Heat capacity from drop calorimetry

The low temperature heat capacity, 14.0-315 K was measured by Getting (7). Janz et al. (8) measured the heat content by drop calorimetry in the temperature range 630-1250 K, and gave enthalpy and heat capacity equations based on their measurements. The above information was used in a Shomate analysis in order to smooth the enthalpy and calculate heat capacity above 298.15 K. The values from the low and high temperature sources join smoothly at 298.15 K. The heat capacity was graphically extrapolated above the melting point. The entropy at 14.0 K was calculated from the extrapolated low temperature... 

Todd (9) measured the low temperature heat capacities from 52.6 to 296.7 K, and made an extrapolation to 0 K which yielded an entropy of 8.12 cal mol" at 51 K. We adopt the measured heat capacities but make our own extrapolation to 0 K, based on the ratio of the measured heat capacities of ZrF (10), TiP (1 1) and TiCl ( ) from 6 to 50 K. This extrapolation gives S (50 K) = 6.758 0.7 cal K" mol which is adopted. Coughlin and King ( 3) measured high temperature enthalpy data from 335.9 to 566.8 K by drop calorimetry. Their data are smoothly joined with Todd s low temperature heat capacities. 

Smith et al. (5) measured low temperature heat capacities from 18.3 to 299.8 K. King et al. (6) measured high temperature enthalpy data from 399.3 to 1063.9 K by drop calorimetry. The adopted heat capacities are derived from these two sets of data, subject to the constraint that they join smoothly near 300 K. Deviations of the enthalpy data from the adopted values are -0.65% to +0.17%. Seitz et al. (7) have also measured low temperature heat capacities from 70 to 298.7 K which are not in agreement with the values adopted the discrepancy has been discussed by Smith. Cosgrove and Snyder ( ) measured high temperture enthalpy data... 

Johnson et al. [143] used low-temperature adiabatic calorimetry and high-temperature drop calorimetry to obtain the heat capacity of both forms of mordenite as a function of the temperature. These results and the results of the reaction-solution calorimetric studies discussed herein, enabled the tabulation of the thermodynamic properties (C°, S°, Af H°, and Af G°) of mordenite from 0 K to 500 K and dehydrated mordenite from 0 K to 900 K. 

Pulse calorimeters pass electrical current through an electrically conducting sample to force a temperature increase, which is measured along with the voltage drop across the sample. If the heat loss from the sample is known (or estimated by calibration), the energy input divided by the temperature increase determines the true heat capacity, if the temperature change is small. Pulse calorimetry eliminates many of the drawbacks of drop calorimetry. It is fast, reproducible, and, with proper calibration, accurate. However, its use is limited to conductive materials. 

Differential scanning calorimetry (DSC) can be used to determine experimentally the glass transition temperature. The glass transition process is illustrated in Fig. 1.5b for a glassy polymer which does not crystallize and is being slowly heated from a temperature below Tg. Here, the drop which is marked Tg at its midpoint, represents the increase in energy which is supplied to the sample to maintain it at the same temperature as the reference material. This is necessary due to the relatively rapid increase in the heat capacity of the sample as its temperature is increases pass Tg. The addition of heat energy corresponds to the endothermal direction. 

Moore (8) measured high temperature enthalpy data from 670.5 to 941 K by drop calorimetry. The low temperature heat capacities and high temperature enthalpy data were smoothly joined at 298.15 K. The C values above 941 K were obtained by graphical extrapolation. Getting and Gregory ( ) measured high temperature heat capacities in the temperature range from 60 to... 

Welty (1 ) has measured the enthalpy changes for fClg(p,cr) in the temperature range from 508 to 553 K by drop calorimetry. Because of the short temperature range, poor distribution of pints and lack of identification of the phase present at the conclusion of each drop, we feel that the enthalpy data are insufficient to define the heat capacity accurately. The adopted heat capacities are estimated so that they are consistent with the enthalpy data within their probable uncertainty. 

The heat capacity is taken from the drop calorimetry of Dworkln and Bredig (384 to 1260 K) (6). Between 298 and 820 K, the observed enthalpy differences and the constraint of passing through zero at 298.15 K are fit by a linear least squares technique Cp = 15.99 + 6.22 X 10 T cal K" mol" (298-820 K). The heat capacity in the observed diffuse lambda transition region, 820-1100 K, was adjusted to properly reproduce the observed enthalpies. The sharp heat capacity maximum occurs at 1050 K (6) and... 

The low temperature heat capacity data (52-296 K) are taken from Weller and Kelley (6). High temperature enthalpies of NiS Qg were measured by Conard et al. (7) via drop calorimetry. We have joined these values smoothly with the low temperature C ... 

In the high-temperature region, the main method of measurement is the drop calorimetry, where the sample is heated to the chosen temperature outside the calorimeter in a furnace and the heat capacity is calculated from the temperature dependence of the enthalpy changes measured after dropping the sample into the calorimeter. The application of this technique affects, however, the behavior of the sample heated in the furnace (decomposition, reaction with the crucible, etc. should be avoided) as well as at the cooling from the furnace temperature to that of the calorimeter. Sometimes the sample does not complete its phase transition at cooling (e.g. at the temperature of fusion, a part of the sample crystallizes while the other part becomes glassy). In such a case, the drop calorimeter must be supplemented by a solution calorimeter in order to get the enthalpy differences of all the samples to a defined reference state. 

The heat capacity was also derived from heat content measurements using drop calorimetry in the temperature range 800 to 1512 K by Yamaguchi, Kameda, Takeda, and Itagaki [94YAM/KAM]. The high temperature heat capacity results are summarised in Figure V-18. The selected heat capacity expression is ... 

Stuve et al. [78STU/FER] also reported the results of a limited set of drop calorimetry experiments (402.9 to 1001.5 K). The authors fitted an equation to the experimental enthalpy differences such that the heat capacity values meshed smoothly with the value obtained tfom adiabatic calorimetry for 298.15 K. The authors indicated that their equation was applicable, within 0.6 per cent for temperatures between 298 and 1200 K. As discussed below, NiS04 decomposes towards the upper end of this temperature range, and extrapolation of the heat capacities to 1200 K does not seem justified. Conversion of the equation from calorie to joule units leads to ... 

The authors reported drop calorimetry results obtained from samples initially at temperatures between 381.9 K and 1461.7 K. The scatter in the enthalpy difference results, based on measurements done at similar temperatures, seems to be of the order of 200 kJ-mol . Direct fitting of the drop calorimetry results without incorporating some low temperature heat capacity constraint leads to a poor extrapolation for temperatures below 400 K. The authors fitted an equation to their values of (// (7 )-//"(298.15K)), weighting the point at 298.15 K for the best fit of all results . This seems to have entailed the use of some of the heat capacity results of Catalano and Stout [55CAT/STO]. The reported value of C (298.15K) (62.93 JK mol ) differs by 1.1 JK mol from the value of [55CAT/STO], though the 5 value from that soiuce is used. Also, the expression reported by Binford and Hebert... 

In the same report, the authors reported low-temperature calorimetry heat capacity measurements (9 to 70 K) for anhydrous NiS04(cr). Limited sets of drop-calorimetry measurements were carried out for the same solid (403 to 1001.5 K), and these were used to generate equations for thermodynamic functions for NiS04 (cr) from 298 to 1200 K. 

Enthalpy increments from 298.15 to 1197 K were measured on 382 by means of drop calorimetry, leading to heat capacity values in this temperature region. The samples were prepared by solid state reaction from the elements and characterised properly (X-ray diffraction). The transition temperature for the phase transformation between the high- and low-temperature form was found to be 834 K. The heat capacity at 298.15 K amounts to 117.7 J K mol, which is in fair agreement with that obtained by Stolen et al. [91STO/GRO], (298.15 K) = 118.2 J K -mol. ... 

Figure 5.10 The heat capacity of muscovite, determined from drop caiorimetry and from differential scanning calorimetry.

The enthalpy as a function of time is readily available from, for example, drop calorimetry experiments or from adiabatic calorimeters with incremental temperature increases. Scanning calorimeters, however, furnish the heat capacity of the sample. In these cases, the phase transition shows as a peak and the enthalpy of transition is calculated by integration of the peak area. Traditionally, this is done after constructing a proper baseline under the peak between the start and the end of the peak. The definition of the start and the end of the peak and the shape of the baseline under the peak are somehow arbitrary, particularly when the phase transition is accompanied by a heat capacity change. The enthalpy change at the transition temperature trs can be calculated from the heat capacity curve by... 

Drop Calorimetry. In one type of drop calorimeter a sample at some elevated (or lower) temperature is dropped into a specimen receiver of known or calibrated thermal properties. By monitoring the temperature rise (or drop) of the specimen receiver, the heat capacity of the sample can be determined. A second type, known as the Bunsen ice calorimeter, uses the volume change of an ice-water mixture that results when heat is transferred from the sample to the mixture. 

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