Molar Specific Heat Capacity Research Articles

Theoretical and Experimental Studies on the Critical Size Effect on Surface Heat Capacity Using In Situ Microcalorimetry: During the Solid–Liquid Reactions of Cu2O Nanocubes

Phase transition, energy storage, and other activities depend critically on the size variations of nanomaterials for their heat capacity. The size variation of the nanomaterial is also equally important to the thermodynamic properties for chemical reaction processes. Based on this, it will be fascinating to examine how the surface heat capacity of nanomaterials changes with size. Herein, we used an in situ microcalorimeter to report a general approach to obtaining the regular patterns of numerical changes in the surface heat capacity at different sizes and temperatures when the chemical reactions of cuprous oxide (Cu2O) take place in the liquid phase. We synthesized four Cu2O nanocubes with uniform size distributions, which range from 40 to 120 nm, by using the liquid-phase reduction method. Combined with the principle of thermodynamic cycle and transition state theory, the effects of size and temperature changes on the standard molar formation thermodynamic properties, surface thermodynamic properties, and specific surface thermodynamic properties of Cu2O nanocubes were calculated and analyzed. The calculated results are in agreement with the established thermodynamic model. It is inspiring that we find that Cu2O nanocubes also have a critical size in the range of 55–67 nm, and their molar surface heat capacity and specific surface heat capacity are 59.35 and 59.31 nm, respectively. This property allows them to exhibit differences in thermal resistance from bulk materials within an acceptable range of error. This work has important scientific significance and values for enriching and developing the surface physical chemistry and understanding the energy storage and other processes of nanomaterials.

Theoretical prediction of Gibbs free energy and specific heat capacity of gaseous molecules

• Highly efficient equations for the prediction of molar Gibbs free energy and molar specific heat capacity are presented. • The equations are based on the improved generalized Pöschl-Teller oscillator. • The analytical models are applicable to large class of diatomic and triatomic molecules. • The equations require only three molecular constants of the molecule as input data. Using the improved generalized Pöschl-Teller oscillator to model the internal vibration of a diatomic molecule, analytical equations to predict molar Gibbs free energy and specific heat capacity at constant pressure were obtained. The equations were applied to ground-state Br 2 , Cl 2 diatomic molecules, and CO gaseous molecule. Average absolute deviations of 0.0755%, 0.0787%, and 0.3583%, were obtained using the equation of reduced molar Gibbs free energy. The expression of molar specific heat capacity yielded average absolute deviations of 4.5055%, 2.5308%, and 2.3665%, respectively from experimental data for the diatomic molecules. The results are in good agreement with existing literature data on the diatomic molecules.

Effects of Charged Solute-Solvent Interaction on Reservoir Temperature during Subsurface CO2 Injection

A short-term side-effect of CO2 injection is a developing low-pH front that forms ahead of the bulk water injectant, due to differences in solute diffusivity. Observations of downhole well temperature show a reduction in aqueous-phase temperature with the arrival of a low-pH front, followed by a gradual rise in temperature upon the arrival of a high concentration of bicarbonate ion. In this work, we model aqueous-phase transient heat advection and diffusion, with the volumetric energy generation rate computed from solute-solvent interaction using the Helgeson–Kirkham–Flowers (HKF) model, which is based on the Born Solvation model, for computing specific molar heat capacity and the enthalpy of charged electrolytes. A computed injectant water temperature profile is shown to agree with the actual bottom hole sampled temperature acquired from sensors. The modeling of aqueous-phase temperature during subsurface injection simulation is important for the accurate modeling of mineral dissolution and precipitation because forward dissolution rates are governed by a temperature-dependent Arrhenius model.

Morse potential specific heat with applications: an integral equations theory based

The specific heat in its molar form or mass form is a significant thermal property in the study of the thermal capacity of the described system. There are two basic methods for the determination of the molar specific heat capacity, one of them is the experimental procedure and the other is the theoretical procedure. The present study deals with finding a formula of the molar specific heat capacity using the theory of the integral equations for Morse interaction which is a very important potential for the study of the general oscillations in the quantum mechanics. We use the approximation (Mean-Spherical) for finding the total energy of the compositions described by Morse interaction. We find two formulas of the heat capacity, one at a constant pressure and the other at a constant volume. We conclude that the Morse molar specific heat is temperature dependent via the inverse square low with respect to temperature. Besides, we find that the Morse molar specific heat is proportional to the square of the Morse interaction well depth. Also, we find that the Morse molar specific heat depends on the particles’ diameter, the bond distance of Morse interaction, the width parameter of Morse interaction, and the volumetric density of the system. We apply the formula of the specific heat for finding the specific heat of the vibrational part for two dimer which are the lithium and caesium dimers and for the hydrogen fluoride, hydrogen chloride, nitrogen, and hydrogen molecules.

Non-equilibrium Nucleation: Application to Solidification and Molar-Specific Heat Capacity of Pure Metals and Phases

Non-equilibrium Nucleation: Application to Solidification and Molar-Specific Heat Capacity of Pure Metals and Phases

Thermophysical Properties of Mixtures of Titanium(IV) Isopropoxide (TTIP) and 2-Propanol (iPOH)

The present work provides thermophysical data on binary mixtures of titanium(IV) isopropoxide (TTIP) and 2-propanol (iPOH), which are important precursor solutions in spray flame synthesis of nanoparticles. The specific density, viscosity, thermal conductivity, and molar isobaric heat capacity were measured at 101.3 kPa and temperatures ranging from 293.15 to 333.15 K. The vapor–liquid equilibrium (VLE) was measured at pressures ranging from 20 to 80 kPa. Furthermore, self-diffusion coefficients of pure iPOH were measured at 101.3 kPa and temperatures ranging from 293.15 to 333.15 K. A qualitative study using 1H NMR spectroscopy provides evidence for a cross-association between TTIP and iPOH in the mixture. Correlations for all studied thermophysical properties are provided. The results establish a rational basis for the design of spray flame synthesis processes.

Crystal structure, thermal properties and detonation characterization of bis(5-amino-1,2,4-triazol-4-ium-3-yl)methane dinitrate.

Bis(5-amino-1,2,4-triazol-4-ium-3-yl)methane dinitrate, BATZM·(NO3)2 or C5H10N82+·2NO3-, was synthesized and its crystal structure determined by single-crystal X-ray diffraction. It crystallizes in the space group Pbcn (orthorhombic) with Z = 4. BATZM·(NO3)2 is a V-shaped molecule where hydrogen bonds form a two-dimensional corrugated sheet with reasonable chemical geometry and no disorder. The specific molar heat capacity (Cp,m) of BATZM·(NO3)2 was determined using the continuous Cp mode of a microcalorimeter and theoretical calculations, and the Cp,m value is 366.14 J K-1 mol-1 at 298.15 K. The relative deviations between the theoretical and experimental values of Cp,m, HT - H298.15K and ST - S298.15K of BATZM·(NO3)2 are almost equivalent at each temperature. The detonation velocity (D) and detonation pressure (P) were estimated using the nitrogen equivalent equation according to the experimental density; BATZM·(NO3)2 has a higher detonation velocity (7927.47 ± 3.63 m s-1) and detonation pressure (27.50 ± 0.03 GPa) than 2,4,6-trinitrotoluene (TNT). The above results for BATZM·(NO3)2 are compared with those of bis(5-amino-1,2,4-triazol-3-yl)methane (BATZM) and bis(5-amino-1,2,4-triazol-4-ium-3-yl)methane dihydrochloride (BATZM·Cl2), and the effect of nitrate formation is discussed.

Further analysis of the influence of interstage configurations on two-stage vapor compression heat pump systems

Two-stage vapor compression technology can effectively improve system performance, mainly due to the thermal effects of different interstage configurations. The thermal effects should be further analyzed to obtain quantitative results for different refrigerants. Based on mathematical analysis and numerical methods, the influences of the two thermal effects, i.e., subcooling and desuperheating, on the heating coefficient of performance (COPh) are analyzed. The results show that the subcooling promotes the COPh regardless of what refrigerant is employed; and the larger the molar specific heat capacity (evaluated by Cp,m0) of the refrigerant is, the greater the subcooling promotes the COPh. When Cp,m0 is less than 60 J mol−1 K−1, the desuperheating improves the COPh, whereas when Cp,m0 is larger than 70 J mol−1 K−1, it reduces the COPh. The maximum improvement in the COPh caused by interstage subcooling can reach up to 23%, while that caused by desuperheating is less than 6%.

Crystal structure, thermal properties and detonation characterization of bis(5-amino-1,2,4-triazol-4-ium-3-yl)methane dichloride.

Bis(5-amino-1,2,4-triazol-4-ium-3-yl)methane dichloride (BATZM·Cl2 or C5H10N82+·2Cl-) was synthesized and crystallized, and the crystal structure was characterized by single-crystal X-ray diffraction; it belongs to the space group C2/c (monoclinic) with Z = 4. The structure of BATZM·Cl2 can be described as a V-shaped molecule with reasonable chemical geometry and no disorder, and its one-dimensional structure can be described as a rhombic helix. The specific molar heat capacity (Cp,m) of BATZM·Cl2 was determined using the continuous Cp mode of a microcalorimeter and theoretical calculations, and the Cp,m value is 276.18 J K-1 mol-1 at 298.15 K. The relative deviations between the theoretical and experimental values of Cp,m, HT - H298.15K and ST - S298.15K of BATZM·Cl2 are almost equivalent at each temperature. The detonation velocity (D) and detonation pressure (P) of BATZM·Cl2 were estimated using the nitrogen equivalent equation according to the experimental density; BATZM·Cl2 has a higher detonation velocity (7143.60 ± 3.66 m s-1) and detonation pressure (21.49 ± 0.03 GPa) than TNT. The above results for BATZM·Cl2 are compared with those of bis(5-amino-1,2,4-triazol-3-yl)methane (BATZM) and the effect of salt formation on them is discussed.

Crystal structure, thermodynamic properties and detonation characterization of bis(5-amino-1,2,4-triazol-3-yl)methane.

Bis(5-amino-1,2,4-triazol-3-yl)methane (BATZM, C5H8N8) was synthesized and its crystal structure characterized by single-crystal X-ray diffraction; it belongs to the space group Fdd2 (orthorhombic) with Z= 8. The structure of BATZM can be described as a V-shaped molecule with reasonable chemical geometry and no disorder. The specific molar heat capacity (Cp,m) of BATZM was determined using the continuous Cp mode of a microcalorimeter and theoretical calculations, and the Cp,m value is 211.19 J K-1 mol-1 at 298.15 K. The relative deviations between the theoretical and experimental values of Cp,m, HT - H298.15K and ST - S298.15K of BATZM are almost equivalent at each temperature. The detonation velocity (D) and detonation pressure (P) of BATZM were estimated using the nitrogen equivalent equation according to the experimental density; BATZM has a higher detonation velocity (7954.87 ± 3.29 m s-1) and detonation pressure (25.72 ± 0.03 GPa) than TNT.

Determination of heat capacity of pure metals, compounds and alloys by analytical and numerical methods

Phase diagrams are normally calculated from a combination of physical equations and experimental parameters. Gibbs free energy of mixing; thermodynamics activity and enthalpy of mixing; transformation temperatures and the concentration range of the alloys components are calculated to permit an alloy system database to be constructed. The molar specific heat capacity (cv) is normally obtained by numerical derivative of the enthalpy equation with respect to temperature and concentration. The experimental determinations of the topological parameters as a function of concentration and temperature is an enormous task. On the other hand, physical formulations such as Einstein’s and Debye’s equations are physically consistent models for the molar specific heat capacity of the solid, and they depend only on a set of basic physical parameters. Einstein’s formulation works very well for temperatures T > 102 K, however, as it varies in the form of 1/T2, it fails to conform to lower temperature experimental data. Debye assumed only three branches of the vibrational spectrum with the same linear dispersion relation, and derived an equation also consistent for lower temperatures, and as the temperature decreases to absolute zero, it varies as a function of 1/T3 thus permitting experimental scatters to be fitted. Another way for calculating cv is by carrying out polynomial functions [1], which are only recommended for temperatures above 298.15 K, because bellow this temperature, cv is strongly dependent on the quantization of thermal energy, which can be stored in different forms in the material, such as electronic, magnetic, vibrational, rotational and translational energies. In this paper corrections for Debye’s and Einstein’s equations for cv are derived to encompass its thermal history dependence, electronic and rotational energies for both lower and higher temperatures in order to permit the calculation of the molar specific heat capacity of pure metals, phases and single-phase alloys.

A Simple Method of Finding New Dry and Isentropic Working Fluids for Organic Rankine Cycle

One of the most crucial challenges of sustainable development is the use of low-temperature heat sources (60–200 °C), such as thermal solar, geothermal, biomass, or waste heat, for electricity production. Since conventional water-based thermodynamic cycles are not suitable in this temperature range or at least operate with very low efficiency, other working fluids need to be applied. Organic Rankine Cycle (ORC) uses organic working fluids, which results in higher thermal efficiency for low-temperature heat sources. Traditionally, new working fluids are found using a trial-and-error procedure through experience among chemically similar materials. This approach, however, carries a high risk of excluding the ideal working fluid. Therefore, a new method and a simple rule of thumb—based on a correlation related to molar isochoric specific heat capacity of saturated vapor states—were developed. With the application of this thumb rule, novel isentropic and dry working fluids can be found applicable for given low-temperature heat sources. Additionally, the importance of molar quantities—usually ignored by energy engineers—was demonstrated.

Hermetic thermal behaviors and specific heat capacities of bis(aminofurazano)furazan and bis(nitrofurazano)furazan

Thermal behaviors of bis(aminofurazano)furazan (BAFF) and bis(nitrofurazano)furazan (BNFF) were studied by the differential scanning calorimetry (DSC) method with a special hermetic high-pressure crucible and compared to that with a common standard Al crucible. The exothermic decomposition processes of the two compounds were completely revealed. The extrapolated onset temperature, peak temperature and enthalpy of exothermic decomposition at the heating rate of 10 °C min−1 are 290.2, 313.4 °C and − 2174 J g−1 for BAFF, and 265.8, 305.0 °C and − 2351 J g−1 for BNFF, respectively. The apparent activation energies of the decomposition process for the two compounds are 115.7 and 131.7 kJ mol−1, respectively. The self-accelerating decomposition temperatures and critical temperatures of thermal explosion are 247.5 and 368.7 °C for BAFF, and 249.6 and 268.1 °C for BAFF, respectively. Both BAFF and BNFF present high thermal stability. The specific heat capacities for the two compounds were determined with the micro-DSC method, and the specific heat capacities and molar heat capacities at 298.15 K are 1.0921 J g−1 K−1 and 257.9 J mol−1 K−1 for BAFF, and 1.0419 J g−1 K−1 and 308.5 J mol−1 K−1 for BNFF, respectively.

Thermal Behavior, Specific Heat Capacity and Detonation Characterization of 3,3‐Dinitroazetidinium 3,5‐Dinitrobenzoate

Abstract3,3‐Dinitroazetidinium 3,5‐dinitrobenzoate (DNAZ ⋅ DNB) was synthesized, its thermal behavior was studied under a non–isothermal condition by DSC and TG/DTG methods. The intense exothermic decomposition process of DSC curves were analyzed to obtain its kinetic parameters. The specific molar heat capacity (Cp,m) of DNAZ ⋅ DNB was determined by a continuous Cp mode of micro−calorimeter, and the value was 416.81 JK−1 mol−1at 298.15 K. Its detonation velocity (D) and detonation pressure (P) were estimated using the nitrogen equivalent equation according to the experimental density. The above results of DNAZ ⋅ DNB were compared with those of 3,3‐dinitroazetidinium 3,5‐dinitrosalicylate (DNAZ ⋅ DNS) and 3,3‐dinitroazetidinium picrate (DNAZ ⋅ PA), and the effect of phenolic hydroxyl, carboxyl, and nitro group on them were discussed.

Thermophysical Properties of Cold- and Vacuum Plasma-Sprayed Cu-Cr-X Alloys, NiAl and NiCrAlY Coatings II: Specific Heat Capacity

Part I of the paper discussed the temperature dependencies of the electrical resistivities, thermal conductivities, thermal diffusivities and total hemispherical emissivities of several vacuum plasma-sprayed (VPS) and cold-sprayed (CS) copper alloy monolithic coatings, VPS NiAl, VPS NiCrAlY, extruded GRCop-84 and as-cast Cu-17(wt.%)Cr-5%Al. Part II discusses the temperature dependencies of the constant-pressure specific heat capacities, C P, of these coatings. The data were empirically regression-fitted with the equation: $${\varvec{C}}_{\mathbf{P}} = {\mathbf{ AT}}^{\mathbf 4} + {\mathbf{BT}}^{\mathbf 3} + {\mathbf{CT}}^{\mathbf 2} + {\mathbf{DT}} + \varvec{E}$$ where T is the absolute temperature and A, B, C, D and E are regression constants. The temperature dependencies of the molar enthalpy, molar entropy and Gibbs molar free energy determined from experimental values of molar specific heat capacity are reported. Calculated values of C P using the Neumann–Kopp (NK) rule were in poor agreement with experimental data. Instead, a modification of the NK rule was found to predict values closer to the experimental data with an absolute deviation less than 6.5%. The specific molar heat capacities for all the alloys did not agree with the Dulong–Petit law, and C P > 3R, where R is the universal gas constant, were measured for all the alloys except NiAl for which C P < 3R at all temperatures.

Thermal Behavior and Specific Heat Capacity of 1‐t‐Butyl‐3,3‐dinitroazetidinium Perchlorate

Abstract1‐t‐Butyl‐3,3‐dinitroazetidinium perchlorate (TDNAZ ⋅ HClO4) was synthesized, DSC and TG/DTG methods were used to study the thermal behavior of TDNAZ⋅HClO4 under a non–isothermal condition. The intense exothermic decomposition process of DSC curves were analyzed to obtain its kinetic parameters. Continuous specific heat capacity (Cp) mode of micro–calorimeter was used to determine its Cp, its specific molar heat capacity (Cp,m) was 365.70 J mol−1 K−1 at 298.15 K. The self‐accelerating decomposition temperature (TSADT), thermal ignition temperature (TTIT), and critical temperature of thermal explosion (Tb) were obtained to evaluate its thermal stability and safety. The above results of TDNAZ ⋅ HClO4 were compared with those of 3,3‐dinitroazetidinium perchlorate (DNAZ ⋅ HClO4), and the effect of tert‐butyl group on them was discussed.

Investigation on specific heat capacity and thermal behavior of sodium hydroxyethyl sulfonate

The thermal decomposition process was studied by the TG–DTA analyzer. The results show that the decomposition process of sodium hydroxyethyl sulfonate consisted of three stages: the mass loss for the first, the second and third stages may be about the groups of CH3CH2OH, CH3CHO and SO2 volatilized, respectively. The decomposition residuum of three stages was analyzed by FT-IR, and the results of FT-IR agreed with the decomposition process predicted by theoretical weight loss. The specific heat capacity of sodium hydroxyethyl sulfonate was determined by differential scanning calorimetry (DSC). The melting temperature and melting enthalpy were obtained to be 465.41K and 25.69kJ·mol−1, respectively. The molar specific heat capacity of sodium hydroxyethyl sulfonate was determinated from 310.15K to 365.15K and expressed as a function of temperature.

Synthesis, crystal structure and thermodynamic properties of 3-(3,5-dimethylpyrazol-1-yl)-6-(benzylmethylene) hydrazone-s-tetrazine

3-(3,5-Dimethylpyrazol-1-yl)-6-(benzylmethylene) hydrazone-s-tetrazine (DAHBTz) was synthesized and characterized by single crystal X-ray diffraction (XRD). The crystal structure shows that DAHBTz crystallizes in triclinic, space group P-1. The thermal behaviour was studied under non-isothermal condition by DSC method. The specific molar heat capacity (Cp,m) of DAHBTz was determined by a continuous Cp mode of Micro-DSC III and theoretical calculation, and the Cp,m of DAHBTz was 345.68J·K−1·mol−1 at T=298.15K.

Thermodynamic properties of 3,3-dinitroazetidinium nitrate

3,3-Dinitroazetidinium nitrate (DNAZ·HNO3) was synthesized, its thermal behaviour was studied under a non-isothermal condition by DSC and TG/DTG methods. The apparent activation energy (Ea) and pre-exponential factor (A) for the intense exothermic decomposition process were (112.52±1.37)kJ·mol−1 and (1011.91±0.06)s−1, respectively. The specific molar heat capacity (Cp,m) of DNAZ·HNO3 was determined by a continuous Cp mode of micro-calorimeter, and the Cp,m is 248.32J·K−1·mol−1 at T=298.15K. The self-accelerating decomposition temperature (TSADT), thermal ignition temperature (TTIT) and critical temperature of thermal explosion (Tb) were obtained to evaluate its thermal stability and safety. Its Cp,m, thermal stability and safety were compared with 3,3-dinitroazetidinium perchlorate (DNAZ·HClO4) and 3,3-dinitroazetidinium chloride (DNAZ·HCl).

Crystal structure and thermodynamic properties of myclobutanil

Myclobutanil is a high-efficiency, low toxicity and wide spectrum triazole fungicide. Its crystal structure was characterised by single-crystal X-ray diffraction, which belongs to monoclinic system with space group P21/c. The molecules are linked by weak hydrogen bonds and halogen bond to from a 3D structure. This is the main reason for its low melting point. The specific molar heat capacity (Cp,m) of myclobutanil was determined by a continuous Cp mode of micro-calorimeter and theoretical calculation, and the Cp,m of myclobutanil was 362.78J·K−1·mol−1 at T=298.15K.