Review and evaluation of the approximations to the temperature integral

The kinetics of processes involving solids may be determined from experiments under non-isothermal conditions. On analyzing data by integral methods, it is necessary to calculate the temperature integral, which does not have an analytical solution. Instead of performing the numerical integration, most of the researchers prefer to circumvent the problem by using approximate expressions, not always adequate. The widespread use of inaccurate approximations does not contribute to a coherent growth of scientific knowledge. In the present article, a critical review of the known approximations is carried out and a clear ranking is established. Moreover, the deviations of the calculated activation energies relatively to the numerical solution are discussed, and some recommendations are proposed. Namely, it is shown that a novel expression, previously presented in another form in the well known Handbook of Mathematical Functions, approximates very accurately the temperature integral and allows to obtain correct values of the activation energy. (C) 2007 American Institute of Chemical Engineers.