The accuracy and scope of application of previously reported approximations of the temperature integral were evaluated. The
exact solution was obtained independently by solving the temperature integral numerically be Simpson's rule, the trapezoidal
rule and the Gaussian rule.
Two new approximations have been proposed:
whereX=E/RT. The first equation gives higher accuracy, with a deviation of less than 1% and 0.1% from the exact solution forX≥7 andX≥10, respectively. The second equation has a wider scope of application, with a deviation of less than 1% forX≥4 and of less than 0.1% forX≥35.