Heat balances and heat capacity calculations

We present enthalpy and heat capacity calculations under reversible conditions in which a system is allowed to reach equilibrium after incremental steps in temperature. We focus on the binary systems Ag–Cu and 1,3,5 tri-bromo-benzene and 1,3,5 tri-chloro-benzene and show that due to the compositional effect, thermodynamic properties differ up to an order of magnitude in two-phase regions relative to values in single-phase regions. We demonstrate that Planck’s definition of heat capacity needs a minor extension to include the change of phase assemblages due to phase transitions. Dedicated to Professor Su-II Pyun on the occasion of his 65th birthday     

Melting of polymers by non-isothermal, temperature-modulated calorimetry: analysis of various irreversible latent heat contributions to the reversing heat capacity

This paper provides an analysis of contributions to the apparent, reversing heat capacity when measured by temperature-modulated differential scanning analysis (TMDSC) with an underlying heating rate in the temperature range where irreversible transitions with latent heats occur. To deconvolute the data of a TMDSC scan into a total and reversing part, it is common practice to use the sliding averages and the first harmonics of the Fourier series of temperature and heat-flow rate. Under certain conditions, this procedure produces erroneous reversing contributions which are detailed by experiment and simulation. Unless the response to the temperature modulation is linear, the total heat-flow rate is stationary, and the transition is truly reversible and occurs only once during the temperature scan, one cannot expect a true deconvolution of total and reversible effects. In the presence of multiple, irreversible transitions within a modulation period, however, each process involving latent heat can increase the modulation amplitude, as demonstrated by computer-simulation of polymer melting. As a result, the multiple transitions may give erroneously high latent heats when integrating the apparent reversing heat capacity with respect to temperature.     

Some remarks on heat capacity measurements by temperature-modulated calorimetry

In temperature-modulated calorimetry, the condition in sample amount, especially thickness, required for high-accuracy heat capacity measurement should be made clear. We propose the condition of maximum thickness of a sample for measuring heat capacity within an accuracy of 1%. The other important factor for high-accuracy heat capacity measurement is thermal contact conductance between a sample and a sample pan and also that between a pan and a base plate of an apparatus. The conditions in these thermal contact conductances required for high-accuracy heat capacity measurement are discussed. Among them, if only thermal contact conductance between a pan and a base plate is significant, there is an ingenious method to measure heat capacity with high accuracy. Furthermore, if the thermal contact conductance between a pan and a base plate is infinite, we offer a simple method to obtain complex heat capacity.     

High temperature enthalpy and heat capacity of GaN

The heat capacity and the heat content of gallium nitride were measured by calvet calorimetry (320-570 K) and by drop calorimetry (670-1270 K), respectively. The temperature dependence of the heat capacity in the form C_pm=49.552+5.440×10⁻³T−2.190×10⁶T⁻²+2.460×10⁸T⁻³ was derived by the least squares method. Furthermore, thermodynamic functions calculated on the basis of our experimental results and literature data on the molar entropy and the heat of formation of GaN are given.     

Anomalously high heat capacity of core-softened liquids

Heat capacity is among the most important thermodynamic characteristics of a substance. The behaviour of the heat capacity is well understood in gases and crystals, but not in liquids. A common view on the heat capacity of liquids is that it should be close to the solid-like values close to the melting line and it should approach the gas values in the limit of high temperatures. However, some liquids can show anomalously high magnitudes of isochoric heat capacity. In the present paper, I show that core-softened liquids can demonstrate unusually high magnitude of the heat capacity induced by a structural crossover of the liquid.     

Heat capacity and thermodynamic functions of LuPO4 in the range 0-320 K

The heat capacity of LuPO₄ was measured in the temperature range 6.51-318.03 K. Smoothed experimental values of the heat capacity were used to calculate the entropy, enthalpy and Gibbs free energy from 0 to 320 K. Under standard conditions these thermodynamic values are: (298.15 K) = 100.0 ± 0.1 J K⁻¹ mol⁻¹, S⁰(298.15 K) = 99.74 ± 0.32 J K⁻¹ mol⁻¹, H⁰(298.15 K) − H⁰(0) = 16.43 ± 0.02 kJ mol⁻¹, −[G⁰(298.15 K) − H⁰(0)]/T = 44.62 ± 0.33 J K⁻¹ mol⁻¹. The standard Gibbs free energy of formation of LuPO₄ from elements Δ_fG⁰(298.15 K) = −1835.4 ± 4.2 kJ mol⁻¹ was calculated based on obtained and literature data.     

Phase transition of pyridinium tetrachloroiodate(III), PyHICl4, studied by a single crystal X-ray analysis and dielectric and heat capacity measurements

Change of a local environment of a polar pyridinium ion, which is associated with the phase transition of crystalline pyridinium tetrachloroiodate(III) at T_c = 217 K, was investigated by a single crystal X-ray analysis and dielectric and heat capacity measurements. The site symmetry 2/m of the ion at T > T_c indicates an orientational disorder in the high-temperature phase (HTP). The energy difference ΔE between the stable and meta-stable orientations of the pyridinium ion at the 2/m site was estimated to be ΔE/R ? 560 K at 280 K in the HTP. Below the T_c, an antiferroelectric ordering of the ions was revealed.     

Zeolite 4A: heat capacity and thermodynamic properties

The heat capacity of zeolite 4A (also known as LTA, Linde Type A and sodium zeolite A), in the temperature range from 37 to 311 K, is reported. The heat capacity shows no anomalies in this temperature range. Thermodynamic parameters, H, S and G, relative to their values at T=0 K were derived. From these data, we find that zeolite 4A is stabilized by strong enthalpic interactions. Furthermore, its thermodynamic stability results from the strong Si---O and Al---O bonds in the primary building units, with bond strengths very close to those in other similar materials.     

Isobaric specific heat capacity of typical lithium chloride liquid desiccants using scanning calorimetry

Three kinds of lithium chloride desiccants were selected, which are considered to be potential and interesting working fluids for a desiccant/dehumidification or absorption refrigeration system, and their isobaric specific heat capacities were determined in this context. Experiments were conducted at a high accuracy twin-cell scanning calorimeter. The temperature accuracy and heat flux resolution of the calorimeter are ±0.05 K and 0.1 μW respectively. The data of lithium chloride + water and lithium chloride + triethylene glycol (TEG)/propylene glycol (PG) + water systems were achieved at temperatures from 308.15 K to 343.15 K and atmospheric pressure. The mass fraction of LiCl ranged from 15% to 45% in the LiCl + H₂O system, and the mass fraction of LiCl and glycol ranged from 10% to 23.3% and 20% to 46.7% in the ternary systems respectively. Based on the experimental heat capacity data, a universal empirical formula was correlated as a function of temperature and solute mass fraction. In the experimental mass fractions and temperatures range, the average absolute deviation (AAD) between experiment results and calculated values is no more than 0.15%, and maximum absolute deviation (MAD) is within 0.38%. These thermodynamic data of lithium chloride solutions can be effectively used for analysis and design of desiccant/dehumidification systems and absorption refrigeration systems in both refrigeration and chemical industry.     

Importance of heat capacity determination in homogeneous nucleation: application to progesterone

Progesterone is known to exist under different crystallographic forms in the solid state. The thermodynamic stable form (I), melts at 129.2 °C (402.35 K) under atmospheric pressure. After melting and cooling a metastable form (II) can be obtained which melts at 122 °C (395.15 K). This uncommon behaviour can be explained with the theory of nucleation, only if heat capacity of the different forms are known.     

Heat capacity, enthalpy and entropy of ternary bismuth tantalum oxides

Heat capacity and enthalpy increments of ternary bismuth tantalum oxides Bi₄Ta₂O₁₁, Bi₇Ta₃O₁₈ and Bi₃TaO₇ were measured by the relaxation time method (2-280 K), DSC (265-353 K) and drop calorimetry (622-1322 K). Temperature dependencies of the molar heat capacity in the form C_pm=445.8+0.005451T−7.489×10⁶/T² J K⁻¹ mol⁻¹, C_pm=699.0+0.05276T−9.956×10⁶/T² J K⁻¹ mol⁻¹ and C_pm=251.6+0.06705T−3.237×10⁶/T² J K⁻¹ mol⁻¹ for Bi₃TaO₇, Bi₄Ta₂O₁₁ and for Bi₇Ta₃O₁₈, respectively, were derived by the least-squares method from the experimental data. The molar entropies at 298.15 K, S°_m(298.15 K)=449.6±2.3 J K⁻¹ mol⁻¹ for Bi₄Ta₂O₁₁, S°_m(298.15 K)=743.0±3.8 J K⁻¹ mol⁻¹ for Bi₇Ta₃O₁₈ and S°_m(298.15 K)=304.3±1.6 J K⁻¹ mol⁻¹ for Bi₃TaO₇, were evaluated from the low-temperature heat capacity measurements.     

Low-temperature heat capacity and thermodynamic properties of endo-Tricyclo[5.2.1.0]decane

Endo-Tricyclo[5.2.1.0^2,6]decane (CAS 6004-38-2) is an important intermediate compound for synthesizing diamantane. The lack of data on the thermodynamic properties of the compound limits its development and application. In this study, endo-Tricyclo[5.2.1.0^2,6]decane was synthesized and the low temperature heat capacities were measured with a high-precision adiabatic calorimeter in the temperature range from (80 to 360) K. Two phase transitions were observed: the solid-solid phase transition in the temperature range from (198.79 to 210.27) K, with peak temperature 204.33 K; the solid-liquid phase transition in the temperature range from 333.76 K to 350.97 K, with peak temperature 345.28 K. The molar enthalpy increments, ΔH_m, and entropy increments, ΔS_m, of these phase transitions are ΔH_m=2.57 kJ · mol⁻¹ and ΔS_m=12.57 J · K⁻¹ · mol⁻¹ for the solid-solid phase transition at 204.33 K, and, Δ_fusH_m=3.07 kJ · mol⁻¹ and Δ_fusS_m=8.89 J · K⁻¹ · mol⁻¹ for the solid-liquid phase transition at 345.28 K. The thermal stability of the compound was investigated by thermogravimetric analysis. TG result shows that endo-Tricyclo[5.2.1.0^2,6]decane starts to sublime at 300 K and completely changes into vapor when the temperature reaches 423 K, reaching the maximal rate of weight loss at 408 K.     

Thermodynamics of linear polyurethanes on basis of 1,4-diisocyanatobutane with 1,4-butanediol and 1,6-hexanediol in the range from T → 0 to 490 K

The temperature dependence of heat capacity and characteristics of physical transformations of partially crystalline linear aliphatic polyurethanes based on 1,4-diisocyanatobutane with 1,4-butanediol and 1,6-hexanediol have been studied over the range 6.5-490 K by precision adiabatic vacuum and dynamic calorimetry. The calorimetric data were used to determine the thermodynamic quantities of devitrification and fusion and to calculate the standard thermodynamic functions , H⁰(T) − H⁰(0), S⁰(T) and G⁰(T) − H⁰(0) of linear polyurethanes in totally crystalline and amorphous states. The values of the fractal dimension D in the function of multifractal generalization of Debye's theory of the heat capacity of solids were estimated and the character of heterodynamics of their structures was detected. The energies of combustion of the substances were measured in a calorimeter with an isothermal shield and a static bomb. The enthalpies of combustion and the standard thermodynamic characteristics of formation of the polymers at T = 298.15 K were calculated too. The standard thermodynamic characteristics of polycondensation processes in bulk of 1,4-diisocyanatobutane with 1,4-butanediol and 1,6-hexanediol followed by the formation of linear polyurethanes were determined in the range from 0 to 350 K. A comparative analysis of the corresponding standard thermodynamic properties of the polymers under consideration and polyurethanes of isomeric structure was made and some dependences of their change on various conditions were found.     

Phonon dispersion and heat capacity in polyoxacyclobutane modification I

Normal modes of vibration and their dispersion for polyoxacyclobutane modification I (POCB I) have been obtained by using Urey-Bradley force field and the Wilson's GF matrix method as modified by Higgs. Characteristic features of the dispersion curves such as crossing, repulsion and regions of high density-of-states have been explained. Heat capacity measurements have been interpreted and the limitations of the present work discussed.