Heat capacity of crystalline GaN

The heat capacity of gallium nitride has been measured by DSC method using DuPont Thermal Analyst 2100, DSC 951 unit in the temperature range (300–850 K). The temperature dependence of the heat capacity can be presented in the following form: C _p=32.960+0.162·10⁻¹ T+2360170T ⁻²-775370000T ⁻³.     

Thermodynamic investigation of several natural polyols (II)

The low-temperature heat capacity C _p,m of sorbitol was precisely measured in the temperature range from 80 to 390 K by means of a small sample automated adiabatic calorimeter. A solid-liquid phase transition was found at T=369.157 K from the experimental C _p-T curve. The dependence of heat capacity on the temperature was fitted to the following polynomial equations with least square method. In the temperature range of 80 to 355 K, C _p,m/J K⁻¹ mol⁻¹=170.17+157.75x+128.03x ²-146.44x ³-335.66x ⁴+177.71x ⁵+306.15x ⁶, x= [(T/K)−217.5]/137.5. In the temperature range of 375 to 390 K, C _p,m/J K⁻¹ mol⁻¹=518.13+3.2819x, x=[(T/K)-382.5]/7.5. The molar enthalpy and entropy of this transition were determined to be 30.35±0.15 kJ mol⁻¹ and 82.22±0.41 J K⁻¹ mol⁻¹ respectively. The thermodynamic functions [H _T-H _298.15] and [S _T-S 298.15], were derived from the heat capacity data in the temperature range of 80 to 390 K with an interval of 5 K. DSC and TG measurements were performed to study the thermostability of the compound. The results were in agreement with those obtained from heat capacity measurements.     

Low-temperature heat capacities and thermodynamic properties of 2,2-dimethyl-1,3-propanediol

The molar heat capacities C _p,m of 2,2-dimethyl-1,3-propanediol were measured in the temperature range from 78 to 410 K by means of a small sample automated adiabatic calorimeter. A solid-solid and a solid-liquid phase transitions were found at T-314.304 and 402.402 K, respectively, from the experimental C _p-T curve. The molar enthalpies and entropies of these transitions were determined to be 14.78 kJ mol⁻¹, 47.01 J K⁻¹ mol⁻ for the solid-solid transition and 7.518 kJ mol⁻¹, 18.68 J K⁻¹ mol⁻¹ for the solid-liquid transition, respectively. The dependence of heat capacity on the temperature was fitted to the following polynomial equations with least square method. In the temperature range of 80 to 310 K, C _p,m/(J K⁻¹ mol⁻¹)=117.72+58.8022x+3.0964x ²+6.87363x ³−13.922x ⁴+9.8889x ⁵+16.195x ⁶; x=[(T/K)−195]/115. In the temperature range of 325 to 395 K, C _p,m/(J K⁻¹ mol⁻¹)=290.74+22.767x−0.6247x ²−0.8716x ³−4.0159x ⁴−0.2878x ⁵+1.7244x ⁶; x=[(T/K)−360]/35. The thermodynamic functions H _T−H _298.15 and S _T−S _298.15, were derived from the heat capacity data in the temperature range of 80 to 410 K with an interval of 5 K. The thermostability of the compound was further tested by DSC and TG measurements. The results were in agreement with those obtained by adiabatic calorimetry.     

Thermodynamic properties of α-platinum dichloride

The heat capacity of crystalline α-platinum dichloride was measured for the first time in the temperature intervals from 11 to 300 K (vacuum adiabatic microcalorimeter) and from 300 to 620 K (differential scanning calorimetry). In the 300–620 K temperature interval, the C° _p values for α-PtCl₂ (cr) coincide with the heat capacity of CrCl₂ (cr) within the limits of experimental error, which made it possible to estimate the heat capacity of α-PtCl₂ (cr) at higher temperatures. The approximating equation of the temperature dependence of the heat capacity in the interval from 298 to 900 K C° _p (±0.8) = 63.5 + 21.4·10⁻³ T + 0.883·10⁵/T ² (J mol⁻¹ K⁻¹) was derived using the experimental values, as well as the literature data on the heat capacity of CrCl₂ (cr). For the standard conditions, the C° _p,298.15 and S°_298.15 values are 70.92±0.08 and 100.9±0.33 J mol⁻¹ K, respectively; H°_298.15 − H°₀ = 14 120±42 J mol⁻¹. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1136–1138, June, 2008.     

Low-temperature thermodynamic properties of <Emphasis Type="Italic">L</Emphasis>-cysteine

Heat capacity C _p(T) of the orthorhombic polymorph of L-cysteine was measured in the temperature range 6–300 K by adiabatic calorimetry; thermodynamic functions were calculated based on these measurements. At 298.15 K the values of heat capacity, C _p; entropy, S _m⁰(T)-S _m⁰(0); difference in the enthalpy, H _m⁰(T)-H _m⁰(0), are equal, respectively, to 144.6±0.3 J K⁻¹ mol⁻¹, 169.0±0.4 J K⁻¹ mol⁻¹ and 24960±50 J mol⁻¹. An anomaly of heat capacity near 70 K was registered as a small, 3–5% height, diffuse ‘jump’ accompanied by the substantial increase in the thermal relaxation time. The shape of the anomaly is sensitive to thermal pre-history of the sample.     

Heat capacity of methacetin in a temperature range of 6 to 300 K

Heat capacity of methacetin (N-(4-methoxyphenyl)-acetamide) has been measured in the temperature range 5.8–300 K. No anomalies in the C _p(T) dependence were observed. Thermodynamic functions were calculated. At 298.15 K, the values of entropy and enthalpy are equal to 243.1 J K⁻¹ mol⁻¹ and 36360 J mol⁻¹, respectively. The heat capacity of methacetin in the temperature range 6–10 K is well fitted by Debye equation C _p = AT ³. The thermodynamic data obtained for methacetin are compared with those for the monoclinic and orthorhombic polymorphs of paracetamol.     

Thermal behavior of 3,4,5-triamino-1,2,4-triazole dinitramide

The thermal decomposition behavior of 3,4,5-triamino-1,2,4-triazole dinitramide was measured using a C-500 type Calvet microcalorimeter at four different temperatures under atmospheric pressure. The apparent activation energy and pre-exponential factor of the exothermic decomposition reaction are 165.57 kJ mol⁻¹ and 10^18.04 s⁻¹, respectively. The critical temperature of thermal explosion is 431.71 K. The entropy of activation (ΔS ^≠), enthalpy of activation (ΔH ^≠), and free energy of activation (ΔG ^≠) are 97.19 J mol⁻¹ K⁻¹, 161.90 kJ mol⁻¹, and 118.98 kJ mol⁻¹, respectively. The self-accelerating decomposition temperature (T _SADT) is 422.28 K. The specific heat capacity of 3,4,5-triamino-1,2,4-triazole dinitramide was determined with a micro-DSC method and a theoretical calculation method. Specific heat capacity (J g⁻¹ K⁻¹) equation is C _p = 0.252 + 3.131 × 10⁻³  T (283.1 K < T < 353.2 K). The molar heat capacity of 3,4,5-triamino-1,2,4-triazole dinitramide is 264.52 J mol⁻¹ K⁻¹ at 298.15 K. The adiabatic time-to-explosion of 3,4,5-triamino-1,2,4-triazole dinitramide is calculated to be a certain value between 123.36 and 128.56 s.     

Thermodynamic investigation of several natural polyols

The low-temperature heat capacity C _p,m of erythritol (C₄H₁₀O₄, CAS 149-32-6) was precisely measured in the temperature range from 80 to 410 K by means of a small sample automated adiabatic calorimeter. A solid-liquid phase transition was found at T=390.254 K from the experimental C _p-T curve. The molar enthalpy and entropy of this transition were determined to be 37.92±0.19 kJ mol⁻¹ and 97.17±0.49 J K⁻¹ mol⁻¹, respectively. The thermodynamic functions [H _T-H _298.15] and [S _T-S _298.15], were derived from the heat capacity data in the temperature range of 80 to 410 K with an interval of 5 K. The standard molar enthalpy of combustion and the standard molar enthalpy of formation of the compound have been determined: Δ_c H _m⁰(C₄H₁₀O₄, cr)= −2102.90±1.56 kJ mol⁻¹ and Δ_f H _m⁰(C₄H₁₀O₄, cr)= − 900.29±0.84 kJ mol⁻¹, by means of a precision oxygen-bomb combustion calorimeter at T=298.15 K. DSC and TG measurements were performed to study the thermostability of the compound. The results were in agreement with those obtained from heat capacity measurements.     

The thermodynamic functions of fullerene derivative (<Emphasis Type="Italic">t</Emphasis>-Bu)<Subscript>12</Subscript>C<Subscript>60</Subscript> over the temperature range from <Emphasis Type="Italic">T</Emphasis> → 0 to 420 K

The temperature dependence of heat capacity C _p ^o = f(T) of fullerene derivative (t-Bu)₁₂C₆₀ has been measured by a adiabatic vacuum calorimeter over the temperature range T = 6–350 K and by a differential scanning calorimeter over the temperature range T = 330–420 K for the first time. The low-temperature (T ≤ 50 K) dependence of the heat capacity was analyzed based on Debye’s the heat capacity theory of solids and its fractal variant. As a consequence, the conclusion about structure heterodynamicity is given. The experimental results have been used to calculate the standard thermodynamic functions C _p ^o (T), H ^o(T)−H ^o(0), S ^o(T) and G ^o(T) − H ^o(0) over the range from T → 0 to 420 K. The standard entropy of formation at 298.15 K of fullerene derivative under study was calculated. The temperature of decomposition onset of derivative was determined by differential scanning calorimetery and thermogravimetric analysis. The standard thermodynamic characteristics of (t-Bu)₁₂C₆₀ and C₆₀ fullerite were compared.     

Thermodynamic properties of strontium metaniobate SrNb<Subscript>2</Subscript>O<Subscript>6</Subscript>

The heat capacity and the enthalpy increments of strontium metaniobate SrNb₂O₆ were measured by the relaxation method (2-276 K), micro DSC calorimetry (260-320 K) and drop calorimetry (723-1472 K). Temperature dependence of the molar heat capacity in the form C _pm=(200.47±5.51)+(0.02937±0.0760)T-(3.4728±0.3115)·10⁶/T ² J K⁻¹ mol⁻¹ (298-1500 K) was derived by the least-squares method from the experimental data. Furthermore, the standard molar entropy at 298.15 K S _m⁰ (298.15 K)=173.88±0.39 J K⁻¹ mol⁻¹ was evaluated from the low temperature heat capacity measurements. The standard enthalpy of formation Δ_f H ⁰ (298.15 K)=-2826.78 kJ mol⁻¹ was derived from total energies obtained by full potential LAPW electronic structure calculations within density functional theory.     

Heat capacity,enthalpy and entropy of calcium niobates

Heat capacity and enthalpy increments of calcium niobates CaNb₂O₆ and Ca₂Nb₂O₇ were measured by the relaxation time method (2–300 K), DSC (260–360 K) and drop calorimetry (669–1421 K). Temperature dependencies of the molar heat capacity in the form C _pm=200.4+0.03432T−3.450·10⁶/T ² J K⁻¹ mol⁻¹ for CaNb₂O₆ and C _pm=257.2+0.03621T−4.435·10⁶/T ² J K⁻¹ mol⁻¹ for Ca₂Nb₂O₇ were derived by the least-squares method from the experimental data. The molar entropies at 298.15 K, S _m⁰(CaNb₂O₆, 298.15 K)=167.3±0.9 J K⁻¹ mol⁻¹ and S _m⁰(Ca₂Nb₂O₇, 298.15 K)=212.4±1.2 J K⁻¹ mol⁻¹, were evaluated from the low temperature heat capacity measurements. Standard enthalpies of formation at 298.15 K were derived using published values of Gibbs energy of formation and presented heat capacity and entropy data: Δ_f H ⁰(CaNb₂O₆, 298.15 K)= −2664.52 kJ mol^t-1 and Δ_f H ⁰(Ca₂Nb₂O₇, 298.15 K)= −3346.91 kJ mol⁻¹.     

The thermodynamic properties of (2,2′-dipyridyl)bis(4-chloro-3,6-di-tert-butyl-<Emphasis Type="Italic">o</Emphasis>-benzosemiquinone)cobalt

The heat capacity of paramagnetic (2,2′-dipyridyl)bis(4-chloro-3,6-di-tert-butyl-o-benzosemi-quinone)cobalt was studied over the temperature range 8–390 K by precision adiabatic vacuum and high-accuracy dynamic calorimetry. The physical transformation observed at 309–388 K was caused by the transition of the semiquinone-catecholate to bis-semiquinone form of the complex. Above 388 K, thermal destruction was superimposed on the physical transition. The experimental data were used to calculate the standard thermodynamic functions C _p ^o (T), H ^o(T)−H ^o(0), S ^o(T), and G ^o(T)−H ^o(0) at temperatures from T → 0 to 300 K. An analysis of the low-temperature heat capacity of the complex in terms of the Debye theory of the heat capacity of solids and its multifractal generalization led us to conclude that the complex had a predominantly chain structure.     

Molar heat capacity and thermodynamic properties of 1,2-cyclohexane dicarboxylic anhydride [C8H10O3]

The molar heat capacity C _p,m of 1,2-cyclohexane dicarboxylic anhydride was measured in the temperature range from T=80 to 390 K with a small sample automated adiabatic calorimeter. The melting point T _m, the molar enthalpy Δ_fus H _m and the entropy Δ_fus S _m of fusion for the compound were determined to be 303.80 K, 14.71 kJ mol⁻¹ and 48.43 J K⁻¹ mol⁻¹, respectively. The thermodynamic functions [H _T-H _273.15] and [S _T-S _273.15] were derived in the temperature range from T=80 to 385 K with temperature interval of 5 K. The thermal stability of the compound was investigated by differential scanning calorimeter (DSC) and thermogravimetry (TG), when the process of the mass-loss was due to the evaporation, instead of its thermal decomposition.     

The thermodynamic properties of natural margarite

Thermal, IR spectroscopic, and thermochemical studies of natural brittle mica, margarite Ca_1.00Na_0.10Mg_0.02Al_3.89Fe_0.01³⁺Si_2.03Ti_0.01O₁₀(OH)_1.74F_0.26, were performed. The enthalpy of formation of natural margarite from the elements (−6269 ± 12 kJ/mol) was determined by melt solution calorimetry on a high-temperature heat-conducting Calvet microcalorimeter (Setaram, France). Enthalpy growth over the temperature range 298.15–973 K was determined by the drop method. Equations for the temperature dependences of the enthalpy and heat capacity were obtained, H°(T)−H°(298.15 K), J/mol = 435.21T + 36.46 × 10⁻³ T ² + 109.91 × 10⁵/T − 169863 and C° _p , J/(mol K) = 435.21 + 72.92 × 10⁻³ T − 109.91 × 10⁵/T ². The experimental data were used to estimate the thermodynamic properties of margarite of the theoretical composition, CaAl₂[Al₂Si₂O₁₀](OH)₂.     

Determination of heat capacities of PbCrO4(s), Pb2CrO5(s), and Pb5CrO8(s)

Abstract  

Heat capacities of PbCrO₄(s), Pb₂CrO₅(s), and Pb₅CrO₈(s) were measured by differential scanning calorimetry. The measured heat capacities as a function of temperature are expressed as C _p <PbCrO₄> J K⁻¹ mol⁻¹ = 150.37 + 27.74 × 10⁻³ T − 2.80 × 10⁶ T ⁻² (T = 300–750 K), C _p <Pb₂CrO₅> J K⁻¹ mol⁻¹ = 194.55 + 76.09 × 10⁻³ T − 4.64 × 10⁶ T ⁻² (T = 300–700 K), and C _p  <Pb₅CrO₈> J K⁻¹ mol⁻¹ = 323.35 + 184.80 × 10⁻³ T − 5.48 × 10⁶ T ⁻² (T = 300–600 K). From the measured heat capacity data, thermodynamic functions such as enthalpy increments, entropies, and Gibbs energy functions were derived.     

Heat Capacities and Thermodynamic Properties of a H2O + Li2B4O7 Solution in the Temperature Range from 80 to 356 K

The molar heat capacities of an aqueous Li₂B₄O₇ solution were measured with a precision automated adiabatic calorimeter in the temperature range from 80 to 356 K at a concentration of 0.3492 mol⋅kg⁻¹. The occurrence of a phase transition was determined based on the changes in the curve of the heat capacity with temperature. A phase transition was observed at 271.72 K corresponding to the solid-liquid phase transition; the enthalpy and entropy of the phase transition were evaluated to be Δ H _m = 4.110 kJ⋅mol⁻¹ and Δ S _m = 15.13 J⋅K⁻¹⋅mol⁻¹, respectively. Using polynomial equations and thermodynamic relationship, the thermodynamic functions [H _T −H _298.15] and [S _T −S _298.15] of the aqueous Li₂B₄O₇ solution relative to 298.15 K were calculated in temperature range 80 to 355 K at intervals of 5 K. Values of the relative apparent molar heat capacities of the aqueous Li₂B₄O₇ solution, C _p,φ, were calculated at every 5 K in temperature range from 80 to 355 K from the experimental heat capacities of the solution and the heat capacities of pure water.     

Heat capacity at constant pressure and thermodynamic properties of phase transitions in PbMO<Subscript>3</Subscript> (<Emphasis Type="Italic">M</Emphasis>=Ti,Zr and Hf)

The heat capacity of PbMO₃ (M=Ti, Zr and Hf) at constant pressure was measured using a differential scanning calorimeter (DSC) from room temperature up to 870 K. Large anomalies were found in the heat capacity curves, corresponding to the ferroelectricparaelectric phase transition in PbTiO₃ (PT), the antiferroelectric-paraelectric phase transitions in PbZrO₃ (PZ) and PbHfO₃ (PH). The transition entropies were estimated as 7.3 J K⁻¹ mol⁻¹ (PT), 9.9 J K⁻¹ mol⁻¹ (PZ) and 9.3 J K⁻¹ mol⁻¹ (PH). These values of transition entropies are much larger than that of a typical displacive-type phase transition.     

Molar heat capacities and standard molar enthalpy of formation of 2-amino-5-methylpyridine

The heat capacities (C _p,m) of 2-amino-5-methylpyridine (AMP) were measured by a precision automated adiabatic calorimeter over the temperature range from 80 to 398 K. A solid-liquid phase transition was found in the range from 336 to 351 K with the peak heat capacity at 350.426 K. The melting temperature (T _m), the molar enthalpy (Δ_fus H _m⁰), and the molar entropy (Δ_fus S _m⁰) of fusion were determined to be 350.431±0.018 K, 18.108 kJ mol⁻¹ and 51.676 J K⁻¹ mol⁻¹, respectively. The mole fraction purity of the sample used was determined to be 0.99734 through the Van’t Hoff equation. The thermodynamic functions (H _T-H _298.15 and S _T-S _298.15) were calculated. The molar energy of combustion and the standard molar enthalpy of combustion were determined, ΔU _c(C₆H₈N₂,cr)= −3500.15±1.51 kJ mol⁻¹ and Δ_c H _m⁰ (C₆H₈N₂,cr)= −3502.64±1.51 kJ mol⁻¹, by means of a precision oxygen-bomb combustion calorimeter at T=298.15 K. The standard molar enthalpy of formation of the crystalline compound was derived, Δ_r H _m⁰ (C₆H₈N₂,cr)= −1.74±0.57 kJ mol⁻¹.     

Thermodynamic investigation of room temperature ionic liquid

The molar heat capacities of the room temperature ionic liquid 1-butylpyridinium tetrafluoroborate (BPBF₄) were measured by an adiabatic calorimeter in temperature range from 80 to 390 K. The dependence of the molar heat capacity on temperature is given as a function of the reduced temperature X by polynomial equations, C _p,m [J K⁻¹ mol⁻¹]=181.43+51.297X −4.7816X ²−1.9734X ³+8.1048X ⁴+11.108X ⁵ [X=(T−135)/55] for the solid phase (80–190 K), C _p,m [J K⁻¹ mol⁻¹]= 349.96+25.106X+9.1320X ²+19.368X ³+2.23X ⁴−8.8201X ⁵ [X=(T−225)/27] for the glass state (198–252 K), and C _p,m[J K⁻¹ mol⁻¹]= 402.40+21.982X−3.0304X ²+3.6514X ³+3.4585X ⁴ [X=(T−338)/52] for the liquid phase (286–390 K), respectively. According to the polynomial equations and thermodynamic relationship, the values of thermodynamic function of the BPBF₄ relative to 298.15 K were calculated in temperature range from 80 to 390 K with an interval of 5 K. The glass transition of BPBF₄ was observed at 194.09 K, the enthalpy and entropy of the glass transition were determined to be ΔH _g=2.157 kJ mol⁻¹ and ΔS _g=11.12 J K⁻¹ mol⁻¹, respectively. The result showed that the melting point of the BPBF₄ is 279.79 K, the enthalpy and entropy of phase transition were calculated to be ΔH _m = 8.453 kJ mol⁻¹ and ΔS _m=30.21 J K⁻¹ mol⁻¹. Using oxygen-bomb combustion calorimeter, the molar enthalpy of combustion of BPBF₄ was determined to be Δ_c H _m⁰ = −5451±3 kJ mol⁻¹. The standard molar enthalpy of formation of BPBF₄ was evaluated to be Δ_f H _m⁰ = −1356.3±0.8 kJ mol⁻¹ at T=298.150±0.001 K.     

Thermal behavior of 1,2,3-triazole nitrate

The thermal decomposition behaviors of 1,2,3-triazole nitrate were studied using a Calvet Microcalorimeter at four different heating rates. Its apparent activation energy and pre-exponential factor of exothermic decomposition reaction are 133.77 kJ mol⁻¹ and 10^14.58 s⁻¹, respectively. The critical temperature of thermal explosion is 374.97 K. The entropy of activation (ΔS ^≠), the enthalpy of activation (ΔH ^≠), and the free energy of activation (ΔG ^≠) of the decomposition reaction are 23.88 J mol⁻¹ K⁻¹, 130.62 kJ mol⁻¹, and 121.55 kJ mol⁻¹, respectively. The self-accelerating decomposition temperature (T _SADT) is 368.65 K. The specific heat capacity was determined by a Micro-DSC method and a theoretical calculation method. Specific heat capacity equation is C_\textp ( \textJ mol ^{- 1} \text K ^{- 1} ) = - 42.6218 + 0.6807T C_{\text{p}} \left( {{\text{J mol}}^{ - 1} {\text{ K}}^{ - 1} } \right) = - 42.6218 + 0.6807T (283.1 K < T < 353.2 K). The adiabatic time-to-explosion is calculated to be a certain value between 98.82 and 100.00 s. The critical temperature of hot-spot initiation is 637.14 K, and the characteristic drop height of impact sensitivity (H ₅₀) is 9.16 cm.