, AG, AS, ACp, and AV for the study of electrolyte solutions will be discussed. 

Both the heat capacity and entropy are given in units of cal mol-1 K-1. The reader will note the absence of a superscript on both quantities because the species is not in its standard state. 

EFI/PRO] Efimov, M. E., Prokopenko, L V., Tsirelnikov, V. L, Troyanov, S. L, Medvedev, V. A., Berezovskii, G. A., Paukov, L E., Thermodynamic properties of zirconium chlorides. I. The standard molar enthalpy of formation, the low-temperature heat capacity, the standard molar entropy, and the standard molar Gibbs energy of formation of zirconium trichloride, J. Chem. Thermodyn., 19, (1987), 353-358. Cited on pages 163, 164, 333,335,338. 

Sorai et al. [69SOR/KOS] measured the heat capacity of Ni(OH)2(cr) at low temperatures. These data have been used to determine the standard entropy, 5° (298.15 K), which has been accepted for the selected thermodynamic data of nickel compounds [76MAH/PAN]. Sorai et al. [69SOR/KOS] investigated three samples, (iii), (ii), and (i), of Ni(OH)2(cr) with different particle sizes, and reported values up to 104K and 300 K for the coarsest (iii) and the finer crystals (ii, i), respectively. As shown in Figure V-10 the heat capacity and consequently the entropy turned out to depend on the particle size and thus on the specific surface area s. 

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