, Volume 11, Issue 3, pp 445-447

Rational approximations of the integral of the Arrhenius function

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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 Zsakó empirical approximation when E/RT < 1 and E/RT > 5. The third and higher degree rational approximations are found to be more accurate than any other previous approximation.

We wish to acknowledge Meyer Steinberg for his helpful discussion with respect to this communication.
This work was performed under the auspices of the United States Energy Research and Development Administration under Contract No. E(30-1)-16. By acceptance of this article, the publisher and/or recipient acknowledges the U. S. Government's right to retain a nonexclusive, royalty-free license in and to any copyright covering this paper.