Heat Capacity Equations Research Articles

A technique for calculating the enthalpy of silicate melt of arbitrary composition

The Kirchhoff equation was used to develop a method for calculating the enthalpy of silicate melt of any arbitrarily chosen composition with regard for the latent heat of fusion. To do this, the following two problems were solved: (a) the coefficients of the heat capacity equation of a silicate melt were revised and (b) the partial molar enthalpies of formation of melt components from elements at standard state were determined. The uncertainty in calculating the heat capacity of silicate melt at 95% significance level is no greater than ± 0.7 J · mol–1 · K–1. A weak but statistically significant temperature dependence of the heat capacity was determined. The enthalpies of melts calculated using the method are comparable with the values obtained by other techniques. The calculation error at 95% significance level is ±2 relative %.

A simple generalized equation for compressed liquid isochoric heat capacity of pure and mixture refrigerants

This work aims to develop a generalized equation for compressed liquid isochoric specific heat capacity (cv). The form of the equation was proposed based on the isochoric specific heat capacity calculation equation derived by the Peng-Robinson equation of state. The generalized coefficients were determined by 1734 liquid experimental cv data from 17 refrigerants. With known critical point, acentric factor and idea gas isochoric specific heat capacity, the developed equation can represent the liquid cv of 17 refrigerants well with the average absolute relative deviation of 1.55%. Large deviations are most likely to appear near the critical point. Comparisons were made to the calculation deviations from the Peng-Robinson equation of state and the multiproperty equations in REFPROP 9.1 software. It indicates that the developed equation provide a simple and reliable method for the calculation of the liquid cv. Additionally, 9 mixture refrigerants were calculated by the proposed generalized equation with the average absolute relative deviation of 3.13%.

A Technique for Calculating the Enthalpy of Silicate Melt of Any Composition

The Kirchhoff equation was used to develop a method for calculating the enthalpy of silicate melt of any arbitrarily chosen composition with regard for the latent heat of fusion. To do this, the following two problems were solved: (a) the coefficients of the heat capacity equation of a silicate melt were revised and (b) the partial molar enthalpies of formation of melt components from elements at standard state were determined. The uncertainty in calculating the heat capacity of silicate melt at 95% significance level is no greater than ±0.7 J mol–1 K–1. A weak but statistically significant temperature dependence of the heat capacity was determined. The enthalpies of melts calculated using the method are comparable with the values obtained by other techniques. The calculation error at 95% significance level is ±2 relative %.

First-principles calculations of high pressure phase transition of Ce-La-Th alloy

The lanthanide and actinide metals and alloys are of great interest in experimental and theoretical high-pressure research, because of the unique behavior of the f electrons under pressure and their delocalization and participation in bonding. Cerium (Ce) metal is the first lanthanide element with a 4f electron. It has a very complex phase diagram and displays intriguing physical and chemical properties. In addition, it is expected to be an excellent surrogate candidate for plutonium (Pu), one of the radioactive transuranic actinides with a 5f electron. The bulk properties and phase transformation characteristics of Ce-based alloys are similar to those of Pu and its compounds. Thus, the investigations of Ce-based alloys are necessary and can potentially advance the understanding of the behavior of Pu. In this work, the equation of state, phase transition, elastic and thermodynamic properties of Ce<sub>0.8</sub>La<sub>0.1</sub>Th<sub>0.1</sub> alloy at high pressure are investigated by using first-principles calculations based on the density-functional theory. The structural properties of the Ce<sub>0.8</sub>La<sub>0.1</sub>Th<sub>0.1</sub> alloy are in good agreement with the available experimental and theoretical data. The lattice constant <i>a</i> decreases with pressure increasing, while <i>c</i> shows an opposite variation. It is found that the lattice parameter <i>c</i> shows abnormal jump. And the critical volume is located at 20.1 Å<sup>3</sup>. The axial ratio jumps from a value of about <inline-formula><tex-math id="M90">\begin{document}$\sqrt 2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20182128_M90.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20182128_M90.png"/></alternatives></inline-formula> (corresponding to the fcc structure) to a higher value, which indicates that the fcc-bct transition occurs. And the corresponding transition pressure is located at ~31.6 GPa. When the pressure rises to 34.9 GPa, the bct structure displays a saturated <i>c/a</i> axial ratio close to about 1.67. The Young's modulus <i>E</i>, shear modulus <i>G</i> and the Debye temperature of the fcc phase tend to be " softened” around the phase transition pressure. The vibrational free energy is obtained by using the quasi-harmonic Debye model. And then the thermodynamic properties including the thermal equation of state, heat capacity and entropy under high pressure and high temperature are also predicted successfully. The results show that the heat capacity and entropy increase rapidly with temperature increasing, and decrease with pressure increasing. The high pressure can suppress part of the anharmonicity caused by temperature.

Thermodynamic Properties of Condensed Uranium Dioxide

In the context of the development of the IVTANTHERMO information and reference system, heat capacity equations have been derived for solid and liquid stoichiometric uranium dioxide in the temperature ranges of 298.15–3130 K and 3130–8000 K, respectively, on the basis of an analysis of experimental data available in the literature. The appearance of new experimental data on the UO2 enthalpy and heat capacity up to 8000 K made it necessary to recalculate the temperature dependences of the heat capacity. The refined values of thermodynamic functions (heat capacities, entropy, enthalpy increments, and the reduced Gibbs energy) obtained by numerical integration of these equations in a range of 100–8000 K have been entered into the IVTANTHERMO database.

Experimental and computational thermochemistry of 3- and 4-nitrophthalic acids

Abstract In this work, we present experimental and theoretical thermochemistry of the 3- and 4-nitrophtalic acids. We report their standard molar enthalpies of formation in crystalline phase, at T = 298.15 K, which were obtained from their energies of combustion. The latter were determined through an isoperibolic bomb calorimeter. We measured the change-phase enthalpies, as well as the fusion and sublimation enthalpies, by differential scanning calorimetry (DSC) and thermogravimetry (TG). Also via DSC, we found the heat capacity equations (in crystalline phase) for both isomers as functions of temperature. We determined the enthalpies of formation in both crystal- and gas-phase from the previous measurements. In addition, we computed the enthalpies of formation in gas-phase of both isomers using the composite Gaussian-G4 method and atomization reactions. The final theoretical enthalpies were computed using a weighted Boltzmann averaging procedure, and the weights were estimated using the Gibbs free energy at T = 298.15 K. The absolute differences between theoretical and experimental enthalpies are below 3.3 kJ · mo l −1 . Finally, we apply our results for obtaining the isomerization enthalpy of 3- to 4-nitrophthalic acid, and difference enthalpies between the nitrophthalic acids and their anhydrides.

Thermodynamic properties of San Carlos olivine at high temperature and high pressure

In this study, the thermal expansion and heat capacity of San Carlos olivine under high temperature and high pressure are reported. Combining accurate sound velocity data under different P–T conditions with density and heat capacity data at ambient pressure, the density, adiabatic bulk modulus, shear modulus, and most importantly, thermal expansion and heat capacity, of San Carlos are extracted to 14 GPa by a numerical procedure using classic thermodynamic relationships. These data are in agreement with published findings. To estimate the temperature gradient in the upper mantle, we also report the fitting equations of thermal expansion and heat capacity of San Carlos olivine as a function of both temperature and pressure to the P–T condition of the 410 km discontinuity, which provide the thermodynamic properties with increasing depth in the Earth’s interior.

Quantization Heat Capacity Equations at Constant Volume According to Energy Levels and Planck Constant

The quantization thermal excitation isotherms based on the maximum triad spin number (G) of each energy level for metal cluster were derived as a function of temperature by expanding the binomial theorems according to energy levels. From them the quantized geometric mean heat capacity equations are expressed in sequence. Among them the five quantized geometric heat capacity equations, fit the best to the experimental heat capacity data of metal atoms at constant pressure. In the derivations we assume that the triad spin composed of an electron, its proton and its neutron in a metal cluster become a basic unit of thermal excitation. Boltzmann constant (kB) is found to be an average specific heat of an energy level in a metal cluster. And then the constant (kK) is found to be an average specific heat of a photon in a metal cluster. The core triad spin made of free neutrons may exist as the second one additional energy level. The energy levels are grouped according to the forms of four spins throughout two axes. Planck constant is theoretically obtained with the ratio of the internal energy of metal (U) to total isotherm number (N) through Equipartition theorem.

Research on the Thermodynamic Property of Weakly Interacting Fermi Gases Through N-E-V Distribution and Pseudopotential Method

As the experiments of quantum system are conducted in the external field where the volume, energy and particle number are variable, the thermodynamic property of weakly interacting Fermi system is studied in this paper through the statistical distribution (N-E-V distribution) of a completely open system where the volume, energy and particle number are variable. Firstly, analytical expressions of internal energy, the equation of state, entropy and heat capacity expressed by Fermi integral are worked out. On that basis, the analytical expression and results of numerical calculation of the above thermodynamic quantities in extremely low temperature conditions can be known. Then, comparison between the calculations of N-E-V distribution and pseudopotential method (the volume and particle number remain the same) is drawn. The results show that the calculation of N-E-V distribution always makes up for the deviation of that of pseudopotential method. Besides, the most special thing about the calculation derived from N-E-V distribution is that the temperature variation curve of internal energy and that in the ideal Fermi system intersect. The characteristics of energy transfer between “attractive force” and “repulsive force” at the intersection temperature tc, which indicates that there is a phase transition. The intersection temperature does not change with the scattering length a (a0 repulsive force). Moreover, the intersection temperature of all weakly interacting Fermi system is 0.184 times as large as Fermi temperature, which is within the range of temperature for BEC and BCS phase transition and BEC-BCS crossover.

Influence of spin polarizability on liquid gas phase transition in the nuclear matter

In this paper, we investigate the liquid gas phase transition for the spin polarized nuclear matter. Applying the lowest order constrained variational (LOCV) method, and using two microscopic potentials, AV18 and UV14+TNI, we calculate the free energy, equation of state (EOS), order parameter, entropy, heat capacity and compressibility to derive the critical properties of spin polarized nuclear matter. Our results indicate that for the spin polarized nuclear matter, the second-order phase transition takes place at lower temperatures with respect to the unpolarized one. It is also shown that the critical temperature of our spin polarized nuclear matter with a specific value of spin polarization parameter is in good agreement with the experimental result.

Thermal behavior and safety of dihydroxylammonium 5,5′-bistetrazole-1,1′-diolate

The thermal decomposition behaviors of dihydroxylammonium 5,5′-bistetrazole-1,1′- diolate (TKX-50) were studied by using a C-500 type Calvet microcalorimeter at five heating rates. The kinetic and thermodynamic parameters of the first decomposition reaction were obtained. The specific heat capacity of TKX-50 was determined with a Micro-DSCIII calorimeter, and the specific heat capacity equation and the molar specific heat capacity at 298.15 K were also obtained. The self-accelerating decomposition temperature and the critical temperature of thermal explosion are 466.17 and 475.36 K, respectively. The adiabatic time-to-explosion is calculated to be a certain value between 112.65 and 113.93 s.

Development of a Debye heat capacity model for vibrational modes with a gap in the density of states

Low-energy vibrational modes that have a gap in the density of states (DOS) have often been observed in heat capacity data in the form of ‘boson’ peaks, but the functions used to model these modes are often inadequate or are not physically meaningful. We have adapted the Debye model to represent these gapped modes and have derived the heat capacity equations for these modes in one, two, and three dimensions. Applying these equations to the low-temperature heat capacity data fitting for a large variety of materials substantially improves the fit quality relative to conventional fits. From the fitting parameters, the underlying DOS were estimated, which we show to be comparable to those reported in the literature. This model expands the methods of theoretical low-temperature heat capacity data analysis and improves the procedure of approximating a material’s DOS from its low-temperature heat capacity.

Thermal behavior and safety of 4,10-dinitro-2,6,8,12-tetraoxa-4,10-diazaisowutrzitane

The thermal decomposition behaviors of 4,10-dinitro-2,6,8,12-tetraoxa-4,10-diazaisowutrzitane (TEX) were studied by using a C-500 type Calvet microcalorimeter at five heating rates. The kinetic and thermodynamic parameters of exothermic decomposition reaction were obtained. The specific heat capacity of TEX was determined with a Micro-DSC III calorimeter, the specific heat capacity equation and the molar specific heat capacity were also obtained. The self-accelerating decomposition temperature, adiabatic decomposition temperature rise, and critical temperature of thermal explosion are 512.69, 7115.59, and 527.42 K, respectively. The adiabatic time-to-explosion is calculated to be a certain value between 53.69 and 54.05 s.

Crystal structure and thermochemical properties of 2-pyrazine carboxylate lithium monohydrate [Li(pyza)(H2O)] n (s)(pyza=2-pyrazine carboxylate)

A 2-pyrazine carboxylate lithium monohydrate [Li(pyza)(H2O)] n was synthesized in a mixed solution of redistilled water and anhydrous ethanol. X-Ray crystallography was applied to characterizing its crystal structure. Low temperature molar heat capacities were measured in a temperature range of from 78 K to 400 K with a precision automatic adiabatic calorimeter. Two polynomial equations of experimental molar heat capacity as a function of temperature were obtained by the least-squares method. The smoothed molar heat capacities and thermodynamic functions of the compound were calculated based on the fitted polynomial equations. In accordance with Hess’s law, a reasonable thermochemical cycle was designed based on the preparation reaction of the target compound. The standard molar enthalpies of dissolution for the reactants and products of the designed thermochemical reaction were measured by an isoperibol solution-reaction calorimeter, and the enthalpy change of the reaction was obtained, i.e., Δr H m θ =-(30.084±0.329) kJ/mol. The standard molar enthalpy of the formation of the target compound was determined as $\Delta _f H_{m\{ [Li(pyza)(H_2 O)]_n (s)\} }^\theta = - (260.844 \pm 1.178)$ kJ/mol based on the enthalpy change of the reaction and standard molar enthalpies of the formation of other reactants and products. In addition, UV-Vis spectroscopy and the data of the refractive indexes were used to confirm whether the designed Hess thermochemical cycle was reasonable and reliable.

Thermodynamic properties of electron gas in complex-shaped quantum well

Thermodynamic properties of degenerate two-dimensional electron gas in complex-shaped quantum well are studied. We determine the equation of state, chemical potential, entropy and heat capacity of the electron gas. An influence of profile and parameters of the quantum well on thermodynamic characteristics are investigated.

Experimental Measurements and Thermodynamic Modelling of Carbon Dioxide Capture with use of 2-(Ethylamino) Ethanol

Carbon dioxide solubility was studied in 2.5 mass % and 5 mass % aqueous 2 (Ethylamino)ethanol (EAE; CAS 110- 73-6) solution, an interesting secondary amine prepared mainly from renewable resources, at high loading rates, at three temperature ranges (293.00K, 313.15 K, 333.15 K), and in pressure range from 289 to 1011 kPa. In addition to that, heat capacity (cp) was measured of examined solution, allowing determination of temperature dependent coefficients of ideal gas heat capacity equation. Afterwards, the electrolyte Non Random Two-Liquid model’s parameters were determined to represent the thermodynamic behaviour of the CO2 – EAE – H2O system with use of ASPEN® Plus V8.0 simulation software, indicating a good correlation between experimental and simulation results. As a consequence, model based calculation of the carbon dioxide capture with use of 2-(Ethylamino) ethanol is possible.

Calculation of Thermodynamic Properties of the Quasi-one Dimensional Liquid 3He at Finite Temperature

3He such as the energy, entropy, free energy, equation of state and heat capacity at finite temperature. We have employed the Lennard-Jones potential as the inter-atomic interaction. We have seen that the total energy increases by increasing both temperature and density. As expected, it is seen that the entropy decreases by increasing density and decreasing temperature. There is no minimum point in the free energy curve, showing that there is not any bond state for the quasi-one dimensional liquid 3 He. The results of our calculations indicate that the equation of state of this system becomes stiffer as the temperature increases. Our results for the specific heat show that there is not any lambda transition for this system.

Effect of N, N-M-Phenylenebismaleimide on Thermodynamics Properties of Epoxidised Natural Rubber by Using Differential Scanning Calorimeter

The thermodynamics properties of pure epoxidised natural rubber (ENR-50) and epoxidised natural rubber/N, N-M-Phenylenebismaleimide (ENR-50/HVA-2) compound were measured by differential scanning calorimeter (DSC) at a heat rate 10 K/min and at temperatures ranging from 273.15 to 453.15 K. The equations and values of heat capacity, enthalpy, entropy, Gibbs free energy and internal energy of pure ENR-50 and ENR-50/HVA-2 were found to be functions of temperature. The equations of heat capacity, enthalpy and internal energy of pure ENR-50 and ENR-50/HVA-2 compound behaved as polynomial equations with temperature at different order, while entropy and Gibbs free energy of pure ENR-50 and ENR-50/HVA-2 compound behaved as exponential equations with temperature. The Gibbs free energy for both substances was a negative value for all temperatures ranging from 273.15 to 453.15 K.

Molar heat capacity and thermodynamic properties of N-alklypyridinium hexafluorophosphate salts, [Cnpy][PF6] (n = 2, 3, 5)

Molar heat capacities (Cp,m) of the ionic liquids (ILs) N-alkylpyridinium hexafluorophosphate [Cnpy][PF6] (n=2, 3, 5) were measured with a high-precision automated adiabatic calorimeter (AC). The melting temperatures were determined. The molar enthalpy and entropy of phase transition were calculated according to the data obtained of the molar heat capacities by the empirical equation. The polynomial equations of molar heat capacity as a function of the temperature were fitted before and after the phase transition for each IL compounds. The thermodynamic functions (HT−H298.15) and (ST−S298.15) were derived from the molar heat capacity values over the temperature range from (80 to 400)K with an interval of 5K.

Heat capacity equations for nonstoichiometric solids

The equations for heat capacity measured under isodynamical conditions (fixed activity of a single component) are derived for partly open systems exchanging one component with the surroundings while keeping the contents of all other components constant. Compared to conventional isobaric (and isoplethal) heat capacity of a strictly stoichiometric phase, the isodynamical heat capacity of a nonstoichiometric phase is found to involve two additional terms—the saturation contribution due to incorporation (or release) of the free component and the contribution due to deviation from stoichiometry reflecting a different number of the involved phonon modes (due to different free component content) and in some cases a variation of free component incorporation mechanism.