# Calculate an equivalent heat process at a higher (or lower temperature) knowing the z-value and the F (P) value at the reference temperature

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 T_{ref} 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 T_{ref} 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 F_{ref} 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.

Go to the Thermal process equivalence calculator

## Literature cited

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

**How to cite this article**

Mullan, W.M.A. (2016).
[On-line]. Available from: __https://www.dairyscience.info/index.php/thermal-processing/302-equivalent-process.html .__ Accessed: 24 October, 2016.