New approximate formulae for the generalized temperature integral

Abstract

The generalized temperature integral $\int\limits_0^T {T^m } \exp ( - E/RT)dT$ frequently occurs in non-isothermal kinetic analysis. Here E is the activation energy, R the universal gas constant and T the absolute temperature. The exponent m arises from the temperature dependence of the pre-exponential factor. This paper has proposed two new approximate formulae for the generalized temperature integral, which are in the following forms:

$$ \begin{gathered} h_m (x) = \frac{x} {{(1.00141 + 0.00060m)x + (1.89376 + 0.95276m)}} \hfill \\ h_m (x) = \frac{{x + (0.74981 - 0.06396m)}} {{(1.00017 + 0.00013m)x + (2.73166 + 0.92246m)}} \hfill \\ \end{gathered} $$

where h _m(x) is the equivalent form of the generalized temperature integral. For commonly used values of m in kinetic analysis, the deviations of the new approximations from the numerical values of the integral are within 0.2 and 0.03%, respectively. In contrast to other approximations, both the present approaches are simple, accurate and can be used easily in kinetic analysis.