#  # Introduction

As previously discussed (Mullan, 2016), there will be occasions when a food manufacturer who has been using two different but equivalent thermal processes from a lethality perspective wishes to use a different, but equivalent lethal thermal process. This is straightforward if the z-value is known (Mullan, 2016). How does the processor calculate the equivalent lethal process if z is unknown?

This article explains how to calculate z using the time and temperature values of the two different, but equivalent lethal processes, and provides access to a free On Line calculator for checking your calculations.

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.  Equation 1 has been derived from Stumbo (1973).

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.
FR is the F value at the reference temperature.
TR is the reference temperature 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.  Note it is the decimal reduction value, D, that is a measure of the resistance of a microorganism to heat. The z-value provides information on how this heat resistance changes with temperature.

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

## Practical example

An example of how manufacturers can calculate equivalent thermal processes for the pasteurisation of ice cream mix given limited regulatory authority information has been provided (Mullan, 2020).

## Qualifications

Caution is necessary when calculating z at temperatures significantly lower or higher than TR. It can be shown using the Arrhenius equation that z is a function of the processing temperature.

## Literature cited

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: 14 November, 2020. Updated August 2018.

Mullan, W.M.A. (2020). 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: 14 November, 2020.

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