Authors: J. Cai 1 and R. Liu 1
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  • 1 Shanghai Jiao Tong University Biomass Energy Engineering Research Center, School of Agriculture and Biology 2678 Qixin Road Shanghai 201101 P. R. China
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A new approximation has been proposed for calculation of the general temperature integral
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\int\limits_0^T {T^m } e^{ - E/RT} dT$$ \end{document}
, which frequently occurs in the nonisothermal kinetic analysis with the dependence of the frequency factor on the temperature (A=A0Tm). It is in the following form:
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\int\limits_0^T {T^m } e^{ - E/RT} dT = \frac{{RT^{m + 2} }} {E}e^{ - E/RT} \frac{{0.99954E + (0.044967m + 0.58058)RT}} {{E + (0.94057m + 2.5400)RT}}$$ \end{document}
The accuracy of the newly proposed approximation is tested by numerical analyses. Compared with other existed approximations for the general temperature integral, the new approximation is significantly more accurate than other approximations.