Heat Capacity Functions Research Articles

Low-temperature heat capacity, phase transitions and thermodynamic functions of 2-furfurylamine

Heat capacities of 2-furfurylamine were measured by low-temperature adiabatic calorimetry in the temperature range from 5.6 to 356.1 K. Two phase transitions, solid phase transition and melting, were revealed at temperatures of 180.6 K and 228.17 K. Thermodynamic characteristics determined from experimental data show that the mechanism of solid phase transition is intermediate between order-disorder and displacive type. This conclusion is in agreement with X-ray crystallography data (Seidel et al., 2019). The standard thermodynamic functions in the condensed state (molar heat capacity, enthalpy, entropy and Gibbs energy) were calculated in the temperature range 5 - 350 K. Using the determined value of entropy for liquid 2-furfurylamine and available value of ΔfHm∘(l), the properties of formation, ΔfSm∘(l) and ΔfGm∘(l), were obtained. The thermodynamic functions of gaseous 2-furfurylamine were calculated taking into account the internal rotation in this molecule. The required molecular constants were determined from quantum chemical calculations.

A new activity model for biotite and its application

A new activity model for biotite is formulated in the system K2O-FeO-MgO-Al2O3-SiO2-H2O-TiO2-O2 (KFMASHTO), which extends that for the KFMASH system by introducing a titanium-biotite and a ferric-biotite end-member (tbio: K(TiMg2)[(O)2(AlSi3)O10] and fbio: K(Fe3+Mg2)[(OH)2(Al2Si2)O10]), as well as a pyrophyllite end-member (pyp: Al2[(OH)2Si4O10]) that accounts for the presence of octahedral excess-Al in natural biotites. Phonon calculations applying density functional theory (DFT) using the software Castep yielded the standard entropies of tbio and fbio as Sotbio = 328.06 J/(mol·K) and Sofbio = 301.69 J/(mol·K), and their heat capacity functions. From experimental phase-equilibrium data, the enthalpy of formation value of tbio was constrained as ΔHf,tbioo\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta {H}_{f,tbio}^{o}$$\\end{document} = −6124.68 ± 3.33 kJ/mol. Natural data were used to derive ΔHf,fbioo\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta {H}_{f,fbio}^{o}$$\\end{document}= −5935.3 ± 6.6 kJ/mol. The single-defect DFT method was applied to parameterize important macroscopic mixing properties (macro-W’s) involving tbio and pyp end-members in the model (fbio was treated ideal). Castep-derived microscopic interaction energies (micro-w’s) are presented herein for KFMASH-biotite. The octahedral same-site (M1) Mg–Al mixing micro-w (wMgAl(M1)), the same-site tetrahedral Si-Al mixing parameter (wSiAl(T1)) and the related cross-site term are: wMgAl(M1) = 82.5 kJ/mol, wSiAl(T1) = 95.6 kJ/mol (two T1-sites) and wMgAlAlSi(M1T1)=\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${w}_{MgAlAlSi(M1T1)}=$$\\end{document} 175.1 kJ/mol. The linear combination of these micro-w’s gives a macroscopic Wphleas = 18.8 kJ/mol, that is not transferable to other mineral groups. Micro w’s for Mg-Fe mixing in biotite (wMgFe(M1), wMgFe(M2),wMgMgFeFe(M1M2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${w}_{MgMgFeFe(M1M2)}$$\\end{document}), are all close to ideality. The biotite activity model of this study is thus a first example of next-generation activity models that use DFT- and thus physically based micro-w’s and reassembled macro-W’s for petrological calculations. Test calculations on 5 samples from low- to high-grade metamorphic environments covering metapelite to greywacke bulk-compositions using Perple_X suite of programs illustrate the performance of the new biotite activity model. Computed mineral-chemistries are in all cases in better agreement with measured compositions than resulting from published activity models of biotite.

Heat Capacity and Thermodynamic Functions of Yb2O3⋅2HfO2 Solid Solution

Heat Capacity and Thermodynamic Functions of Yb2O3⋅2HfO2 Solid Solution

The scandium effect in Gd-rich BMGs: How and why does this ingredient work better than others?

Scandium is commonly known as a superior modifier for most alloys and compounds, substantially improving their phase stability and physical properties, as well as glass-forming ability. A special case is rare-earth based magnetic metallic glasses, which are an unique platform for intra-elemental substitution due to the chemical affinity of the lanthanides, yttrium and scandium. The latter, used as an alloying additive and being the smallest atom among the entire family, can drastically affect structure formation and magnetism in these metallic glasses. The main issue is that its modifying role is not well understood due to scarce information on the scandium effects in such rare-earth systems. This study is focused on thermal and magnetic analysis of some popular Gd-based BMGs redesigned with minor Sc additives. Here, we consider temperature behavior of specific heat capacity and entropy functions for both amorphous and crystalline phases to estimate the scandium effect on GFA and thermal stability of the glasses. As well, we inspect magnetic and magnetocaloric properties of these BMGs to understand whether this very expensive metal can radically improve the alloy magnetism and make these materials suitable for potential applications.

CFD simulation of solid/liquid phase change in commercial PCMs using the slPCMlib library

Modelling the solidification and melting behavior of phase change materials (PCMs) can present several challenges, including non-isothermal phase change, multi-step transitions, complex enthalpy-temperature relations and convective heat transfer. To tackle these challenges, this study proposes a novel numerical method based on real experimental data for modelling complex phase change behavior of commercial PCMs in Ansys Fluent CFD software. The phase transition of PCMs is simulated with the apparent heat capacity (AHC) method, which is implemented as a User-Defined Function (UDF). Heat convection is simulated with the Boussinesq approximation. The method is validated by comparing to the Ansys Fluent built-in Solidification and Melting (S&M) model for the case of piecewise constant heat capacity. The results show that AHC method provides excellent agreement with S&M model for a piecewise constant heat capacity model. In addition, the AHC method solves convergence problems even for narrow phase change temperature ranges when a smooth heat capacity function is assumed. Finally, the AHC model is also tested on a set of commercial PCMs exhibiting complex phase change behavior. Temperature dependent specific heat capacities are determined from heat capacity data provided by PCM manufacturing companies and are imported as cubic Hermite spline functions from the solid-liquid phase change material library slPCMlib available at https://slpcmlib.ait.ac.at/. From the presented case study and tested PCMs it can be concluded that the AHC method is numerically robust when used with sufficiently smooth heat capacity functions, and it can be recommended for the analysis of heat transfer with PCMs showing a complex phase change behavior.

Theoretical investigation on the solid-liquid phase transition of gallium through free energy analysis.

Gallium, renowned for its notably low melting point and unique property of becoming liquid at room temperature, is a valuable constituent in phase change materials. In this study, we investigate the solid-liquid phase transition of gallium using the modified embedded atom method (MEAM) potential. It addresses the technique to compute the free energy difference between the solid and liquid without using a reference state. We examine various thermodynamic and dynamic properties, including density, specific heat capacity, diffusivity, and radial distribution functions. We compute the coexistence temperature of the solid-liquid phase transitions of gallium from free energy analysis. This information is crucial for understanding the behavior of the material under different pressure conditions and can be valuable for various applications, such as materials processing and high-pressure studies. The analysis, findings, and insights of the present work will be of great significance to the broad scientific and engineering communities in the field of phase transformation of materials. A series of molecular dynamics(MD) simulations were conducted using the LAMMPS software packages. The gallium atoms are modeled using the modified embedded atom method (MEAM) potential. To accurately predict the solid-liquid phase transitions of gallium, we calculated free energy by employing the "constrained λ integration" method, coupled with multiple histogram reweighting (MHR). The solid-liquid coexistence line is determined through the Gibbs-Duhem integration technique.

Influence of lithium on the temperature dependence of heat capacity and thermodynamic functions changes in AK1 alloy based on high-purity aluminum

The heat capacity of the AK1 alloy based on high-purity aluminum with lithium was determined in the cooling mode using the known heat capacity of the reference aluminum sample. By means of mathematical processing of cooling rate curves of samples from AK1 alloy with lithium and the reference sample, polynomials describing their cooling rates were obtained. Further, the polynomials of the temperature dependence of the heat capacity of alloys, described by a four-member equation, were established using the experimentally found values of the cooling rates of samples from alloys and the standard, taking into account their mass. Using integrals from specific heat capacity, models of temperature dependence of enthalpy, entropy and Gibbs energy changes were established. It was found that the heat capacity of the alloys increases with rising temperature. The addition of lithium when the temperature is up to 600 K significantly increases the heat capacity, and at temperatures above 600 K lithium in amounts of 0.5 wt. % reduces the heat capacity of the initial alloy AK1. It is shown that lithium addition increases the enthalpy and entropy of the initial AK1 alloy and decreases the Gibbs energy value.

Thermodynamic and kinetic study of the thermal dehydrogenation of Sr(AlH4)2 taking into account the by-products NaCl and LiCl

The presented work sets out to investigate the influence of LiCl and NaCl, the typical by-products of the mechanochemical synthesis of complex metal hydrides such as alanates and boranates, on the kinetics and thermodynamics of the dehydrogenation of Sr(AlH4)2. We found no effect of NaCl on the decomposition pathway of Sr(AlH4)2. Although LiCl does not affect the first dehydrogenation to SrAlH5, it does alter the further decomposition to the final products. Thermodynamic properties such as the heat capacity functions, enthalpies of formation and absolute entropies were determined for Sr(AlH4)2 itself and its decomposition product SrAlH5 within this study.

Heat Capacity Function, Enthalpy of Formation and Absolute Entropy of Mg(AlH4 )2.

In this investigation, we set out first to characterize the thermodynamics of Mg(AlH4 )2 and secondly to use the determined data to reevaluate and update existing estimation procedures for heat capacity functions, enthalpies of formation and absolute entropies of alanates. Within this study, we report the heat capacity function of Mg(AlH4 )2 in the temperature range from 2 K to 370 K and its enthalpy of formation and absolute entropy at 298.15 K, being kJ mol-1 and 133.06 J (K mol)-1 , respectively. Using these values, we updated and expanded methods for the estimation of thermodynamic data of alanates.

Heat Capacity and Thermodynamic Functions of Solid Solution Er2O3⋅2HfO2

Heat Capacity and Thermodynamic Functions of Solid Solution Er2O3⋅2HfO2

Low-Temperature Heat Capacity and Thermodynamic Functions of Europium(III) Heptafluorodimethyloctanedionate

Low-Temperature Heat Capacity and Thermodynamic Functions of Europium(III) Heptafluorodimethyloctanedionate

Heat Capacity and Thermodynamic Functions of the Aluminum Alloy AlCu4.5Mg1 Alloyed with Barium

Heat Capacity and Thermodynamic Functions of the Aluminum Alloy AlCu4.5Mg1 Alloyed with Barium

Heat capacity and thermodynamic functions of sodium rare earth ternary fluorides

Sodium rare earth ternary fluorides, NaREF4 (RE = rare earth), are intermediate phases for rare earth element extraction and have important technological applications. To better understand their physical properties, energetics, and stability, we measured the heat capacity of three β-structured NaREF4 compounds, NaNdF4, NaYbF4, and NaYF4, from 1.8 to 300 K. Our measurements show an upturn in the low-temperature heat capacity of each sample which we attribute to the splitting of degenerate nuclear magnetic states. We provide calculations of the effective field causing the splitting for each sample. We also report standard entropy, enthalpy, and Gibbs energy increments at selected temperatures from 0 to 300 K. The enthalpy of formation of the three NaREF4 from the elements (ΔΗ°f,el) and the fluorides (ΔΗ°f,fl) were measured previously, enabling us to calculate the Gibbs energies of formation from the elements and fluorides. The Gibbs energy of NaREF4 relative to the elements at 298.15 K was calculated to be −1483.5 kJ∙mol−1, −1502.2 kJ∙mol−1, and −1497.8 kJ∙mol−1 with an estimated standard uncertainty of 1% for NaNdF4, NaYF4, and NaYbF4 respectively. The Gibbs energy of NaREF4 relative to the fluorides at 298.15 K was calculated to be –5.39 kJ∙mol−1, −18.12 kJ∙mol−1, and −19.1 kJ∙mol−1 with an estimated standard uncertainty of 1% for NaNdF4, NaYF4, and NaYbF4 respectively. Each sample’s negative Gibbs energy relative to both the elements and the fluorides indicates stability relative to these compounds. The results confirm that these three NaREF4 compounds are thermodynamically stable relative to the elements and binary fluorides.

Численное моделирование и верификация точечного лазерного нагрева нержавеющей стали AISI 316L

The paper considers the laser spot heating process in the AISI 316L stainless steel sample and its three-dimensional mathematical model. It proposes an option in this process numerical simulation by introducing a laser radiation source specified as the super Gaussian distribution with refined and experimentally selected dimensionless coefficients. Boundary conditions of convection and radiative heat transfer, as well as the Marangoni convection on the melting pool free surface, were taken into account. Metal phase transition from solid to the liquid aggregation state was realized within the solidus and liquidus temperature ranges due to effective functions of heat capacity and viscosity. Geometrical characteristics of the melt pools obtained during a number of practical experiments were compared with the data determined by numerical solution. It is shown that the results in both the options quantitatively and qualitatively coincide with the insignificant error. Conclusions are made on the error in the numerical solution.

Heat Capacity and Thermodynamic Functions of Titanium-Manganites of Lanthanum, Lithium and Sodium of LaLi2TiMnO6 and LaNa2TiMnO6.

Titanium-manganites of LaLi2TiMnO6 and LaNa2TiMnO6 were synthesized by the methods of ceramic technology from the oxides of lanthanum, titanium (IV), manganese (III), and the carbonates of lithium and sodium. The types of their syngony and the parameters of their gratings were determined radiographically. The isobaric heat capacities of titanium-manganites were measured with experimental calorimetry in the range of 298.15-673 K. It was found that on the dependence curve of heat capacity versus temperature of C°p~f(T), for LaLi2TiMnO6 at 348 K and 598 K, and LaNa2TiMnO6 at 348 K, there are abnormal jumps in heat capacity, probably related to phase transitions of the second kind. Taking into account the temperatures of the phase transitions, the equations of the temperature dependence of the heat capacity of titanium-manganites were derived. Their standard entropies were calculated by the ion increments method. Temperature dependences of the thermodynamic functions of S°(T), H°(T)-H°(298.15), and Φxx(T) were calculated using the experimental data on heat capacities and the calculated values of the standard entropies. The standard heat capacities of the studied compounds were calculated by the independent methods of ion increments and Debye, the values of which were in satisfactory agreement with the experimental data. The standard enthalpy of the formation of LaLi2TiMnO6 and LaNa2TiMnO6 was calculated according to the methodology developed by the authors. The conducted electrophysical studies determined the nature of the second-order phase transition and the semiconductor features of their conductivity. Thus, all the above-mentioned data on the experimental and calculated studies of the temperature dependence of heat capacity, the thermodynamic functions to determine a standard enthalpy of formation of LaLi2TiMnO6 and LaNa2TiMnO6, and the investigation of their electrical properties are absolutely new, and they have no analogues.

High-Temperature Heat Capacity and Thermodynamic Functions of the LiNaGe4O9 Germanate

High-Temperature Heat Capacity and Thermodynamic Functions of the LiNaGe4O9 Germanate

Chemical Modeling of Constant-Volume Combustion of the Mixture of Methane and Hydrogen Used in Spark Ignition Otto Cycles

This paper develops a chemical model for a closed constant-volume combustion of a gaseous mixture of methane and hydrogen. Since the combustion is strongly dependent on temperature, pressure and fuel composition, these had chosen the actual corresponding thermodynamic systems in this kind of combustion, i.e., spark ignition (SI) reciprocating engines, to assess combustion parameters and flue gas composition. The actual cycles impose extra restrictive operational conditions through the engine’s-volumetric-compression ratio, the geometry of the combustion volume, the preparation method of the mixture of methane and hydrogen, (e.g., one fueling way of a homogeneous mixture obtained in a specific device or by two separate fueling ways for components), the cooling system and the delivered power. The chemical model avoided the unknown influences in order to accurately explain the influence of hydrogen upon constant-volume combustion and flue gas composition. The model adopted hypotheses allowing to generalize evaluated results, i.e., the isentropic compression and expansion processes, in closed constant-volume combustion caused by two successive steps that obey the energy and mass conservation laws, and the flue gas exhaust, which is also described by two steps, i.e., isentropic expansion through the flow section of exhaust valves followed by a constant pressure stagnation (this process, in fact, corresponds to a direct throttling process). The chemical model assumed the homogeneous mixtures of gases with variable heat capacity functions of temperatures, the Mendeleev—Clapeyron ideal gas state equation, and the variable chemical equilibrium constants for the chosen chemical reactions. It was assumed that the flue gas chemistry prevails during isentropic expansion and during throttling of exhaust flue gas. The chemical model allowed for evaluation of flue gas composition and noxious emissions. The numerical results were compared with those recently reported in other parallel studies.

Heat Capacity and Thermodynamic Functions of Sodium-Alloyed Lead Babbitt BNa (PbSb15Sn10Na)

The heat capacity of sodium-alloyed lead babbitt BNa (PbSb15Sn10Na) is determined experimentally, and the temperature dependences of the changes in the thermodynamic functions of this alloy are calculated. The temperature dependence of the heat capacity of babbitt BNa is studied in the cooling mode using the SigmaPlot 10.0 software. Polynomials are determined for the temperature dependences of the heat capacity and the changes in the thermodynamic functions (enthalpy, entropy, and Gibbs free energy) of babbitt BNa and a reference sample (S00-grade Pb), that describe these dependences with coefficient of correlation Rcorr = 0.999. It is shown that the heat capacity of babbitt BNa grows along with the content of sodium, its enthalpy and entropy grow along with temperature and the content of sodium, and its Gibbs energy falls.

Heat Capacity and Thermodynamic Functions of Sodium-Alloyed Lead Babbitt BNa (PbSb15Sn10Na)

Heat Capacity and Thermodynamic Functions of Sodium-Alloyed Lead Babbitt BNa (PbSb15Sn10Na)

Modeling of the drying process of a capillary-porous cylindrical body

In the process of drying capillary-porous materials, the movable surface of the phase transition, which separates the dried and wet zones in the body, depends on the properties of the material and the temperature due to external influence of the drying agent, is a function of coordinates and time. We assume that the above properties of the material are functions of porosity, density and heat capacity of body components.