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

The integral is calculated numerically (Nelson, 1983). The nonisothermal
approach requires very good temperature control and small experimental error in the
concentration measurements. Yoshioka et al. (1987) in a statistical evaluation showed that
a larger number of samples need to be measured to a higher reactant conversion than the
isothermal method. The nonisothermal approach is very sensitive to experimental error in
concentration measurements. Even at the precicion level of 2%, the one step isothermal
method with experiments at three temperatures gave better accuracy in the estimation of the
Arrhenius parameters than the nonisothermal method with a linearly increasing temperature
in the same range and for the same total number of data points. Another usually
overlooked factor is the nonuniform temperature within the samples due to the unsteady
state heat transfer occurring during the nonisothermal experiment (Labuza, 1984). The
nonisothermal method also does not allow for recognition of possible deviation of the
reaction from an Arrhenius behavior above or below a certain temperature that sometimes
occurs in foods.
Temperature dependence has been traditionally expressed in the food
industry and the food science and biochemistry literature as Q 10 the ratio of the reaction
rate constants at temperatures differing by 10°C or the change of shelf life θ s when the
food is stored at a temperature higher by 10°C . The majority of the earlier food literature
reports end-point data rather than complete kinetic modelling of quality loss. The Q 10
approach in essence introduces a temperature dependence equation of the form
k(T) = k o e bT or ln k = ln k o + bT (30)
which implies that if ln k is plotted vs. temperature (instead of 1/T of the Arrhenius
equation) a straight line is obtained. Equivalently, ln θ s can be plotted vs. temperature.
Such plots are often called shelf life plots, where b is the slope of the shelf life plot and k o
is the intercept. The shelf life plots are true straight lines only for narrow temperature
ranges of 10 to 20 °C (Labuza, 1982). For such a narrow interval, data from an Arrhenius
24