Rational approximations of the integral of the Arrhenius function
01 Jun 1977-Journal of Thermal Analysis and Calorimetry (Akadémiai Kiadó, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic Publishers B.V.)-Vol. 11, Iss: 3, pp 445-447
TL;DR: Rational approximations have been derived for the integral of the Arrhenius function dT which is important in the kinetic analysis of thermogravimetric data and is found to be equivalent to the Gorbachev approximation.
Abstract: Rational approximations have been derived for the integral of the Arrhenius function
$$\int\limits_0^T {\exp ( - E/RT)}$$
dT which is important in the kinetic analysis of thermogravimetric data. The first degree rational approximation is found to be equivalent to the Gorbachev approximation, i.e., RT2
exp (−E/RT)/(E+2RT). The second degree rational approximation is more accurate than the Zsako empirical approximation when E/RT 5. The third and higher degree rational approximations are found to be more accurate than any other previous approximation.
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TL;DR: In this article, a thermocouple is used to measure the sample temperature in a Stanton HT-D thermobalance, the bead of which is positioned in or near the sample, depending on crucible design.
Abstract: THE use of thermogravimetric data to evaluate kinetic parameters of solid-state reactions involving weight loss (or gain) has been investigated by a number of workers1–4. Freeman and Carroll2 have stated some of the advantages of this method over conventional isothermal studies. To these reasons may be added the advantage of using one single sample for investigation. However, the importance of procedural details, such as crucible geometry, heating rate, pre-history of sample, and particle size, on the parameters has yet to be fully investigated. It is also necessary to ensure accurate temperature measurement, both for precision and also to detect any departure from a linear heating rate due to endo- or exo-thermic reactions. (The effect of these may be largely eliminated by the use of small samples.) In our present work (using a Stanton HT–D thermobalance) the sample temperature is measured directly by means of a thermocouple the bead of which is positioned in or near the sample, depending on crucible design, the wires of which run down a twin-bore rise rod. The connexion between the end of the thermocouple wires on the balance arm and the terminal block is made by 0.001 in. platinum and platinum/rhodium wires5. It has been shown that these wires do not affect the performance of the balance but act merely as a subsidiary damping. From the terminal block compensated cable leads to the cold junction and a potentiometric arrangement for direct measurement of the thermocouple output.
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01 Jan 1975
576 citations
"Rational approximations of the inte..." refers background or methods in this paper
...Rational approximations for f(x) can be derived knowing Eq. (2) and thus simply using the exponential integral rational approximation already given by Luke [ 6 ]....
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...The rational approximations f~(x) are given in Table 1. Higher degree approximations may be found by consulting Luke [ 6 ]....
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...Most often, rational approximations are derived from the power series expansion of the function, such as the methods given by Luke [ 6 ]....
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