Convergence of Bigelow and Arrhenius models over a wide range of heating temperatures

Abstract

The heat resistance of the bacterial spores of Moorella thermoacetica, Clostridium sporogenes, Geobacillus stearothermophilus and Bacillus coagulans was determined over a wide range of temperatures using the capillary method and thermoresistometer Mastia. The results showed that the two experimental methods gave similar heat resistance values excepted for Geobacillus stearothermophilus.The effect of temperature on thermal resistance was evaluated using the Arrhenius and Bigelow models. The fit of the heat sensitivity parameters of the Arrhenius and Bigelow models on the heat resistance parameter values obtained over a wide temperature range was equally good. Despite the apparent mathematical incompatibility of the two equations, it is recognized that they yield the same goodness of fit. This paper finds a mathematical reason for this convergence and explains why inside a temperature range of at least 100 °C, no significant difference in the quality of fit between these two models can be found.