A mathematical method in which the time-temperature data are used to measure changes I in lethality during heating and cooling. By using standard time intervals the lethal value: is computed in stages and the cumulative L value for the process is found without the need for graphical representation of the heating and cooling curves.
The Fo value for the process is calculated by summing all the L values and multiplying this value by the standard time interval between readings.
The trapezoidal method also allows simple calculation of the contribution to total process lethality of the heating and cooling portions of the process.
In Table 2 are shown L values and in Table 3 is shown a worked example in which temperature was recorded at 5 minute intervals for a process of 60 minutes at 121.1 °C.
To calculate Fo for the process: Summing the L values gives 2.925 which when multiplied by 5 (the time interval between readings) gives an Fo value of 14.6 min.
To calculate Fo for the heating phase: The sum of L values at time 25 and 60 min (0 and 0.776) is divided by 2 and this value (0.388) is added to the sum of L values from time 30 to 55 min. This gives 1.730 which when multiplied by 5 yields on Fo of 8.6 min for the process lethality at the stage when the steam was turned off.
The Improved General Method which relies on a temperature-time plot. for the entire process is the most accurate of all methods for calculating Fo value and for this reason is frequently quoted as the "reference method". Like the Trapezoidal Method there are no assumptions made regarding product heating and cooling characteristics, however the benefits of accuracy have to be balanced against the lack of versatility. Data from one set of trials cannot easily be used to calculate Fo values when product temperature and/or retort temperature are (is) altered. This means that once process conditions are altered new temperature-time data must be collected under the new experimental conditions.
Table 2. Values of L for temperature ranging
from 90 ºC to 130.9 ºC in 0.1 ºC intervals
from 90 ºC to 130.9 ºC in 0.1 ºC intervals
oC | 0.0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 |
90 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
91 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
92 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.002 |
93 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 |
94 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 |
95 | 0.002 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 |
96 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.004 | 0.004 | 0.004 | 0.004 |
97 | 0.004 | 0.004 | 0.004 | 0.004 | 0.004 | 0.004 | 0.004 | 0.005 | 0.005 | 0.005 |
98 | .005 | 0.005 | 0.005 | .005 | 0.005 | 0.005 | 0.006 | 0.006 | 0.006 | 0.006 |
99 | 0.006 | 0.006 | 0.006 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.007 | 0.008 |
100 | 0.008 | 0.008 | 0.008 | 0.008 | 0.009 | 0.009 | 0.009 | 0.009 | 0.009 | 0.010 |
101 | 0.010 | 0.010 | 0.010 | 0.010 | 0.011 | 0.011 | 0.011 | 0.011 | 0.012 | 0.012 |
102 | 0.012 | 0.013 | 0.013 | 0.013 | 0.013 | 0.014 | 0.014 | 0.014 | 0.015 | 0.015 |
103 | 0.015 | 0.016 | 0.016 | 0.017 | 0.017 | 0.017 | 0.018 | 0.018 | 0.019 | 0.019 |
104 | 0.019 | 0.020 | 0.020 | 0.021 | 0.021 | 0.022 | 0.022 | 0.023 | 0.023 | 0.024 |
105 | 0.025 | 0.025 | 0.026 | 0.026 | 0.027 | 0.028 | 0.028 | 0.029 | 0.030 | 0.030 |
106 | 0.031 | 0.032 | 0.032 | 0.033 | 0.034 | 0.035 | 0.035 | 0.036 | 0.037 | 0.038 |
107 | 0.039 | 0.040 | 0.041 | 0.042 | 0.043 | 0.044 | 0.045 | 0.046 | 0.047 | 0.048 |
108 | 0.049 | 0.050 | 0.051 | 0.052 | 0.054 | 0.055 | 0.056 | 0.058 | 0.059 | 0.060 |
109 | 0.062 | 0.063 | 0.065 | 0.066 | 0.068 | 0.069 | 0.071 | 0.072 | 0.074 | 0.076 |
110 | 0.078 | 0.079 | 0.081 | 0.083 | 0.085 | 0.087 | 0.089 | 0.091 | 0.093 | 0.095 |
111 | 0.098 | 0.100 | 0.102 | 0.105 | 0.107 | 0.110 | 0.112 | 0.115 | 0.117 | 0.120 |
112 | 0.123 | 0.126 | 0.129 | 0.132 | 0.135 | 0.138 | 0.141 | 0.145 | 0.148 | 0.151 |
113 | 0.155 | 0.158 | 0.162 | 0.166 | 0.170 | 0.174 | 0.178 | 0.182 | 0.186 | 0.191 |
114 | 0.195 | 0.200 | 0.204 | 0.209 | 0.214 | 0.219 | 0.224 | 0.229 | 0.234 | 0.240 |
115 | 0.245 | 0.251 | 0.257 | 0.263 | 0.269 | 0.275 | 0.282 | 0.288 | 0.295 | 0.302 |
116 | 0.309 | 0.316 | 0.324 | 0.331 | 0.339 | 0.347 | 0.355 | 0.363 | 0.372 | 0.380 |
117 | 0.389 | 0.398 | 0.407 | 0.417 | 0.427 | 0.437 | 0.447 | 0.457 | 0.468 | 0.479 |
118 | 0.490 | 0.501 | 0.513 | 0.525 | 0.537 | 0.550 | 0.562 | 0.575 | 0.589 | 0.603 |
119 | 0.617 | 0.631 | 0.646 | 0.661 | 0.676 | 0.692 | 0.708 | 0.724 | 0.741 | 0.759 |
120 | 0.776 | 0.794 | 0.813 | 0.832 | 0.851 | 0.871 | 0.891 | 0.912 | 0.933 | 0.955 |
121 | 0.977 | 1.000 | 1.023 | 1.047 | 1.072 | 1.096 | 1.122 | 1.148 | 1.175 | 1.202 |
122 | 1.230 | 1.259 | 1.288 | 1.318 | 1.349 | 1.380 | 1.413 | 1.445 | 1.479 | 1.514 |
123 | 1.549 | 1.585 | 1.622 | 1.660 | 1.698 | 1.738 | 1.778 | 1.820 | 1.862 | 1.905 |
124 | 1.950 | 1.995 | 2.042 | 2.089 | 2.138 | 2.188 | 2.239 | 2.291 | 2.344 | 2.399 |
125 | 2.455 | 2.512 | 2.570 | 2.630 | 2.692 | 2.754 | 2.818 | 2.884 | 2.951 | 3.020 |
126 | 3.090 | 3.162 | 3.236 | 3.311 | 3.388 | 3.467 | 3.548 | 3.631 | 3.715 | 3.802 |
127 | 3.890 | 3.981 | 4.074 | 4.169 | 4.266 | 4.365 | 4.467 | 4.571 | 4.677 | 4.786 |
128 | 4.898 | 5.012 | 5.129 | 5.248 | 5.370 | 5.495 | 5.623 | 5.754 | 5.888 | 6.026 |
129 | 6.166 | 6.310 | 6.457 | 6.607 | 6.761 | 6.918 | 7.079 | 7.244 | 7.413 | 7.586 |
130 | 7.762 | 7.943 | 8.128 | 8.318 | 8.511 | 8.710 | 8.913 | 9.120 | 9.333 | 9.550 |
Note:
z = 10 ºC T = product temperature |
Table 3. Trapezoidal method for integration of
lethal rate data to calculate Fo value
Time (min) | Temperatur (oC) | L | L/t | Fo (min) |
0 | 24 | 0 | ||
5 | 24.5 | 0 | ||
10 | 34 | 0 | ||
15 | 54 | 0 | ||
20 | 72.5 | 0 | ||
25 | 87 | 0 | ||
30 | 98 | 0.005 | ||
35 | 105 | 0.025 | ||
40 | 110.5 | 0.087 | ||
45 | 114.5 | 0.219 | ||
50 | 117 | 0.389 | ||
55 | 119 | 0.617 | ||
60 | 120 | 0.776 | 1.730 | 8.6 |
* STEAM OFF | ||||
65 | 120 | 0.776 | ||
70 | 106 | 0.031 | ||
75 | 88 | 0 | 2.925 | 14.6 |
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