Approximations for the generalized temperature integral: a method based on quadrature rules

  • Jorge M. V. Capela
  • Marisa V. Capela
  • Clóvis A. Ribeiro
Article
First Online:

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.

Keywords

Non-isothermal kinetics Generalized temperature integral Gaussian quadrature 
This is a preview of subscription content, log in to check access.

References

  1. 1.
    Brown ME. Introduction to thermal analysis: techniques and applications. London: Chapman &Hall; 1995.Google Scholar
  2. 2.
    Criado JM, Pérez-Maqueda LA. In: Sϕrensen OT, Rouquerol J, editors. Sample controlled thermal analysis-origin, goals, multiple forms, applications and future. Dordrecht: Kluwer; 2003.Google Scholar
  3. 3.
    Criado JM, Pérez-Maqueda LA, Sánchez–Jiménez PE. Dependence of the preexponential factor on temperature: errors in the activation energies calculated by assuming that A is constant. J Therm Anal Calorim. 2005;82:671–5.CrossRefGoogle Scholar
  4. 4.
    Vyazovkin S, Dollimore D. Linear and nonlinear procedures in isoconversional computations of the activation energy of nonisothermal reactions in solids. J Chem Inf Comput Sci. 1996;36:42–5.Google Scholar
  5. 5.
    Galwey AK, Brown ME. Thermal decomposition of ionic solids. Amsterdam: Elsevier; 1997.Google Scholar
  6. 6.
    Cai JM, Liu RH. New approximation for the general temperature integral. J Therm Anal Calorim. 2007;90:469–74.CrossRefGoogle Scholar
  7. 7.
    Cai J, Liu R. Dependence of the frequency factor on the temperature: a new integral method of nonisothermal kinetic analysis. J Math Chem. 2008;43:637–46.CrossRefGoogle Scholar
  8. 8.
    Singh SD, Devi WG, Singh AKM, Bhattacharya M, Mazumdar PS. Calculation of the Integral ∫T0T′mexp(–E/RT′)T′. J Therm Anal Calorim. 2000;61:1013–8.CrossRefGoogle Scholar
  9. 9.
    Gartia RK, Singh SD, Singh TJ, Mazumdar PS. Evaluation of temperature integral for temperature dependent frequency factors. J Therm Anal Calorim. 1994;42:1001–5.CrossRefGoogle Scholar
  10. 10.
    Wanjun T, Yuwen L, Xil Y, Zhiyong W, Cunxin W. Approximate formulae for calculation of the integral òT 0Tmexp(−E/RT)dT. J Therm Anal Calorim. 2005;81:347–9.CrossRefGoogle Scholar
  11. 11.
    Chihara TS. An introduction to orthogonal polynomials, mathematics and its applications series. New York: Gordon and Brach; 1978.Google Scholar
  12. 12.
    Capela JMV, Capela MV, Ribeiro CA. Rational approximations of the Arrhenius integral using Jacobi fractions and gaussian quadrature. J Math Chem. 2009;45:769–75.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2009

Authors and Affiliations

  • Jorge M. V. Capela
    • 1
  • Marisa V. Capela
    • 1
  • Clóvis A. Ribeiro
    • 1
  1. 1.Instituto de QuímicaUniversidade Estadual PaulistaAraraquaraBrazil

Personalised recommendations