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

Regardless of the value of m, equation (13) can be expressed in the form:
Q(A) = k t (14)
where the expression Q(A) is defined as the quality function of the food.
The form of the quality function of the food for an apparent zero, 1st, 2nd and
mth order reaction can be derived from the eq.(14) and is shown in the following Table 1.
The half life time of the reaction i.e. the time for the concentration of the quality index A to
reduce to half its inital value is also included.
Table 1. Quality function form and half life times for different order reactions.
Apparent Reaction Quality Function Half Life time
Order Q(A)t t 1/2
0 A o - A t A o /(2k o )
1 ln ( A o /A t ) ln2/k 1
2 1/A o -1/A t 1/(k 2 A o )
m(m≠1)
1
m-1 (A1-m t -Ao 1-m ) 2 m-1 -1
k m (m-1) A1-m o
To determine the quality function one assumes different values of m (0, 1 or
other) and tries out a graphical or a least square linear fit to the corresponding equations
(Table 1) of the experimental data. If the experiment has been carried out to at least 50%
conversion and preferably 75%, it is usually easy to determine which reaction order and
equation gives the best fit, either graphically or by using statistical goodness of fit criteria.
The coefficient of determination (R 2 ) of the linear regression is in most cases a sufficient
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