Search Results

You are looking at 11 - 20 of 71 items for :

  • "temperature integral" x
  • All content x
Clear All

Abstract  

The generalized temperature integral I(m, x) appears in non-isothermal kinetic analysis when the frequency factor depends on the temperature. A procedure based on Gaussian quadrature to obtain analytical approximations for the integral I(m, x) was proposed. The results showed good agreement between the obtained approximation values and those obtained by numerical integration. Unless other approximations found in literature, the methodology presented in this paper can be easily generalized in order to obtain approximations with the maximum of accurate.

Restricted access

Non-isothermal kinetics in solids

The precision of some integral methods for the determination of the activation energy without neglecting the temperature integral at the starting temperature

Journal of Thermal Analysis and Calorimetry
Authors: J. Cai and R. Liu

Abstract  

The integral methods, which are obtained from the various approximations for the temperature integral, have been extensively used in the non-isothermal kinetic analysis. In order to obtain the precision of the integral methods for the determination of the activation energy, several authors have calculated the relative errors of the activation energy obtained from the integral methods. However, in their calculations, the temperature integral at the starting temperature was neglected. In this work, we have performed a systematic analysis of the precision of the activation energy calculated by the integral methods without doing any simplifications. The results have shown that the relative error involved in the activation energy determined from the integral methods depends on two dimensionless quantities: the normalized temperature θ=T/T 0, and the dimensionless activation energy x 0=E/RT 0 (where E is the activation energy, T is the temperature, T 0 is the starting temperature, R is the gas constant).

Restricted access

Isoconversional analysis of solid state transformations

A critical review. Part I. Single step transformations with constant activation energy

Journal of Thermal Analysis and Calorimetry
Authors: J. Farjas and P. Roura

= constant is the heating rate. Upon integration over the variables α and T , one can easily obtain the evolution of α , 4 where is the temperature integral [ 10 ] (in Appendix 1 , we provide some numerical and analytical recipes to evaluate p ( x

Restricted access

A simple procedure to obtain the derivative of the temperature integral with respect to the activation energy is presented.

Restricted access

Integrating Eq. 2 gives, 3 where p ( x ) is the famous temperature integral, which has no analytical solution [ 11 ]. In the classic integral isoconversional methods, such as Ozawa–Flynn–Wall method (OFW) [ 12 , 13 ], the approximations of p ( x ) [ 14

Restricted access

Use of the logistic rule is proposed for programmed heating in thermal analysis. An algorithm is presented for solving the temperature integral of non-isothermal kinetics.

Restricted access