#  The 2017 milk pasteurisation ordnance in the US (PMO 2017) provides only two equivalent  HTST time/temperatures for pasteurising ice cream mix (Table 1). A lower temperature-time treatment of 69°C for 30 minutes is also given. Previously 3-HTST equivalent temperatures were given (PMO 2011) although a range of time values (1-3 s) was given for 90°C.

### Table 1. Minimum pasteurization temperature vs. time continuous flow (HTST) pasteurization requirements for ice cream mix in the US.

Temperature

Time

80°C (175°F)

25 s

83°C (180°F)

15 s

Source: PMO (2017)

## How can manufacturers calculate other equivalent or higher temperatures using this data?

Since both HTST heat treatments have been designated as equivalent, other equivalent heat treatments can readily be calculated by first calculating the z value for the heat treatment processes. The z value can be calculated using equation 1 (Mullan, 2016; Mullan, 2020).

FT = FR x 10^TR-T   Equation 1
z
Where FT is the F value at the required temperature. This is the time at the reference temperature required to achieve the desired lethality and can take into account the lethal effects during heating, holding, and cooling at the target processing temperature. Only holding time at the reference temperature is considered for HTST pasteurisation.  FR is the F value at the reference temperature, in this case, 80°C. TR is the reference temperature, 80°C and T is the Temperature for which we require the F value.  z is the thermal constant and is a value expressing the increase in temperature necessary to obtain the same lethal effect in 1/10 of the time.  The higher the Z value of the organism, the greater its heat resistance. Once the z value has been calculated this can be used to calculate other equivalent F values. To do this we need to solve Equation 1 for z.

## Solving  for z

Isolating the exponential function gives equation 2.

FT = 10^TR-T    Equation 2
FR             z

Taking logs to base 10 and simplifying gives equation 3.

Log (FT) =   TR-T x log(10)
FR           z

logFT-logFR = TR-T x 1
z

1 = logFT-logFR  Equation 3
z           TR-T

The z value of the equivalent processes over the temperature range 80°C to 83°C has been calculated using Equation 3 and is shown in Table 2.

### Table 2. Calculated z values for  equivalent F values knowing reference F value and z values from minimum time-temperature data specified in PMO (2017)

Equivalent F values

z° C

80 °C,25 s and 83 °C,15 s

13.5227

Using this value potential equivalent time/temperatures to those specified in Table 1 to meet the PMO (2017) ordnance requirements for ice cream mix were calculated using equation 1 (Table 3).

### Table 3. Time-temperature treatments* for pasteurizing ice cream mix between 80°C and 90°C that meet those cited in PMO (2017).

Temperature, °C

Time, s

80**

25

81

21

82

18

83**

15

84

13

85

11

86

9

87

8

88

7

89

6

90

5

Notes.

*   Calculated using equation 1 and a z value of  13.5227 ° C
**  Specified within PMO (2017).
Decimals are rounded upwards to the nearest integer e.g. 4.5 to 5.

## References

Mullan, W.M.A. (2016). How to derive an equivalent heat process at a higher (or lower) temperature. [On-line]. Available from: https://www.dairyscience.info/index.php/thermal-processing/302-equivalent-process.html . Accessed: 15 November, 2020. Updated August 2018.

Mullan, W.M.A. (2020). How do you calculate the z-value given two equivalent thermal processes?. [On-line]. Available from: https://www.dairyscience.info/index.php/thermal-processing/386-z-value-calculation.html . Accessed: 15 November, 2020.

PMO. (2011). Grade A Pasteurized Milk Ordinance. Food and Drug Administration, College Park, MD. Available from: Regulation/GuidanceDocumentsRegulatoryInformation/Milk/ucm2007966.htm. Accessed 21st December 2015.

PMO. (2017). Grade A Pasteurized Milk Ordinance. Food and Drug Administration, College Park, MD. Available from https://agriculture.ny.gov/system/files/documents/2019/07/2017_PasteurizedMilkOrdinance.pdf . Accessed 10th October 2020.

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