Measuring Thermal Data

Differential Thermal Analysis (DTA). The differential thermal analysis test serves to examine transitions and reactions which occur on the order between seconds and minutes, and involve a measurable energy differential of less than 0.04 J/g. Usually, the measuring is done dynamically (i.e., with linear temperature variations in time). However, in some cases isothermal measurements are also done. DTA is mainly used to determine the transition temperatures. The principle is shown schematically in Fig. 2.20. Here, the sample, S, and an inert substance, /, are placed in an oven that has the ability to raise its temperature linearly. 

Two thermocouples that monitor the samples are connected opposite to one another such that no voltage is measured as long as S and / are at the same temperature  

However, if a transition or a reaction occurs in the sample at a temperature, Tc, then heat is consumed or released, in which case AT -/ 0. This thermal disturbance in time can be recorded and used to interpret possible information about the reaction temperature, Tc, the heat of transition or reaction, AH, or simply about the existence of a transition or reaction. 

The degree of crystallinity, X, is determined from the ratio of the heat of fusion of a polymer sample, AH sc, and the enthalpy of fusion of a 100% crystalline sample A He- 

In a DSC analysis of a semi-crystalline polymer, a jump in the specific heat curve, as shown in Fig. 2.22, becomes visible. The glass transition temperature, Tg, is determined at the inflection point of the specific heat curve. The release of residual stresses as a material s temperature is raised above the glass transition temperature is often observed in a DSC analysis. 

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Laboratory furnaces. Several types of furnaces are used in the laboratory these are often available as commercial rigs, generally equipped with more or less sophisticated temperature measurement and control devices. As an alternative, a lab-made or commercial furnace and its temperature measuring devices may be connected to a multi-channel data acquisition/actuator/switch unit, to be programmed by a personal computer, in order to plan and carry out thermal treatments, to collect and retrieve measured thermal data, etc. 

Figures 7 and 8 show thermal conductivity data for CBCF after exposure to temperatures of 2673, 2873, 3073, and 3273 K, for 5.7 and 15 7 seconds, respectively. The symbols in the Figs. 7 and 8 represent measured thermal conductivity values, and the solid lines are the predicted behavior from Eqs. (5) through (8) The model clearly accounts for the effects of measurement temperature, exposure tune, and exposure temperature The fit to the data is good (typically within 10%). However, the fit to the as fabricated CBCF data (Fig 6) was less good (-20%), although the scatter in the data was larger because of the much lower heat treatment temperature (1873 K) in that case.

Thermal Expansion Measurement. Thermal expansion measurements were made with a laser interferometer dilatometer (2Q) with a strain resolution of approximately 2x10 6. The temperature cycle for all tests went from room temperature to a maximum of 121°C (except where noted), down to -157°C and back to room temperature. Thermal strain data were taken at approximately 20°C increments with a 30-minute hold at each temperature to allow the specimen and interferometer to reach thermal... 

The first five measure the activity of the solvent and the last five measure the activity of the solute. The boiling point method is generally not included in evaluations for two reasons there are little data from these measurements or the thermal data are not adequate to apply an accurate correction to obtain an activity at 298 K. 

We can calculate AH from thermal data alone, that is, from calorimetric measurements of enthalpies of reaction and heat capacities. It would be advantageous if we could also compute AS from thermal data alone, for then we could calculate AG or Ay without using equilibrium data. The requirement of measurements for an equilibrium state or the need for a reversible reaction thus could be avoided. The thermal-data method would be of particular advantage for reactions for which AG or AT is very large (either positive or negative) because equilibrium measurements are most difficult in these cases. 

Several cases exist in which calculations of the entropy change of a reaction from values of the entropy obtained from thermal data and the third law disagree with values calculated directly from measurements of AH and determinations of AG from experimental equilibrium constants. For example, for the reaction... 

The interest in thermal data for hydrocarbons stems from two sources. The first relates to a need to establish the chemical potential (21) or the free energy (44) of pure compounds from measurements of the heat capacity from low absolute temperatures to the temperatures of interest. Such measurements and the third law of thermodynamics permit the evaluation of the free energy. The second industrial interest in thermodynamic properties arises from a need to evaluate the heat and work associated with changes in state of hydrocarbon systems. The measurements by Rossini (57), Huffman (17), and Parks (32, 53) are worthy of mention in a field replete with a host of careful investigators. Such thermal measurements have been of primary utility in predicting chemical equilib-... 

Rule 2. Fit experimentally measured thermal conductivites as a function of temperature for the pure species (if viscosity data are not available) to Eq. 12.101 (presented later), using e and a as the adjustable parameters. 

Titration calorimetry or thermometric titration calorimetry is a technique in which one reactant is titrated continuously into the other reactant, and either the temperature change or heat produced in the system is measured as a function of titrant added. In isoperibol titration calorimetry, the temperature of a reaction vessel in a constant-temperature environment is monitored as a function of time (Figure 8.4) (Hansen et al., 1985 Winnike, 1989). A single titration calorimetric experiment yields thermal data as a function of the ratio of the concentrations of the reactants. 

Kinetic simulation methods are used as advisory controls in potentially thermally hazardous batch amination reactions of nitroaromatic compounds. Time—temperature process data are fed as input to a kinetic simulation computer program which calculates conversions, heat release and pressure profdes. Results are compared continuously on-line with measured batch data to detect any deviations from normal operating conditions. 

The postulates of Nernst are those that are required when we wish to determine equilibrium conditions for chemical reactions from thermal data alone. In order to calculate the equilibrium conditions, we need to know the value of AGe for the change of state involved. We take the standard states of the individual substances to be the pure substances at the chosen temperature and pressure. The value of AH° can be determined from measurements of the heat of reaction. We now have... 

These functions are particularly useful when the low-temperature thermal data are not available. Under such circumstances the values of Se(T) must be obtained from equilibrium measurements as indicated in Section 15.5. 

L. Mandelcorn and E. W. R. Steacie, Can. J. Chem., 32,474 (1954), have made rather crude measurements of rea( tion 20. They find A 20 = 4 X 10 —7000/RT liters/mole-sec with E20 = 7.0 1.5 Kcal. This value of E20 is in very poor agreement with present thermal data together with the values for E of the reverse reaction. 

The experimental activation energy calculated on the basis of a %-order reaction is found to be 46 Kcal. If we use the simple scheme, this should be equal [Eq. (XIII.14.6)] to E2 + HiEi — E ). The value of E2 has been measured at 7.5 Kcal (Table XII.6), while Eb = 0. If the bond energy of the H in the HCO radical is assigned the value 15 Kcal, current thermal data give a value of 82.4 Kcal to the enthalpy change of reaction 1, so that if there is no activation energy for the back reaction, this can be taken as the minimum value of Ei and the calculated value of the chain decomposition is then 48.7 Kcal — 22T/2 48 Kcal at 800°K, which may be considered to be in excellent agreement with the data. 

In general chemistry, in particular in discussion of isomerization equilibria, we may well require accuracy a good deal higher than this. Our only information about heats of isomerization of 1 or 2 kcal rnnle t may well come from combustion experiments where the total heat quantities measured are perhaps some thousands of kcal mole b At present the greatest accuracy normally attained is about 0 02 per cent, but Parks has pointed out that in- .c uraries in thermal data have such a large effect on equilibrium ( instants that a tenfold improvement in accuracy is desirable. 

In later PR-TRMC measurements, the after-pulse relaxation of the microwave conductivity itself in pure gases was monitored with nanosecond time-resolution and this provided a more detailed, quantitative method of monitoring electron thermalization. Of particular importance was a detailed study of thermalization in helium, which could be used to test the predictions of different theoretical treatments for this well-characterized gas. Detailed thermalization data were also obtained for oxygen, for which the concurrent three-body attachment process provides an interesting complication. The dramatic influence of small concentrations of water vapor on the thermalization process was also demonstrated for samples of dry and humid air. ° The (unexpectedly) high thermalization... 

Entropy evaluations from published cryothermal data on the lanthanide (III) oxides are summarized in Table II with an indication of the lowest temperature of the measurements and the estimated magnetic entropy increments below this temperature. Their original assignment of crystalline field levels from thermal data still appears to be in good accord with recent findings e.g., 17). Unfortunately, measurements on these substances were made only down to about 8°K. because the finely divided oxide samples tend to absorb the helium gas utilized to enhance thermal equilibration between sample and calorimeter. 

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