# Introduction

There will be occasions when a food manufacturer wishes to use a different, but equivalent lethal thermal process. How does the processor calculate the equivalent process?

This article explains how to calculate an equivalent thermal or heat process at a higher or lower temperature and provides access to a free On Line calculator for checking your calculations.

Providing that the F value at Tref and the z value are known then the F value at the required temperature, T, can be calculated using equation 1.

Equation 1.

Equation 1 has been derived from Stumbo (1973).

An example of how to use equation 1 is given for a fruit drink product.  The product was previously produced using a Tref of 85°C and a holding time of 15 minutes.  The processor has installed a continuous pasteurizer and wishes to use a temperature of 102°C to produce the drink. Calculate the holding time at 102°C, that will give an equivalent lethality to 85°C for 15 minutes given the z-value is 8.7°C.

We will use equation 1 to do the calculation. Firstly breaking down the terms in the equation, we will first calculate:

=85-102
8.7

= -1.954

Going back to equation 1 we can now insert the -1.954 we have calculated.

Finally, we can add the value for Fref and complete the calculation.

F = 0.167 minutes or 10 seconds.

The same equation and approach to the calculation can also be used to calculate equivalent process lethality at a lower temperature.

Note this approach should be used carefully since the linearity of the D-values (implied in the calculation) may only apply over a limited range of temperature.

## How do you find z if this value has not been provided?

Equation 1 can be solved for z. This has been discussed by Mullan (2020a).

## Further examples using milk pasteurisation

1. Calculate the holding time at 72°C that is equivalent to pasteurising milk at 63°C for 30 minutes. The current target pathogen for milk pasteurisation is Coxiella burnetii. C. burnetii has a z-value of 4.34°C over the temperature range 60°C to 72°C.

Knowing the z-value, the holding time at 72°C can be calculated using Equation 1 as 15 seconds. This examples illustrates the basis of the current high temperature short time (HTST) treatment of milk.

2. Calculate the holding time at 72°C that is equivalent to pasteurising milk at 63°C for 30 minutes using Mycobacterium avium subsp. paratuberculosis (MAP) as the target pathogen. MAP is increasingly being linked to Crohn's Disease.

There is no agreement on the  z-value of MAP but it is likely to be in the range 7°C-10 °C.

Assuming a high value of 10 °C, the equivalent holding time at 72°C can be calculated using Equation 1 as 227 seconds.

Using a lower estimate for z, say 8°C, the equivalent holding time at 72°C can be calculated as 135 seconds.

This finding is significant and illustrates that the current HTST process for commercial milk is only equivalent in lethality terms to the older holder method of 63°C for 30 minutes if the target pathogen has the same z-value as C. burnetti , namely 4.34°C.

### Calculation of equivalent time temperatures between 80° and 90°C for the pasteurisation of ice cream mixes to meet the US Grade A Pasteurized Milk Ordinance (2017)

This can be done using Equation 1 (Mullan 2020b).

## Literature cited

Mullan, W.M.A. (2020a). 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.

Mullan, W.M.A. (2020b). Calculation of equivalent time temperatures between 80° and 90°C for the pasteurisation of ice cream mixes to meet the US Grade A Pasteurized Milk Ordinance (2017). [On-line]. Available from: https://www.dairyscience.info/index.php/ice-cream/385-pmo-2017.html . Accessed: 15 November, 2020.

Stumbo, C. R. (1973). Thermobacteriology in food processing, 2nd ed. Academic Press, New York.