New Approximate Formula for the Arrhenius Temperature Integral by Using Incomplete Gamma Functions

A new analytical formula for the Arrhenius integral has been proposed by using incomplete gamma functions, which is simple, accurate and reliable. The proposed formula has compared with several published the Arrhenius integral approaches, and is in agreement with the other approaches. Compared with the other approximate formulas proposed in the literature, our proposed method gives more accurate values in the precision of the activation energy as a function of x and temperature.

Keywords:

Arrhenius integral, Kinetics reaction Non-isothermal kinetic, Incomplete gamma function,

PDF

___

Referans1 M.E. Brown, Introduction to Thermal Analysis: Techniques and Applications, second ed., Kluwer Academic Publishers, Boston, 2001.
Referans2 W.W. Wendlandt in Thermal Methods of Analysis, 2nd Edition, John Wiley & Sons, New York, 1974.
Referans3 J. Cai, F. He, W. Yi and F. Yao, Chemical Engineering Journal 124 (2006) 15
Referans4 J. Cai, F. Yao, W. Yi and F. He, AIChE Journal 2006, 52 (4), 1554
Referans5 G.R. Heal, Thermochimica Acta 340-341 (1999) 69.
Referans6 D.W. Van Krevelen, C. Va Heerden and F.J. Huntjens, Fuel, 30 (1951) 253
Referans7 C.D. Doyle, Journal of Applied Polymer Science, 6 (1962) 639.
Referans8 C. D. Doyle, Anal Chem 1961, 33, 77.
Referans9 C. D. Doyle, J Appl Polym Sci 1961, 5, 285–292.
Referans10 C. D. Doyle, Nature 1965, 207, 290.
Referans11 A.W. Coats, J.P. Redfern, Nature 1964, 201, 68.
Referans12 A.W. Coats, J.P. Redfern, J Polym Sci, Part B: Polym Lett 1965, 3, 917.
Referans13 H.H. Horowitz, G. Metzger, Anal Chem 1963, 35, 1464–1468.
Referans14 J.R. MacCallum, J. Tanner, Eur Polym J 1970, 6, 1033–1039.
Referans15 J.R. MacCallum, J. Tanner, Eur Polym J 1970, 6, 907–917.
Referans16 G. Gyulai, E.J. Greenhow, Thermochimica Acta 1973, 6, 239–244.
Referans17 G. Gyulai, E.J. Greenhow, J Thermal Anal 1974, 6, 279–291.
Referans18 J.M.V. Capela, M.V. Capela, C.A. Ribeiro, J Math Chem 2009, 45, 769-775
Referans19 I.S. Gradshteyn and I.M. Ryzhik (1980). Tables of Integrals, Series and Products. Academic Press, New York.
Referans20 F. H. Deindoerfer and A. E. Humphrey, Applied Microbiology 1959, 7(4), 256–264