Heat capacity calorimetry

Experimental heat capacity measurements of α-ZrW₂O₈, and zeolitic polymorphs of SiO₂, BEA and MFI, have been made from 0.6 to 400 K. Measurements on β-ZrMo₂O₈ have been made from 8 to 400 K. Analysis of the results yields evidence for very low frequency modes in all four materials. These modes are responsible for negative thermal expansion behavior in α-ZrW₂O₈ and β-ZrMo₂O₈. Negative thermal expansion has been observed in some pure SiO₂ zeolites, but no studies have been made to look for it in BEA and MFI. The appearance of low frequency modes in these two zeolites suggests that temperature dependent structural investigations would be worthwhile. These modes are lower in energy than the Boson peak in vitreous silica. This revised version was published online in August 2006 with corrections to the Cover Date.     

Uncertainty evaluation for the adiabatic temperature rise in isoperibol calorimetry

This article describes a practical approach for evaluating the uncertainty of results for determinations of the adiabatic (corrected) temperature rise in isoperibol calorimetry. The methodology is firmly based on the recommendations of the Guide to the expression of uncertainty in measurement (GUM). Although developed for a specific modification of the Regnault?CPfaundler method, the approach is sufficiently general to make it applicable to virtually any other scheme for the evaluation of temperature?Ctime curves in temperature-rise calorimetry.     

An update on the electrolytic conductivity values for the primary standard KCl solutions: Conversion to the ITS-90 temperature scale

A new international temperature scale has replaced the 1968 scale. Here, we report the changes required in our previous results for primary conductivity standards for 0.01, 0.1 and 1.0 Demal KCl solutions at 0,18 and 25°C.     

High-precision adiabatic calorimetry and the specific heat of cyclopentane at low temperature

We describe a fully automated adiabatic calorimeter designed for high-precision covering the temperature range 15 to 300 K. Initial measurements were performed on synthetic sapphire (20 g). The statistical error of the apparatus estimated from the scattering of theC _p data of sapphire is about 0.1% and the average absolute error of specific heat between 100 and 300 K was 0.7% compared to values given in the literature. The heat capacity and the three phase transitions of cyclopentane (C₅H₁₀) which is recommended as a standard for the temperature calibration of scanning calorimeters have also been measured. The transition temperatures were determined to be (literature values in parentheses): 122.23 K (122.39 K) 138.35 K (138.07 K) and 178.59 K (179.69 K), with an experimental error of ±40 mK.     

Heat capacity of copper hydride

The heat capacity of copper hydride has been measured in the temperature range 2–60 and 60–250 K using two adiabatic calorimeters. Special procedure for the purification of CuH has been applied and a careful analysis of sample contamination has been performed. The experimental results have been extrapolated up to 300 K due to instability of the copper hydride at room temperature. From the temperature dependence of heat capacity the values of entropy S°(T), thermal part of enthalpy H°(T)−H°(0) and Gibbs function [−(G°(T)−H°(0))] have been calculated assuming S°(0)=0. The standard absolute entropy, standard entropy of formation from the elements and enthalpy of decomposition of copper hydride from the elements have been calculated and found to be 130.8 J K⁻¹ mol⁻¹ (H₂), −85.1 J K⁻¹ mol⁻¹ (H₂), −55.1 kJ mol⁻¹ (H₂), respectively. These new results gave the possibility of discussion on thermodynamic properties of copper hydride. Debye temperature has been for the first time determined experimentally.     

Characterisation of an exothermic reaction using adiabatic and isothermal calorimetry

A simple esterification reaction is used to demonstrate standard procedures for determining the thermokinetic parameters of an exothermic reaction from adiabatic calorimetric data. The influence of variations in the heat capacity of the sample due to changes in temperature and concentration is explored. Shortcomings in the simple interpretation of adiabatic data are identified and isothermal heatflow calorimetry is used to reveal autocatalytic effects which were not apparent from the adiabatic experiments. A more rigourous interpretation of the adiabatic and isothermal data is outlined and used to predict the conditions which can lead to exothermic runaway in a batch reactor. Mathematical simulation of the conditions in a jacketed reactor is used to demonstrate the importance of developing reliable kinetic expressions before assessing the safety of a batch process.

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Zusammenfassung Anhand einer einfachen Veresterungsreaktion wurden Standardverfahren zur Ermittlung thermokinetischer Parameter exothermen Reaktionen aus adiabatischen kalorimetrischen Daten demonstriert. Dabei wurde der Einfluß von Temperatur und Konzentration auf Änderungen der Wärmekapazität untersucht. Fehler bei der einfachen Interpretation adiabatischer Daten wurden identifiziert und isotherme Wärmeflußkalorimetrie wurde angewendet, um autokatalytische Effekte aufzuzeigen, die sich anhand der adiabatischen Experimente nicht ersehen lassen. Es wurde eine gründlichere Interpretation adiabatischer und isothermer Daten umrissen und verwendet, um die Bedingungen vorherzusagen, die in einem Kesselreaktor zu einem exothermen Davonlaufen der Reaktion führen. Mathematische Simulation der Bedingungen in einem Mantelkessel wurde angewendet, um zu zeigen, von welch großer Bedeutung die Entwicklung zuverlässiger kinetischer Ausdrücke ist, bevor man die Sicherheit einer Reaktion in einem Kesselreaktor beurteilt.

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Thermodynamic temperature differences from the ITS-90 for the correction of thermodynamic property data

This paper purpose is to re-calculate thermodynamic or chemical–physical properties according to thermodynamic temperature T, where measured temperature values were obtained according to the ITS-90, T₉₀ (or the reverse). The main aims of the calculations are: to remove the discontinuity of the first derivative at 273.16 K that is intrinsic in the ITS-90 definition; to use a single cubic spline to model the database of the available experimental data over the whole temperature range (2.37 to 1235) K, while maximising the medium-range smoothness of the correction function; to compute corrections using only local polynomial coefficients.     

Uncertainty analysis of theoretical methods for adiabatic temperature rise determination in calorimetry

The main methods for the determination of the temperature rise in calorimetric experiments corrected of heat losses to surroundings (called adiabatic temperature rise) are described thereafter. This corrected temperature rise is obtained analytically from experimental temperature–time curves. The general scheme reported by Henri Régnault and Leopold Pfaundler for the first time in the 19th century is considered as the basis for all methods elaborated afterwards. A bibliographical study raised five methods including Régnault–Pfaundler’s. These methods have been applied on five experimental temperature–time curves obtained with an isoperibolic reference gas calorimeter at the French national metrology and testing institute (LNE) on combustion of pure methane. This paper deeply details a new analytical method elaborated at LNE exposing best heat transfer phenomena representation occurring in the water bath calorimeter. A comparative study of the five methods of the temperature rise determination and of their associated uncertainties is here presented.     

Calibration of capillary melting-point apparatus to the international temperature scale of 1990 (ITS-90) by use of fluxed highly pure metals

Capillary melting-point measurements have always lacked traceability to internationally accepted or precisely determined temperature standards. Highly pure (99.999%) indium, tin, bismuth, and cadmium or lead, when covered with stearic anhydride acting as a flux, gallium covered with 3 M HCl and zinc covered with m-(m- phenoxyphenoxy)benzene containing triphenylboron, give sharp visual melting points which correspond to primary or secondary “fixed points” on the International Temperature Scale of 1990 (ITS-90). Melting is observed to begin with collapse and coalescence to a mush. It ends with the formation of a mercury-like spheroidal droplet, taken as the melting point; the entire range is less than 0.5°C. Readings may be interpolated either graphically or computationally to give tabular corrections yielding true temperatures. The performance of thermometers cannot safely be predicted from information engraved thereon, as > 10° errors were observed. It is recommended that organic chemical publications insist on the use of the phrase “The m.p. apparatus was metal calibrated to ITS-90”.     

Heat capacity of hafnia at low temperature

The low temperature (2 to 300) K heat capacity of monoclinic hafnia (HfO₂) was measured using the heat capacity option of a Quantum Design Physical Property Measurement System (PPMS). The thermodynamic functions in this temperature range were derived by curve fitting. The standard entropy and enthalpy of hafnia at T = 298.15 K was calculated to be 56.15 ± 0.57 J · mol^?1 · K^?1 and 9.34 ± 0.09 kJ · mol^?1, respectively. The results are in fairly good agreement with old data, which only covered temperatures from (50 to 298) K. Hafnia has a higher heat capacity than zirconia at all temperatures from (2 to 300) K.     

DSC and adiabatic calorimetry study of the polymorphs of paracetamol

Monoclinic (I) and orthorhombic (II) polymorphs of paracetamol were studied by DSC and adiabatic calorimetry in the temperature range 5 - 450 K. At all the stages of the study, the samples (single crystals and powders) were characterized using X-ray diffraction. A single crystal → polycrystal II→ I transformation was observed on heating polymorph II, after which polymorph I melted at 442 K. The previously reported fact that the two polymorphs melt at different temperatures could not be confirmed. The temperature of the II→I transformation varied from crystal to crystal. On cooling the crystals of paracetamol II from ambient temperature to 5 K, a II→ I transformation was also observed, if the 'cooling-heating' cycles were repeated several times. Inclusions of solvent (water) into the starting crystals were shown to be important for this transformation. The values of the low-temperature heat-capacity of the I and II polymorphs of paracetamol were compared, and the thermodynamic functions calculated for the two polymorphs. This revised version was published online in July 2006 with corrections to the Cover Date.     

Heat capacity measurements on uranium–cerium mixed oxides by differential scanning calorimetry

Uranium–cerium mixed oxides of three different compositions (U_0.2Ce_0.8)O₂, (U_0.5Ce_0.5)O₂ and (U_0.8Ce_0.2)O₂, were prepared by combustion synthesis and characterized by XRD. The compositional characterization was done by ICP-AES. Heat capacity measurements employed a heat flux type differential scanning calorimeter from 280 to 820 K. The heat capacity values of (U_0.2Ce_0.8)O₂, (U_0.5Ce_0.5)O₂ and (U_0.8Ce_0.2)O₂ at 298 K are 62.8, 64.2 and 70.1 J K⁻¹ mol⁻¹, respectively. Enthalpy increment, entropy and Gibbs energy function were computed from the heat capacity data.     

Combined use of adiabatic calorimetry and heat conduction calorimetry for quantifying propellant cook-off hazards

Recent work performed at DERA (now QinetiQ) has shown how accelerating rate calorimetry (ARC) can be used to obtain time to maximum rate curves using larger samples of energetic materials. The use of larger samples reduces the influence of thermal inertia, permitting experimental data to be gathered at temperatures closer to those likely to be encountered during manufacture, transportation or storage of an explosive device. However, in many cases, extrapolation of the time to maximum rate curve will still be necessary. Because of its low detection limit compared to the ARC, heat conduction calorimetry can be used to obtain data points at, or below, the region where an explosive system might exceed its temperature of no return and undergo a thermal explosion.Paired ARC and heat conduction calorimetry experiments have been conducted on some energetic material samples to explore this possibility further. Examples of where both agreement and disagreement are found between the two techniques are reported and the significance of these discussed. Ways in which combining ARC and heat conduction calorimetry experiments can enhance, complement and validate the results obtained from each technique are examined.     

High-temperature calorimetry of zirconia: Heat capacity and thermodynamics of the monoclinic–tetragonal phase transition

The high-temperature heat capacity of zirconia was directly measured by differential scanning calorimetry between T = (1050 and 1700) K and derived from the heat content measured by transposed temperature drop calorimetry between T = (970 and 1770) K, including the monoclinic–tetragonal (m–t) phase transition region. The enthalpy and entropy of the m–t phase transition are (5.43 ± 0.31) kJ · mol⁻¹ and (3.69 ± 0.21) J · K⁻¹ · mol⁻¹, respectively. Values of thermodynamic functions are provided from room temperature to 2000 K.     

A study on the thermodynamic properties of polyimide BTDA-ODA by adiabatic calorimetry and thermal analysis

Polyimide BTDA-ODA sample was prepared by polycondensation or step-growth polymerization method. Its low temperature heat capacities were measured by an adiabatic calorimeter in the temperature range between 80 and 400 K. No thermal anomaly was found in this temperature range. A DSC experiment was conducted in the temperature region from 373 to 673 K. There was not phase change or decomposition phenomena in this temperature range. However two glass transitions were found at 420.16 and 564.38 K. Corresponding heat capacity increments were 0.068 and 0.824 J g^–1 K^–1, respectively. To study the decomposition characteristics of BTDA-ODA, a TG experiment was carried out and it was found that this polyimide started to decompose at ca 673 K.This revised version was published online in November 2005 with corrections to the Cover Date.     

Determination of the specific heat capacity of hemoglobin- and methemoglobin-water mixtures using an adiabatic calorimeter

The specific heat capacity of bovine hemoglobin-, methemoglobin-, and thermally denatured hemoglobin-water mixtures were measured in the temperature range from 10 to 80°C. The partial specific heat capacities for mass fractions of the protein between 0 and 1 were computed. Significant differences of the partial quantities were obtained for the native, respectively denatured state of protein and for the protein in the native state in fluid mixtures, respectively in rather dry mixtures. For mixtures with protein mass fractions up to 0.45, exceeding the value in living human red cells, partial specific heat capacities of either components are found to be constant. The accuracy of the used adiabatic calorimeter will be described briefly.     

Heat capacity measurement by modulated DSC at constant temperature

The mathematical equations for step-wise measurement of heat capacity (C _p ) by modulated differential scanning calorimetry (MDSC) are discussed for the conditions of negligible temperature gradients within sample and reference. Using a commercial MDSC, applications are evaluated and the limits explored. This new technique permits the determination ofC _p by keeping the sample continually close to equilibrium, a condition conventional DSC is unable to meet. Heat capacity is measured at ‘practically isothermal condition’ (often changing not more than ±1 K). The method provides data with good precision. The effects of sample mass, amplitude and frequency of temperature modulation were studied and methods for optimizing the instrument are proposed. The correction for the differences in sample and reference heating rates, needed for high-precision data by standard DSC, do not apply for this method. Presented in preliminary from at the 22nd NATAS Conference in Denver, CO 9/19-22/93 (Proceedings, pages 59–64, editor K. R. Williams).     

Investigation of copper(II) complexation by glycylglycine using isothermal titration calorimetry

Isothermal titration calorimetry (ITC) and potentiometric titration methods have been used to study the process of proton transfer in the copper(II) ion-glycylglycine reaction. The stoichiometry, conditional stability constants, and thermodynamic parameters (ΔG, ΔH, and ΔS) for the complexation reaction were determined using the ITC method. The measurements were carried out at 298.15 K in solutions with a pH of 6 and the ionic strength maintained with 100 mM NaClO₄. Carrying out the measurements in buffer solutions of equal pH but different enthalpies of ionization of its components (Mes, Pipes, Cacodylate) enabled determination of the enthalpy of complex formation, independent of the enthalpy of buffer ionization. The number of protons released by glycylglycine on account of complexation of the copper(II) ions was determined from calorimetric and potentiometric measurements.     

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.