# Calculator for determining the F value of a thermal process

The calculator converts temperature readings to lethal rates, plots the lethal rates against time, and determines F values for a heat process. The area under the curve is determined using the trapezoid rule. Accurate F determinations for most thermal processes can be obtained. In general the more values, the more accurate the value for F will be.

The lethal effect of high temperatures on microorganisms is dependent on both temperature and holding time.

Because microorganisms in foods are exposed to lethal temperatures as they reach the target processing temperature and during cooling, it is necessary to calculate the cumulative effect of heat on microbial destruction during both heating and cooling as well at the holding time at the target temperature.

The logarithmic reduction in time required to kill the same number of microorganisms as temperature is increased has been well described.  This can be expressed by calculating lethal rate.

The lethal rate is a dimensionless number and can be calculated using equation 1 (Stobo, 1973).

Equation 1, Lethal rate = 10 (T-Tr)/z  where T is the temperature, in Celsius, at which the lethal rate is calculated and Tr is the reference temperature at which the equivalent lethal effect is compared. The z-value measured in °C is the reciprocal of the slope of the thermal death curve for the target microorganism or spore; 10° C is the value frequently used in Fo calculations performed on low acid foods.

Use of this equation can be illustrated using the following example. Calculate the lethal rate at 110° C compared to that at 121.11° C (Tr), given that the most heat resistant organism present has a Z value of 10° C.

Lethal rate= 10 (110-121.11)/10

= 0.077.

Lethal rates when plotted against process time can be used to calculate the F value of a thermal process.  The F value can be defined as the time taken to reduce initial microbial numbers, at a specified temperature, by a particular value, normally a multiple of the D-value for the target organism.

Note the original work on themobacteriology used a reference temperature of 250° F. This is equivalent to 121.11°C.

Tr will vary depending on whether Fo is being calculated or whether a pasteurisation process or other heat treatment is being assessed. A Tr value of 121.11° C is used in the determination of Fo. If F70 or other F value is required then Tr can be set at 70° C or other temperature.

Tr and the Z-value can be varied by the user. There is also a facility to perform a lethality calculation using an uploaded CSV file. Basic instructions are provided in the help file. The application can be tested using internal data and you can also upload a data file for analysis of a process.

The lethal rate calculator was validated using a Microsoft Excel spreadsheet  and following consultation with site users this is now available for download.

The spreadsheet converts temperature to lethal rate and plots lethal rate and temperature against time. The trapezoid rule is used to calculate the area under the curve and depending on the reference temperature chosen Fo or other F value can be calculated. A graph showing lethal rate and temperature against time is also plotted. The download contains a Microsoft Excel spreadsheet and a document in PDF form. The PDF file explains the basis of lethal rate calculation and also how to use Microsoft Excel to calculate the area under a curve using the trapezoid rule. All the cell formulas are unlocked.