Heat Capacity Functions Research Articles

Heat capacity and thermodynamic functions of zirconia and yttria-stabilized zirconia

Heat capacities of pure zirconia ZrO2and 7.76 · 10−2mole fraction yttria-stabilized zirconia (ZrO2)0.9224(Y2O3)7.76·10−2were measured by adiabatic calorimetry at temperatures between 13 K and 300 K. The results were compared and analysed from the standpoint of the effects of yttria doping. The yttria-stabilized zirconia showed excess heat capacity at low temperatures which should be attributed to so-called low-energy modes caused by the defects in the crystal. The smoothed values of molar heat capacities at rounded temperatures were calculated from the experimental data. The thermodynamic functions enthalpy, entropy, and Gibbs free energy were also calculated and tabulated. The standard enthalpy and entropy of pure zirconia and 7.76 · 10−2mole fraction yttria-stabilized zirconia at T= 298.15 K are 8.711 kJ · mol −1 and 49.79 J · K−1 · mol−1, and 9.595 kJ · mol −1 and 56.47 J · K−1 · mol−1, respectively.

Influence of the adsorber heat exchanger design on the performance of the heat pump system

Research activity on adsorption heat pumps is mainly devoted to the improvement of the heat transfer inside the adsorber bed. To achieve this, various new types of heat exchanger designs and use of additives have recently been proposed. In this paper a study is made into the effect of an increased amount of metal in the adsorbent bed on the coefficient of performance (COP) and on the specific power. This correspondingly affects the energy delivered to the user and the investment cost of the system. A simplified dynamic model has been developed to calculate the performances of the machine as a function of the extra heat capacity, the global heat transfer coefficient and the cost of the material. Finally, a general diagram is proposed in order to evaluate the minimum heat transfer improvement that must be obtained with a higher heat exchanger surface, or when additives and metallic structures, are inserted into the adsorber bed in order to increase the specific power of the machine.

Quantum spin liquid in the 2D anisotropic Heisenberg model with frustrated next nearest neighbor exchange

The two-dimensional (2D) Heisenberg model with anisotropic exchange (Δ=1−Jx/Jz) and with negative next nearest neighbor exchange (J2) with S=1/2 is investigated by using the quantum-mechanical Monte-Carlo method. The energy, magnetic moment at a site, heat capacity, and spin-spin correlation functions are calculated. The stability regions for Néel ordering of spins as well as the strip-phase and gapless quantum spin liquid are determined in the interval Δ/2⩽J2/J1⩽1/(2Δ).

Calorimetric measurements on rare earth pyrohafnates RE2Hf2O7 (RE=La,Eu,Gd)

Enthalpy increment measurements have been carried out on La2Hf2O7, Eu2Hf2O7 and Gd2Hf2O7 in the temperature range 980–1740 K by using a high temperature differential calorimeter. From the enthalpy values, other thermodynamic functions, such as heat capacity, entropy and free energy functions have been generated. The high temperature Cp data of the rare earth pyrohafnates obtained in this study are discussed in relation to the crystal chemistry of these pyrochlores.

Heat Capacity and Thermodynamic Functions of Anhydrous 4, 4'-Bipyridine

Heat Capacity and Thermodynamic Functions of Anhydrous 4, 4'-Bipyridine

Low-temperature heat capacities and thermodynamic properties of rare-earth triisothiocyanate hydrates (III) —Sm(NCS)3 · 6H2O, Gd(NCS)3 · 6H20, Yb(NCS)3 · 6H20 and Y(NCS)3 · 6H20

The heat capacities of four RE isothiocyanate hydrates, Sm(NCS)3, · 6H20, Gd(NCS)3 · 6H20, Yb(NCS)3, · 6H2O and Y(NCS)3, · 6H20, have been measured from 13 to 300 K with a fully-automated adiabatic calorimeter. No obvious thermal anomaly was observed for the above-mentioned compounds in the experimental temperature ranges. The polynomial equations for calculating the heat capacities of the four compounds in the range of 13–300 K were obtained by the least-squares fitting based on the experimentalC P, data. TheC P, values below 13 K were estimated by using the Debye-Einstein heat capacity functions. The standard molar thermodynamic functions were calculated from 0 to 300 K. Gibbs energies of formation were also calculated.

Low-temperature heat capacities and thermodynamic properties of rare-earth triisothiocyanate hydrates (III)——Sm(NCS) 3 · 6H 2 O, Gd(NCS) 3 · 6H 2 0, Yb(NCS) 3 · 6H 2 0 and Y(NCS) 3 · 6H 2 0

The heat capacities of four RE isothiocyanate hydrates, Sm(NCS)3, · 6H20, Gd(NCS)3 · 6H20, Yb(NCS)3, · 6H2O and Y(NCS)3, · 6H20, have been measured from 13 to 300 K with a fully-automated adiabatic calorimeter. No obvious thermal anomaly was observed for the above-mentioned compounds in the experimental temperature ranges. The polynomial equations for calculating the heat capacities of the four compounds in the range of 13–300 K were obtained by the least-squares fitting based on the experimental C P, data. The C P, values below 13 K were estimated by using the Debye-Einstein heat capacity functions. The standard molar thermodynamic functions were calculated from 0 to 300 K. Gibbs energies of formation were also calculated.

Conformation and stability of streptokinases from nephritogenic and nonnephritogenic strains of streptococci

Conformation and stability of three Sks from Streptococcus equisimilis strain H46A, Streptococcus pyogenes strain A374, and Streptococcus pyogenes strain AT27 were compared by limited proteolysis, CD, and fluorescence measurements and by DSC. The general similarity of the peptide CD spectra in the spectral region 185 to 260 nm indicates the same type of folding for the three proteins. Fluorescence and aromatic CD spectra are consistent with a predominant surface localization of the aromatic amino acids and a low rigidity of their surroundings. A major difference among the three Sks is shown by deconvolution of their excessive heat capacity functions. Deconvolution reveals two energetic folding units in Sk H46A but three energetic folding units in Sk A374 and Sk AT27. Digestion of the Sks with trypsin indicates a reduced sensitivity of the C-terminal region of Sk A374 and Sk AT27 in comparison to Sk H46A. This suggests that amino acids of the C-terminal region participate in the formation of the third folding unit of Sk A374 and Sk AT27.

Thermodynamic Properties of Aqueous Morpholine and Morpholinium Chloride at Temperatures from 10 to 300 °C: Apparent Molar Volumes, Heat Capacities, and Temperature Dependence of Ionization

Apparent molar heat capacities Cp,φ of aqueous morpholine and morpholinium chloride were determined with a Picker flow microcalorimeter at temperatures from 10 to 55 °C. The apparent molar volumes Vφ have been determined with platinum vibrating tube densitometers at temperatures from 10 to 300 °C and pressures in excess of steam saturation. Values of Vφ for morpholine approach large positive values at elevated temperatures, consistent with a lowering of the critical temperature in the solutions relative to water. The effect in aqueous morpholinium chloride is reversed, confirming the profound effect of ionic charge on the high-temperature thermodynamic properties of aqueous solutes, even for large organic molecules. Standard partial molar heat capacity functions were estimated from the high-temperature Vφ data and low-temperature values of Cp,φ using an empirical model based on the appropriate solvent density derivatives and the revised Helgeson−Kirkham−Flowers model. The results from both models are consistent with literature values for the heat capacity of ionization determined from high-temperature potentiometric measurements to within the combined experimental uncertainties. The results show that the effects of solvent expansion by the neutral species is significant at elevated temperatures. The effective Born radius of ions containing organic groups could be significantly larger than the radius calculated from the formula for simple cations because of this effect.

Heat capacity and thermodynamic functions of crystalline 4,4‴-difluoro-p-quaterphenyl

Abstract The heat capacity of crystalline 4,4‴-difluoro- p -quaterphenyl was measured between 8 and 303 K by adiabatic calorimetry. A broad heat-capacity anomaly was found at 200.5 ± 0.5 K and attributed to a phase transition associated with molecular twisting. Some thermodynamic properties including those concerning the phase transition are reported.

Thermodynamics of finite quantum systems: application to spin magnetism II

We extend our study of thermodynamics of a Kubo particle to temperatures smaller than the mean interlevel spacing. We obtain the distribution functions of spin susceptibility and heat capacity for Poisson and Wigner-Dyson level statistics. We evaluate the line shape of the Knight shift due to spin effects both in a single particle and for the ensemble average and compare it with orbital and spin-orbit contributions.

Heat capacity and thermodynamic functions of zinc metaarsenate in the range 298.15?673 K

The isobaric heat capacity of Zn(AsO3)2 is measured by a calorimetric method in the range 298.15–673 K. From the data obtained the temperature dependences of the functions Ckp/0(T), S0(T), H0(T)−H0(298.15), and φ** are calculated.

Low temperature thermal properties of cobalt(II) bromate hexahydrate

The heat capacity of cobalt(II) bromate hexahydrate Co(H 2O) 6(BrO 3) 2 was measured at temperatures between 13 and 310 K. Infrared and Raman spectra of the crystal were recorded in the frequency range of 400–4000 cm −1 for the former and 50–4000 cm −1 for the latter. The heat capacity data were analyzed in harmonic approximation using Debye and Einstein heat capacity functions. Some of the characteristic frequencies of the heat capacity functions were taken from the vibrational spectra and others determined by non-linear least squares fitting of the heat capacity function to the experimental heat capacity data. One Debye temperature (92 ± 1 K) and three Einstein temperatures (123 ± 2 K, 231 ± 1 K, 614 ± 50 K) were determined as functions of the temperature interval of the heat capacity data used for the fitting. The best-fit characteristic temperatures were constant, except for the third Einstein temperature, against variation of the upper limit temperature of the fitting interval from 16 to 280 K with the lower limit temperature being kept at 13 K. The Debye temperature agreed with a value of 92.4 K derived from the sound velocity. The best-fit Einstein temperatures have counterparts in the Raman spectrum in the lattice vibration region. This is the first detailed analysis of heat capacity data on a structurally complex crystal in which acoustic phonon frequencies from thermal and elastic properties are favorably compared.

Quasi-harmonic and leading order anharmonic parameters for some minerals estimated from available thermodynamic data

The thermodynamics of the Earth's interior is usually approached through the quasi-harmonic theory of solids, relying on the tacit assumption that explicit anharmonic contributions, which are difficult to calculate even for the most simple solids, are not important. The basic qualitative idea assumes that, as anharmonicity increases with temperature but decreases with pressure, in the Earth's interior the two effects are self-cancelling. A safer approach is to consider not the absolute but the homologous temperature, i.e. to take the melting temperature as a scaling factor. Since the geotherm lies rather close to melting, the relative importance of anharmonic terms in the thermodynamics of the Earth's interior is presumably high. At room pressure, the leading order anharmonic coefficients and their volume derivatives, as well as the quasi-harmonic terms from available thermodynamic data, can be estimated by fitting to experiment the theoretical expressions to the fourth order in the Hamiltonian of three functions of compressibility, heat capacity and thermal expansion, tailored to minimize the effect of experimental errors. The capability of this procedure to produce stable and accurate results has been previously tested through extensive applications to NaCl, and to several metals, chosen because of the large number of available independent data, which allowed the study in detail of the effect of external as well as internal errors. Comparatively accurate estimates were found to be possible. The procedure is here applied to forsterite, periclase, rutile and pyrope, allowing the estimation of the relative magnitude of the quasi-harmonic and leading order anharmonic terms. At temperatures of half the melting temperature the difference between the two is of the order of 20% on the Grüneisen parameter and just a few per cent on the heat capacity, which is nevertheless typically 10% from the classical 3 R limit.

Thermodynamics of aqueous zinc: Standard partial molar heat capacities and volumes of Zn 2+(aq) from 10 to 55°C

The apparent molar heat capacities and volumes of aqueous Zn(ClO 4) 2 have been measured from 10–55°C in a Picker flow microcalorimeter and vibrating tube densimeter. The Guggenheim form of the extended Debye-Hückel equation was fitted to the experimental data, to obtain the following expressions for the standard-state properties from 10–55°C: C p 0(Zn(ClO 4) 2, aq)/JK −1 mol −1 = 3850.8 − 150720 T−190 − 8.4956T (1) and V 0(Zn(ClO 4) 2, aq)/cm 3 mol −1 = 116.65 − 4073 T−190 − 0.050374T . (2) The standard partial molar heat capacities and volumes for Zn 2+(aq) were extrapolated to higher temperatures by employing the Helgeson-Kirkham-Flowers (HKF) equations, amended to include a standardstate correction term. Gibbs energies calculated from the extrapolated heat capacity and volume functions are consistent with limited experimental data for the solubility of ZnO in acidic to near-neutral aqueous solutions at 200–300°C ( bourcier and barnes, 1987).

An ab initio study of the structures, barriers for internal rotation, vibrational frequencies, and thermodynamic functions of the hydrochlorofluorocarbon CH3CF2Cl and the corresponding radical CH2CF2Cl

Ab initio molecular orbital calculations were performed using the GAUSSIAN 90 system of programs at the HF/6-31G* level of theory, on the hydrochlorofluorocarbon (HCFC) 1-chloro-1,1-difluoroethane and the 1-chloro-1,1-difluoroethyl radical. Equilibrium geometries, barriers for internal rotation, and harmonic vibrational frequencies were thus calculated. A single conformational minimum in the potential energy surface was located for both the radical and the parent molecule. The radical center in CH2CF2Cl was found to be nonplanar. Transition structures for internal rotation about the C—C bond were located for both the molecule and the radical using analytical methods. The rotation barriers, evaluated at the fourth-order Møller–Plesset perturbation theory ((U)MP4/6-311G**/6-31G*). were calculated after inclusion of zero-point vibrational energy differences to be 1.11 and 4.12 kcal/mol for the radical and the parent molecule, respectively. Computed thermodynamic properties including heat capacity, entropy, enthalpy, and free energy functions are reported as a function of temperature. Using an experimentally measured heat of formation of CH3CF2Cl at 298 K, the heat of formation of CH2CF2Cl was calculated to be −74.3 ± 1.7 kcal/mol. Tabulations of ΔH0f,T, ΔG0f,T, and log10Kf,T over the temperature range of 0–1500 K are also reported for both species.

Thermodynamics of alkali alkanoates IX. Heat capacity and thermodynamic functions of lithium 2-methylpropanoate at temperatures from 7 K to 535 K

The heat capacity of lithium 2-methylpropanoate was measured by equilibrium adiabatic calorimetry at temperatures, T from 7 K up to 350 K and by d.s.c. from 330 K through melting to 535 K. A small diffuse hump was observed in the range T = 125 K to 250 K. A solid-to-solid (intercrystalline) transition was observed at T = 445 K, and melting to the isotropic liquid occurred at 510 K. The enthalpies Δ trs H o m and entropies Δ trs S o m of transition were calculated to be 903 R·K and 2.03 R for the solid-to-solid transformation (assumed to be first order) and 1045 R·K and 2.05 R for melting.

Propriétés thermodynamiques des trifluorocadmiates de rubidium et de césium (RbCdF 3, CsCdF 3) de 10 à 300 K : Transition de phase dans les fluoroperovskites

The heat capacities of cesium and rubidium fluorocadmiates have been determined in the range 10–300 K. The heat capacity and thermodynamic functions have been calculated (C p°, S°, ( G° - H 0°)/ T). Results for RbCdF 3 are examined using the structural phase transition whereas CsCdF 3 remains stable over the whole temperature range studied.

Calorimetric study of the deuteration effect on the phase behaviour in Rb 3H (SeO 4) 2 and Rb 3D (SeO 4) 2

The heat capacities of Rb 3H (SeO 4) 2 and Rb 3D (SeO 4) 2 crystals were measured from 12 to 304 K with an adiabatic calorimeter. In Rb 3H (SeO 4) 2, no thermal anomalies were observed and the experimental heat capacities were reproduced well by a sum of harmonic oscillator heat capacity functions. A higher-order phase transition was found at 95.4 K in Rb 3D (SeO 4) 2. The transition enthalpy and entropy were 3.4 × 10 2 J mol −1 and 4.0 J K −1 mol −1, respectively. The magnitude of the entropy change suggests an order-disorder mechanism for the transition.

Propriétés thermodynamiques des fluoropérovskites de potassium (KCaF 3) et de rubidium (RbCaF 3) (10–300 K): transition de phase

The heat capacities of potassium and rubidium fluoroperovskites have been determined in the range 10–300 K. The heat capacity and thermodynamic functions ( C o p , S o, ( G o- H o o) T ) are calculated.