Arrhenius regression analysis linear

The large deviation between the estimated rate constants for a given temperature extrapolated from classical (Fig. 35) and modified Arrhenius regression analysis (Fig. 37) and the experimental rate constants determined at the actual temperature is due to the linear regression analysis method used. That is, the values of the logarithms of the rate constants do not reflect directly the errors in the experimental data. As Bentley pointed out,317 when the error term e is added to the logarithm of k in accordance with Eq. (2.76), in the linear... 

The activation energy differences of My as well as of and M, and k /kp and kt/kp. were calculated from Arrhenius and Mayo plots, respectively, by linear regression analysis using a computer. Hie AEjjw values given in kcal/mole can be converted to kJ/mole by multiplying with 4.18. 

Comparisons made below refer to kinetic data obtained for processes proceeding under similar conditions. All available values of (log A, E) within each group of related reactions were included in the linear regression analysis (Appendix II) and the compensation line was calculated using these formulas. Unless otherwise stated, the units of A are always molecules m-2 sec-1 at 1 Torr pressure of reactants and those of E are kJ mole-1. The compilation of Arrhenius parameters referred to identical reaction conditions is not always easy (or, indeed, possible in some instances) and it may be necessary to recalculate data from literature sources using an extrapolation. Not all details of the necessary corrections are recorded below, but such estimations were always minimized to preserve the objectivity of the conclusions reached. 

The Arrhenius equation did not describe very well the influence of temperature on viscosity data of concentrated apple and grape juices in the range 60-68 °Brix (Rao et al., 1984, 1986). From non-linear regression analysis, it was determined that the empirical Fulcher equation (see Ferry, 1980 p. 289, Soesanto and Williams, 1981) described the viscosity versus temperature data on those juice samples better than the Arrhenius model (Rao et al., 1986) ... 

Figure 38. Linear Arrhenius regression by weighted least-squares analysis (a) and least-squares analysis (b). y -axis (1) logarithmic scale, (2) arithmetical scale. (Reproduced from Ref. 317 with permission.)...

Our previous MNR Arrhenius parameters have been revised based on weighted linear regression analysis. The present temperature corrections have been based on the new results, which have been included in Appendix A. 

Creep - The creep model used in CARES combines the classical Norton isothermal power law with a thermal process of constant activation energy showing the Arrhenius type of temperature dependence. Material creep data is determined by a log linear regression analysis of specimen steady state creep data determined at a variety of temperatures and stress levels. Similar to the oxidation analysis, data is examined by CARES to determine if it contains outliers. Any outliers are deleted prior to the final determination of the three material constants. 

Degradation rate constants were obtained by linear regression least squares analysis of plots of log % EDB remaining vs time. Pseudo-first order rate constants were used to generate Arrhenius plots (log rate constant vs 1/T °K) to estimate activation energies (E ) and to make extrapolated estimates of rate constants and half-life values at ambient temperature. 

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