Thermometric equation

On the basis of the experimental data of Lindsley and Dixon (1976) on the CaMgSi20g-Mg2Si205 binary join and accounting for the observed compositions of natural pyroxenes coexisting at equilibrium, Kretz (1982) proposed two empirical thermometric equations applicable to clinopyroxene and valid, respectively, for T > 1080 °C and T < 1080 °C ... 

Coupling thermometric equations such as equation 11.174 for different minerals, one obtains solid-solid fractionation expressions of the type... 

More generally, suppose we choose any two fixed temperatures to which we assign the arbitrary values and t2 If yi and 2 are the values of the thermometric property at these temperatures, the thermometric equation, Eq. (6.2), becomes... 

Let us consider unit mass of a fluid in a given state. Since the equations which we shall deduce in this paragraph do not depend on any particular thermometric scale, we shall represent the temperature by 6, where 6 may be the Centigrade temperature, or may be measured on any other temperature scale. The state of the fluid is therefore represented by (v, p, 6). If one of these variables increases by an infinitesimal amount there will, in general, be a corresponding increment in the value of each of the others, and there could be an infinite number of corresponding pairs of values of the latter for one value of the former. But if two variables are fixed, the state of the fluid is completely defined, for it has only two degrees of freedom ( 26). 

The kinetics of polyurethane curing in adiabatic conditions was studied by the thermometric method (see Section 2.2) for a composition based on macro(diisocyanate) and diamine.48 It was proved that in this case, the second-order kinetic equation was inapplicable for the rangep > 0.7. By analyzing the time dependencies of temperature of the reactive medium, it was established that the... 

More recently, Willson et al. (7,8) showed how it is possible to write calorimetric kinetic equations that describe a range of commonly encountered mechanisms. The original and transformed versions of some of these equations are given in Table 4. Many of these fitting equations have been incorporated into the thermometric operating and data capture software Digitam 4.1 . 

The value of a thermometric signal is calculated by means of a mathematical formulation of the heat and material balance in the reaction system, represented by the microcalorimetric column packed with an immobilized enzyme. The microcalorimetric column with an IMB can be defined as the continuous packed bed reactor depicted in Fig. 3. The balance equations were derived according to the following simplifying assumptions, which had been previously verified [27] ... 

The mathematical treatment of FMC data can be accomplished by standard procedures via the solution of mass balance equations, on condition that the data were converted to reaction rate data with Eq. (21). As mentioned above, this requires the determination of the transformation parameter a. Two approaches based on calibration were developed and tested. In the first approach, thermometric signals are combined with the absolute activity of IMB, which had been determined by a separate measurement using an independent analytical technique. Figure 5 shows a calibration for the cephalosporin C transformation catalyzed by D-amino acid oxidase. The activity of the IMB was determined by the reaction rate measurement in a stirred-tank batch reactor. The reaction rate was determined as the initial rate of consumption of cephalosporin C monitored by HPLC analysis. The thermometric response was measured for each IMB packed in the FMC column, and plotted against the corresponding reaction rate. From the calibration results shown in Fig. 5 it can be concluded, independently of the type of immobilized biocatalyst, that the data fall to the same line and that there is a linear correlation between the heat response and the activity of the catalyst packed in the column. The transformation parameter a was determined from... 

This approach was used in the study of the properties of D-amino acid oxidase isolated or fixed in cells of Trigonopsis variabilis and entrapped in calcium pectate or polyacrylamide gel [28]. The approach of a differential reactor (low enzyme activity in the packed bed) was applied. The experimental thermometric data, ATr, were transformed to reaction rates, vobs, according to Eq. (21), whereas parameter a was determined by the calibration shown in Fig. 5. The data were described by the equation... 

Equation (1-4) is used for the mercury or alcohol thermometer, as well as for gas thermometers containing or He. It is found experimentally that the niimerical value of the temperature, except the values at the ice and steam points which are fixed, depends upon the particular system and thermometric property employed. Because there is less variation among gas thermometers, a gas is usually chosen as the standard thermometric substance. 

Temperature-Sensing System. Temperature sensing is the heart of the thermometric titration technique. The principal temperature-sensors used are thermistors. A thermistor is a temperature-sensitive semiconductor whose resistance obeys the equation... 

Thermometric titration depends on measuring the heat generated during a chemical reaction therefore it is another calorimetric technique. Usually the reactions take place at room temperature under conditions such that no heat enters or leaves the titration cell except that brought in by introduction of the titrant. In this procedure a titrant of known concentration is added to a known volume of sample. The titration reaction follows the generalized chemical equation... 

When the time constants r and r" and T(t) are known, it is possible to determine the T (t) and T"(t) values consecutively, and thus P(t). The numerical differential correction method has also been applied to reproduce the thermokinetics in these calorimetric systems, in which time constant vary in time [258-264], such as the TAM 2977 titration microcalorimeter produced by Thermometric. These works extended the applications of the inverse filter method to linear systems with variable coefficients. In many cases [258-262], as in the multidomains method, as a basis of consideration the mathematical models used were particular forms of the general heat balance equation. 

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