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Modified Lethal Rate Paper Technique for Thermal Process Evaluation1
Research Note
Modified Lethal Rate Paper Technique for Thermal Process Evaluation: Kan-ichi Hayakawa Food Science Department Rutgers University New Brunswick, N.l. 08903
Introduction Sterilizing values have been widely used for evaluating thermal processes of food. These values al'e estimated by integrating lethal rates with respect tC' processing times. There are several published procedures available for this estimation (Ball et al., 1957; Hayakawa, 1968, 1970; Pflug, 1968; Stumbo, ] 966). One of the simplest procedures is the method which utilizes lethal rate paper (Schultz et al., 1940). However, one disadvantage of this method is that different types of lethal rate paper are required when different z values are used for the calculations of sterilizing values. In the present investigation, a new method is developed in order to overcome this disadvantage.
Description of Method The preparation of lethal rate paper is described in details by Schultz et al. (1940). The Abscissae and ordinate of this paper are scaled respectively with processing time and lethal rate values. However, temperature which corresponds to lethal rate values of a specified z value, is marked on the ordinate instead of lethal rate values (Figure 1). A lethal rate (L) is defined by the following Equation 1:
L
::
10(T-250)/z
For convenience of discussion, we assume that Zb represents a fixed z value, for which lethal rate paper is prepared, and that Za represents anyone z value to be used for the calculation of sterilizing values. From Equation 1, we have Equation 2 for calculating lethal rate values when z Za:
=
L
::
1 0 ( T - 2 50) / Za
Tm :: (1 / Ks ) (T
::
10
where
K
( ( T - 250)/ Ks ) / zb
s
::
z
a
/ Z
b
(2)
(3)
+
250 (Ks -1) )
(4)
Lethal rate paper for a fixed z value, za, may be used for estimating sterilizing values for any z values when the above Equation 4 is used. The modification of food temperatures by this equation requires con· siderable arithmetic calculations. Therefore, tables of modified temperature are prepared by assuming that Zb = 18 FO. This specific z value is assumed since lethal rate paper for this z value has been frequently prepared. Table 1 is one of the tables prep· ared. These tables and lethal rate paper for a z value of 18 FO are used for estimating sterilizing values of various heat processes. For this estimation several z values are used. Time-temperature data for the heat processes are plotted on the lethal rate paper and lethal rate curves are obtained by connecting the data points plotted. Values are determined by measuring areas, which are enclosed with these curves and a time axis. For this measurement, a planimeter is used. Each of the sterilizing values estimated are compared with respective sterilizing values calculated by applying Simpson's formula to the time-temperature data, As expected, there are no statistically significant differences between values estimated by the two different methods. Figure 1 shows two sample lethal rate curves obtained from temperature data shown in Table 2 by using Table 1. The sterilizing values (Fp) which were determined by measuring areas under these curves are) Fp = 8.44 15 FO and Fp 14.27 min. when z min. when z = 26 FO. Sterilizing values, which were calculated by applying Simpson's rule to the same temperature data, are: Fp 8.36 min. when z 15 FO and Fp = 14.15 min. when z = 26 FO. It will be important to state that the proposed technique requires additional steps for finding modified temperatures although they do not considerably lengthen time required for plotting lethal rate curves. The technique will be useful when one needs to calculate approximately five or less sterilizing values for each different z value since it is not required to
=
1 A pap~r of the Journal Series, New Jersey Agricultural Experiment Station, Rutgers, The State University of New Jersey, Food Science Department, New Brunswick, N.J. 08903.
295
A lethal rate value estimated by Equation 2 must be identical to another lethal rate value of a modified temperature, 'I'm, which is applicable when z = Zb. Therefore, we have:
=
=
=
J. Inst. Can. Sci. Technol. Aliment. Vol. 6, No 4, 1973
Table 1.
An abridged table of modified temperatures. Modified Temperatures ("F) for the following z values (OF)
160.00 162.00 164.00 166.00 168.00 170.00 172.00 174.00 176.00 178.00 180.00 182.00 184.00 186.00 188.00 190.00 192.00 194.00 196.00 198.00 200.00 202.00 204.00 206.00 208.00 210.00 212.00 214.00 216.00 218.00 220.00 222.00 224.00 226.00 228.00 230.00 232.00 234.00 236.00 238.00 240.00 242.00 244.00 246.00 248.00 250.00
10.0
12.0
14.0
16.0
18.0
20.0
22.0
24.0
88.00 91.60 95.20 98.80 102.40 106.00 109.60 113.20 116.80 120.40 124.00 127.60 131.20 134.80 138.40 142.00 145.60 149.20 152.80 156.40 160.00 163.60 167.20 170.80 174.40 178.00 181.60 185.20 188.80 192.40 196.00 199.60 203.20 206.80 210.40 214.00 217.60 221.20 224.80 228.40 232.00 235.60 239.20 242.80 246.40 250.00
115.00 118.00 121.00 124.00 127.00 130.00 133.00 136.00 139.00 142.00 145.00 148.00 151.00 154.00 157.00 160.00 163.00 166.00 169.00 172.00 175.00 178.00 181.00 184.00 187.00 190.00 193.00 196.00 199.00 202.00 205.00 208.00 211.00 214.00 217.00 220.00 223.00 226.00 229.00 232.00 235.00 238.00 241.00 244.00 247.00 250.00
134.29 136.86 139.43 142.00 144.57 147.14 149.71 152.29 154.86 157.43 160.00 162.57 163.14 167.71 170.29 172.86 175.43 178.00 180.57 183.14 185.71 188.29 190.86 193.43 196.00 198.57 201.14 203.71 206.29 208.86 211.43 214.00 216.57 219.14 221.71 224.29 226.86 229.43 232.00 234.57 237.14 239.71 242.29 244.86 247.43 250.00
148.75 151.00 153.25 155.50 157.75 160.00 162.25 164.50 166.75 169.00 171.25 173.50 175.75 178.00 180.25 182.50 184.75 187.00 189.25 191.50 lS3.75 196.00 198.25 200.50 202.75 205.00 207.25 209.50 211.75 214.00 216.25 218.50 220.75 223.00 225.25 227.50 229.75 232.00 234.25 236.50 238.75 241.00 243.25 245.50 247.75 250.00
160.00 162.00 164.00 166.00 168.00 170.00 172.00 174.00 176.00 178.00 180.00 182.00 184.00 186.00 188.00 190.00 192.00 194.00 196.00 198.00 200.00 202.00 204.00 206.00 208.00 210.00 212.00 214.00 216.00 218.00 220.00 222.00 224.00 226.00 228.00 230.00 232.00 234.00 236.00 238.00 240.00 242.00 244.00 246.00 248.00 250.00
169.00 170.80 172.60 174.40 176.20 178.00 179.80 181.60 183.40 185.20 187.00 188.80 190.60 192.40 194.20 196.00 197.80 199.60 201.40 203.20 205.00 206.80 208.60 210.40 212.20 214.00 215.80 217.60 219.40 221.20 223.00 224.80 226.60 228.40 230.20 232.00 233.80 235.60 237.40 239.20 241.00 242.80 244.60 246.40 248.20 250.00
176.36 178.00 179.64 181.27 182.91 184.55 186.18 187.82 189.45 191.09 192.73 194.36 196.00 197.64 199.27 200.91 202.55 204.18 205.82 207.45 209.09 210.73 212.36 214.00 215.64 217.27 218.91 220.55 222.18 223.82 225.45 227.09 228.73 230.36 232.00 233.64 235.27 236.91 238.55 240.18 241.82 243.45 245.09 246.73 248.36 250.00
182.50 184.00 185.50 187.00 188.50 190.00 191.50 193.00 194.50 196.00 197.50 199.00 200.50 202.00 203.50 205.00 206.50 208.00 209.50 211.00 212.50 214.00 215.50 217.00 218.50 220.00 221.50 223.00 224.50 226.00 227.50 229.00 230.50 232.00 233.50 235.00 236.50 238.00 239.50 241.00 242.50 244.00 245.50 247.00 248.50 250.00
prepare lethal rate paper for each of different z values. 'Vhen one needs to calculate approximately six or more sterilizing values for one z value, it would be better to prepare lethal rate paper for this z value without applying the proposed procedure. Sterilizing values may be estimated through plotting lethal rate values against processing time without using lethal rate paper. For this plotting, published lethal rate tables (Ball et aI, 1957 and Stumbo 1965) may be used. Time required for estimat· ing a sterilizing value through the use of a lethal rate table is approximately identical to that required by the proposed technique. It will be important to observe that the table of modified temperature shows more clearly the influence of temperature and a z value on lethal rate since the range of variations in the modified temperatures is greatly wider than that of lethal rate values.
Can. Inst. Food Se!. Teehnol. J. Vol. 6, No. 4, 1973
26.0 187.69 189.08 190.46 191.85 193.23 194.62 196.00 197.38 198.77 200.15 201.54 202.92 204.31 205.69 207.08 208.46 209.85 211.23 212.62 214.00 215.38 216.77 218.15 219.54 220.92 222.31 223.69 225.08 226.46 227.85 229.23 230.62 232.00 233.38 234.77 236.15 237.54 238.92 240.31 241.69 243.08 244.46 245.85 247.23 248.62 250.00
28.0
30.0
192.14 193.43 194.71 196.00 197.29 198.57 199.86 201.14 202.43 203.71 205.00 206.29 207.57 208.86 210.14 211.43 212.71 214.00 215.29 216.57 217.86 219.14 220A3 221.71 223.00 224.29 225.57 226.86 228.14 229.43 230.71 232.00 233.29 234.57 235.86 237.14 238.43 239.71 241.00 242.29 243.57 244.86 246.14 247.43 248.71 250.00
196.00 197.20 198.40 199.60 200.80 202.00 203.20 204.40 205.60 206.80 208.00 209.20 210.40 211.60 212.80 214.00 215.20 216.40 217.60 218.80 220.00 221.20 222.40 223.60 224.80 226.00 227.20 228.40 229.60 230.80 232.00 233.20 234.40 235.60 236.80 238.00 239.20 240.40 241.60 242.80 244.00 245.20 246.40 247.60 248.80 250.00
Conclusion A modified lethal rate paper technique was developed f.or estimating sterilizing values. Through the use of this technique, lethal rate paper for a fixed z value, 18 F O, may be used for the estimation of sterilizing values for any other different z values.
Nomenclature Fp Ks
sterilizing value (min.)
=
Za/7.b
L Lethal I'ate, which is defined as Equation 1 T Temperature of food (OF) T m Modified temperature (OF) Slope index of thermal death time curve (FO) Any z value (F0) Fixed z value (PO)
2!)(i
25l
Table 2.
Time
Temperatures at the center of a 211 x 300 can of spinach puree, which were recorded during a heat process 1/. Temperature
o (Min.)
219
5 10 15 20 25 30 35 40 45
l.L
248
0 ~
W
er
::::::l f-
«
247
er
w L
w
f-
245
Time 50 (Min.) 55 60 65 70 75 80 85 90 95
Temperature 243.0 (OF) 245.3 247.0 233.0 207.0 174.0 147.0 124.0 108.0 95.0
-
11 The food was processed in a still retort. A holding temperature of the retort and temperature of cooling water were respectively equal to 250°F and 55°F.
0...
246
88.0 CF) 95.0 100.0 128.0 167.0 193.0 211.0 223.5 232.0 238.0
References Ball, C. Olin and Olson, F. C, W., 1957. "Sterilization in Food Technology", McGraw Hill Book Company, N.Y. Hayakawa, Kan-ichi, 1968. A procedure for calculating sterilizing value of a thermal process. Food TechnoI. 22: 905. Hayakawa, Kan-ichi, 1970. Experimental formulas for accurate estimation of food temperature and their application to thermal process evaluation, Food TechnoI. 24: 1407. Pflug, I. J. 1968. Evaluating the lethality of heat processes using a method of employing Hick's table. Food TechnoI. 22: 1153. Schultz, O. T, and Olson, F. C. W., 1940. Thermal processing of canned foods in tin containers. Ill. Recent improvements in the general method of thermal process calculations - A special coordinate paper and methods of converting initial and retort temperatures. Food Res. 5: 399. Stumbo, C. R. 1965, "Thermobacteriology in Food Processing" Academic Press, Inc., N.Y.
240
Received February 28, 1973.
230 220
o Figure 1.
2D7
20
40
60
80
100
120
Lethal rate curves for time-temperature data shown in Table 2.
J. Inst. Can. Scl. TechnoI. Aliment. Vo!. 6, No 4, 1973
Modified Lethal Rate Paper Technique for Thermal Process Evaluation: Kan-ichi Hayakawa Food Science Department Rutgers University New Brunswick, N.l. 08903
Introduction Sterilizing values have been widely used for evaluating thermal processes of food. These values al'e estimated by integrating lethal rates with respect tC' processing times. There are several published procedures available for this estimation (Ball et al., 1957; Hayakawa, 1968, 1970; Pflug, 1968; Stumbo, ] 966). One of the simplest procedures is the method which utilizes lethal rate paper (Schultz et al., 1940). However, one disadvantage of this method is that different types of lethal rate paper are required when different z values are used for the calculations of sterilizing values. In the present investigation, a new method is developed in order to overcome this disadvantage.
Description of Method The preparation of lethal rate paper is described in details by Schultz et al. (1940). The Abscissae and ordinate of this paper are scaled respectively with processing time and lethal rate values. However, temperature which corresponds to lethal rate values of a specified z value, is marked on the ordinate instead of lethal rate values (Figure 1). A lethal rate (L) is defined by the following Equation 1:
L
::
10(T-250)/z
For convenience of discussion, we assume that Zb represents a fixed z value, for which lethal rate paper is prepared, and that Za represents anyone z value to be used for the calculation of sterilizing values. From Equation 1, we have Equation 2 for calculating lethal rate values when z Za:
=
L
::
1 0 ( T - 2 50) / Za
Tm :: (1 / Ks ) (T
::
10
where
K
( ( T - 250)/ Ks ) / zb
s
::
z
a
/ Z
b
(2)
(3)
+
250 (Ks -1) )
(4)
Lethal rate paper for a fixed z value, za, may be used for estimating sterilizing values for any z values when the above Equation 4 is used. The modification of food temperatures by this equation requires con· siderable arithmetic calculations. Therefore, tables of modified temperature are prepared by assuming that Zb = 18 FO. This specific z value is assumed since lethal rate paper for this z value has been frequently prepared. Table 1 is one of the tables prep· ared. These tables and lethal rate paper for a z value of 18 FO are used for estimating sterilizing values of various heat processes. For this estimation several z values are used. Time-temperature data for the heat processes are plotted on the lethal rate paper and lethal rate curves are obtained by connecting the data points plotted. Values are determined by measuring areas, which are enclosed with these curves and a time axis. For this measurement, a planimeter is used. Each of the sterilizing values estimated are compared with respective sterilizing values calculated by applying Simpson's formula to the time-temperature data, As expected, there are no statistically significant differences between values estimated by the two different methods. Figure 1 shows two sample lethal rate curves obtained from temperature data shown in Table 2 by using Table 1. The sterilizing values (Fp) which were determined by measuring areas under these curves are) Fp = 8.44 15 FO and Fp 14.27 min. when z min. when z = 26 FO. Sterilizing values, which were calculated by applying Simpson's rule to the same temperature data, are: Fp 8.36 min. when z 15 FO and Fp = 14.15 min. when z = 26 FO. It will be important to state that the proposed technique requires additional steps for finding modified temperatures although they do not considerably lengthen time required for plotting lethal rate curves. The technique will be useful when one needs to calculate approximately five or less sterilizing values for each different z value since it is not required to
=
1 A pap~r of the Journal Series, New Jersey Agricultural Experiment Station, Rutgers, The State University of New Jersey, Food Science Department, New Brunswick, N.J. 08903.
295
A lethal rate value estimated by Equation 2 must be identical to another lethal rate value of a modified temperature, 'I'm, which is applicable when z = Zb. Therefore, we have:
=
=
=
J. Inst. Can. Sci. Technol. Aliment. Vol. 6, No 4, 1973
Table 1.
An abridged table of modified temperatures. Modified Temperatures ("F) for the following z values (OF)
160.00 162.00 164.00 166.00 168.00 170.00 172.00 174.00 176.00 178.00 180.00 182.00 184.00 186.00 188.00 190.00 192.00 194.00 196.00 198.00 200.00 202.00 204.00 206.00 208.00 210.00 212.00 214.00 216.00 218.00 220.00 222.00 224.00 226.00 228.00 230.00 232.00 234.00 236.00 238.00 240.00 242.00 244.00 246.00 248.00 250.00
10.0
12.0
14.0
16.0
18.0
20.0
22.0
24.0
88.00 91.60 95.20 98.80 102.40 106.00 109.60 113.20 116.80 120.40 124.00 127.60 131.20 134.80 138.40 142.00 145.60 149.20 152.80 156.40 160.00 163.60 167.20 170.80 174.40 178.00 181.60 185.20 188.80 192.40 196.00 199.60 203.20 206.80 210.40 214.00 217.60 221.20 224.80 228.40 232.00 235.60 239.20 242.80 246.40 250.00
115.00 118.00 121.00 124.00 127.00 130.00 133.00 136.00 139.00 142.00 145.00 148.00 151.00 154.00 157.00 160.00 163.00 166.00 169.00 172.00 175.00 178.00 181.00 184.00 187.00 190.00 193.00 196.00 199.00 202.00 205.00 208.00 211.00 214.00 217.00 220.00 223.00 226.00 229.00 232.00 235.00 238.00 241.00 244.00 247.00 250.00
134.29 136.86 139.43 142.00 144.57 147.14 149.71 152.29 154.86 157.43 160.00 162.57 163.14 167.71 170.29 172.86 175.43 178.00 180.57 183.14 185.71 188.29 190.86 193.43 196.00 198.57 201.14 203.71 206.29 208.86 211.43 214.00 216.57 219.14 221.71 224.29 226.86 229.43 232.00 234.57 237.14 239.71 242.29 244.86 247.43 250.00
148.75 151.00 153.25 155.50 157.75 160.00 162.25 164.50 166.75 169.00 171.25 173.50 175.75 178.00 180.25 182.50 184.75 187.00 189.25 191.50 lS3.75 196.00 198.25 200.50 202.75 205.00 207.25 209.50 211.75 214.00 216.25 218.50 220.75 223.00 225.25 227.50 229.75 232.00 234.25 236.50 238.75 241.00 243.25 245.50 247.75 250.00
160.00 162.00 164.00 166.00 168.00 170.00 172.00 174.00 176.00 178.00 180.00 182.00 184.00 186.00 188.00 190.00 192.00 194.00 196.00 198.00 200.00 202.00 204.00 206.00 208.00 210.00 212.00 214.00 216.00 218.00 220.00 222.00 224.00 226.00 228.00 230.00 232.00 234.00 236.00 238.00 240.00 242.00 244.00 246.00 248.00 250.00
169.00 170.80 172.60 174.40 176.20 178.00 179.80 181.60 183.40 185.20 187.00 188.80 190.60 192.40 194.20 196.00 197.80 199.60 201.40 203.20 205.00 206.80 208.60 210.40 212.20 214.00 215.80 217.60 219.40 221.20 223.00 224.80 226.60 228.40 230.20 232.00 233.80 235.60 237.40 239.20 241.00 242.80 244.60 246.40 248.20 250.00
176.36 178.00 179.64 181.27 182.91 184.55 186.18 187.82 189.45 191.09 192.73 194.36 196.00 197.64 199.27 200.91 202.55 204.18 205.82 207.45 209.09 210.73 212.36 214.00 215.64 217.27 218.91 220.55 222.18 223.82 225.45 227.09 228.73 230.36 232.00 233.64 235.27 236.91 238.55 240.18 241.82 243.45 245.09 246.73 248.36 250.00
182.50 184.00 185.50 187.00 188.50 190.00 191.50 193.00 194.50 196.00 197.50 199.00 200.50 202.00 203.50 205.00 206.50 208.00 209.50 211.00 212.50 214.00 215.50 217.00 218.50 220.00 221.50 223.00 224.50 226.00 227.50 229.00 230.50 232.00 233.50 235.00 236.50 238.00 239.50 241.00 242.50 244.00 245.50 247.00 248.50 250.00
prepare lethal rate paper for each of different z values. 'Vhen one needs to calculate approximately six or more sterilizing values for one z value, it would be better to prepare lethal rate paper for this z value without applying the proposed procedure. Sterilizing values may be estimated through plotting lethal rate values against processing time without using lethal rate paper. For this plotting, published lethal rate tables (Ball et aI, 1957 and Stumbo 1965) may be used. Time required for estimat· ing a sterilizing value through the use of a lethal rate table is approximately identical to that required by the proposed technique. It will be important to observe that the table of modified temperature shows more clearly the influence of temperature and a z value on lethal rate since the range of variations in the modified temperatures is greatly wider than that of lethal rate values.
Can. Inst. Food Se!. Teehnol. J. Vol. 6, No. 4, 1973
26.0 187.69 189.08 190.46 191.85 193.23 194.62 196.00 197.38 198.77 200.15 201.54 202.92 204.31 205.69 207.08 208.46 209.85 211.23 212.62 214.00 215.38 216.77 218.15 219.54 220.92 222.31 223.69 225.08 226.46 227.85 229.23 230.62 232.00 233.38 234.77 236.15 237.54 238.92 240.31 241.69 243.08 244.46 245.85 247.23 248.62 250.00
28.0
30.0
192.14 193.43 194.71 196.00 197.29 198.57 199.86 201.14 202.43 203.71 205.00 206.29 207.57 208.86 210.14 211.43 212.71 214.00 215.29 216.57 217.86 219.14 220A3 221.71 223.00 224.29 225.57 226.86 228.14 229.43 230.71 232.00 233.29 234.57 235.86 237.14 238.43 239.71 241.00 242.29 243.57 244.86 246.14 247.43 248.71 250.00
196.00 197.20 198.40 199.60 200.80 202.00 203.20 204.40 205.60 206.80 208.00 209.20 210.40 211.60 212.80 214.00 215.20 216.40 217.60 218.80 220.00 221.20 222.40 223.60 224.80 226.00 227.20 228.40 229.60 230.80 232.00 233.20 234.40 235.60 236.80 238.00 239.20 240.40 241.60 242.80 244.00 245.20 246.40 247.60 248.80 250.00
Conclusion A modified lethal rate paper technique was developed f.or estimating sterilizing values. Through the use of this technique, lethal rate paper for a fixed z value, 18 F O, may be used for the estimation of sterilizing values for any other different z values.
Nomenclature Fp Ks
sterilizing value (min.)
=
Za/7.b
L Lethal I'ate, which is defined as Equation 1 T Temperature of food (OF) T m Modified temperature (OF) Slope index of thermal death time curve (FO) Any z value (F0) Fixed z value (PO)
2!)(i
25l
Table 2.
Time
Temperatures at the center of a 211 x 300 can of spinach puree, which were recorded during a heat process 1/. Temperature
o (Min.)
219
5 10 15 20 25 30 35 40 45
l.L
248
0 ~
W
er
::::::l f-
«
247
er
w L
w
f-
245
Time 50 (Min.) 55 60 65 70 75 80 85 90 95
Temperature 243.0 (OF) 245.3 247.0 233.0 207.0 174.0 147.0 124.0 108.0 95.0
-
11 The food was processed in a still retort. A holding temperature of the retort and temperature of cooling water were respectively equal to 250°F and 55°F.
0...
246
88.0 CF) 95.0 100.0 128.0 167.0 193.0 211.0 223.5 232.0 238.0
References Ball, C. Olin and Olson, F. C, W., 1957. "Sterilization in Food Technology", McGraw Hill Book Company, N.Y. Hayakawa, Kan-ichi, 1968. A procedure for calculating sterilizing value of a thermal process. Food TechnoI. 22: 905. Hayakawa, Kan-ichi, 1970. Experimental formulas for accurate estimation of food temperature and their application to thermal process evaluation, Food TechnoI. 24: 1407. Pflug, I. J. 1968. Evaluating the lethality of heat processes using a method of employing Hick's table. Food TechnoI. 22: 1153. Schultz, O. T, and Olson, F. C. W., 1940. Thermal processing of canned foods in tin containers. Ill. Recent improvements in the general method of thermal process calculations - A special coordinate paper and methods of converting initial and retort temperatures. Food Res. 5: 399. Stumbo, C. R. 1965, "Thermobacteriology in Food Processing" Academic Press, Inc., N.Y.
240
Received February 28, 1973.
230 220
o Figure 1.
2D7
20
40
60
80
100
120
Lethal rate curves for time-temperature data shown in Table 2.
J. Inst. Can. Scl. TechnoI. Aliment. Vo!. 6, No 4, 1973