the handbook of food engineering practice crc press chapter 10 ...

In practice, since there is experimental error involved in the determination of the values of k,
calculations of E A from only two points will give a substantial error. The precision of
activation energy calculated from equation (21) is examined by Hills and Grieger-Block
(1980). Usually, the reaction rate is determined at three or more temperatures and k is
plotted vs. 1/T in a semilog graph or a linear regression fit to equation (20) is employed.
It should be pointed out that there is no explicit reference temperature for the
Arrhenius function as expressed in Eq. (19), 0 K, the temperature at which k would be
equal to k A , being implied as such. Alternatively to Eq. (19) it is often recommended that a
reference temperature is chosen corresponding to an average of the temperature range
characteristic of the described process. For most storage applications 300 K is such a
typical temperature, whereas for thermal processes 373.15 K (100.0 ° C) is usually the
choice. The modified Arrhenius equation would then be written as:
k = k ref exp (- E A
R [ 1 T - 1
T ref
] ) (23)
where k ref the rate constant at the reference temperature Tref. Respectively Eq. (20) is
modified to:
ln k = ln k ref - E A
R [ 1 T - 1
T ref
] (24)
The above transformation is critical for enhanced stability during numerical
integration and parameter estimation. Aditionally, by using a reference reaction rate
constant, besides giving the constant a relevant physical meaning, one signals the
applicability of the equation within a finite range of temperatures enclosing the reference
temperature and corresponding to the range of interest. Indeed, as it will be discussed
further in this section the Arrhenius equation may not be uniformly applicable below or
above certain temperatures, usually connected with transition phenomena.
When applying regression techniques statistical analysis is again used to
determine the 95% confidence limits of the Arrhenius parameters. If only three k values
20