Rational approximations of the integral of the Arrhenius function

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.