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Results:

PART 1

T=105C T=110C T=115C T=120C

t

(min) survivors log(surv)

t

(min) survivors log(surv)

t

(min) survivors log(surv)

t

(min) survivors log(surv)

60 9.10E+08 8.96E+00 20 1.20E+09 9.08E+00 3 1.30E+09 9.11E+00 1.33 1.10E+09 9.041393

90 6.80E+08 8.83E+00 30 8.80E+08 8.94E+00 5 9.20E+08 8.96E+00 1.67 7.10E+08 8.851258

120 4.00E+08 8.60E+00 40 4.80E+08 8.68E+00 10 3.30E+08 8.52E+00 2 7.20E+08 8.857332

150 2.80E+08 8.45E+00 60 2.80E+08 8.45E+00 15 1.10E+08 8.04E+00 4 7.60E+07 7.880814

180 2.50E+08 8.40E+00 90 7.00E+07 7.85E+00 20 2.70E+07 7.43E+00 6 7.70E+06 6.886491

300 6.40E+07 7.81E+00 120 8.70E+06 6.94E+00 30 8.40E+05 5.92E+00 8 3.50E+05 5.544068

390 8.20E+06 6.91E+00 180 1.80E+04 4.26E+00 45 1.70E+03 3.23E+00 10 3.62E+03 3.558709

480 1.32E+06 6.12E+00 60 2.00E+01 1.30E+00 12 2.60E+02 2.414973

Table 1 Data of surviving population at time of withdrawal

Graphs 1 through 4 show the calculated decimal reduction times and the first order reaction

rate constant for temperatures 105C, 110C, 115C and 120C.

Graph 1 Survivor Curve Showing Logarithmic Order of Death at 105C

y = -0.0065x + 9.4559

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

6.00E+00

7.00E+00

8.00E+00

9.00E+00

1.00E+01

0 100 200 300 400 500 600

Survivors

Time (min)

Survivor Curve Showing Logarithmic Order of

Death at 105C

D= 147.97 minK=slope=-0.0065

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Graph 2 Survivor Curve Showing Logarithmic Order of Death at 110C

y = -0.029x + 9.9758

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

6.00E+00

7.00E+00

8.00E+00

9.00E+00

1.00E+01

0 20 40 60 80 100 120 140 160 180 200

Survivo

rs

Time (min)

Survivor Curve Showing Logarithmic Order ofDeath at 110C

D= 33.17min

K=slope=-0.029

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Graph 3 Survivor Curve Showing Logarithmic Order of Death at 115C

y = -0.1419x + 9.8994

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

6.00E+00

7.00E+00

8.00E+00

9.00E+00

1.00E+01

0 10 20 30 40 50 60 70

Survivors

Time (min)

Survivor Curve Showing Logarithmic Order of

Death at 115C

D= 7.77 min

K=slope=-0.1419

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Graph 4 Survivor Curve Showing Logarithmic Order of Death at 120C

PART 2

a) Temperature Dependency Factor (Z-value):Temp C D value log(Dval)

105 1.55E+02 2.190332

110 5.10E+01 1.70757

115 7.00E+00 0.845098

120 2.60E+00 0.414973Table 2 Temperature and D value Table

y = -0.6241x + 10.14

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10 12 14

Survivors

Time (min)

Survivor Curve Showing Logarithmic Order of

Death at 120C

D= 1.61 min

K=slope=-0.6241

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Graph 5 Thermal Death Time Curve

b) Arrhenius Energy (Ea):Temp C Temp Kel 1/T Kel -k min ln(k)

105 3.78E+02 2.65E-03 0.0065

-

5.03595

110 3.83E+02 2.61E-03 0.029

-

3.54046

115 3.88E+02 2.58E-03 0.1419

-

1.95263

120 3.93E+02 2.54E-03 0.6241

-

0.47144

Table 3 Reciprocal of absolute temperature and reaction rates in natural log cycles.

y = -0.1238x + 15.214

0

0.5

1

1.5

2

2.5

104 106 108 110 112 114 116 118 120 122

log(Dvalue)(minutes)

Temperature ( C )

Thermal Death Time Curve

Z= 8.0 C

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Graph 6 Arrhenious Plot

PART 3

a) Initial concentration=100 per containerLevel of acceptable spoilage= 1/100000=1E-5

SV=7

PART 4

a) D120 C.botulinum = 0.20 minutes

y = -45399x + 115.04

-6

-5

-4

-3

-2

-1

0

2.52E-03 2.54E-03 2.56E-03 2.58E-03 2.60E-03 2.62E-03 2.64E-03 2.66E-03

ln(k)

1/T (Kel^-1)

Arrhenious Plot

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b) D120 Enzyme = 0.5 minutes with 99% Enzyme reduction needed.

PART 5

a) Process temperature at 113C

b) Process temperature at 135C

PART 6

a) Sterilizing Value (log cycle reduction) at 135C for 1 full minute

Discussion:

In Part 1 of the experiment, the Decimal Reduction Time (D) and the first order reaction rate constant

(K) were calculated graphing the logarithmic order of death of the population through time at eachspecific temperature. By looking at the graph, the time required to get one log cycle in population was

approximated and D was obtained. Also, a more accurate way of finding D is to using the equation

. Moreover, the first order reaction rate constant or K value was calculated by getting

the slope of the best fitted line. Results of these values show that the fastest temperature to complete a

cycle was at the highest temperature of 120C, taking 1.61 minutes. The slowest was 147.97 minutes at

105C.

In Part 2, the temperature dependency factor (Z) was obtained by graphing the Thermal Death Time

Curve and calculating the temperature required for a log cycle to complete. In this case, by looking at

the graph we got 8C. Furthermore, the Arrhenious activation energy was calculated by graphing anArrhenious plot and getting the slope of the best fitted line. This value helped us find the activation

energy (Ea) by multiplying the gas constant times the slope. The Ea was found to be 377.45 kJ/mol.

Part 3 was done by applying the equation of the best fitted line found in the Thermal Death Time Curve

to obtain a D value at 121.1C. Then, the equation was used to get the common

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lethality value. The common lethality curve is essential for food conservation and for the control of

spoilage of food.

For Part 4, the equation was used to calculate the cooking time to provide a safe botch cook

as well as an adequate blanch process under the given conditions. For C.botulism it took 2.4 minutes to

cook safely and for the enzyme, it took 1 minute.

In Part 5 of this experiment, the line equation found in the Thermal Death Time Curve graph was used to

calculate the D value at the different process temperatures. Then, by using a sterility value of 7 log

cycles the critical process hold time was found at 113C and 135C.

Lastly, the sterilizing value in Part 6 was found using the equation,

, for a process of 1 full

minute. Book problems are attached in the appendix section of this lab report.