Since microbial growth is controlled mostly by chemical reactions, and the nature and rate of chemical reactions are affected by temperature, the rate of microbial growth and total biomass growth are affected by temperature. The microbial growth rate increases with temperature to a certain maximum where the corresponding temperature is the optimum temperature (see Figure 7.22.2). Then, growth does not occur after a small increase in temperature above the optimum value, followed by a decline in the growth rate with an increase in temperature beyond the optimum.
For example, bacteria can be divided into three different classes on the basis of their temperature tolerance: psy-chrophilic, mesophilic, and thermophilic. Psychrophilic bacteria tolerate temperatures in the range of —10 to 30°C, with the temperature for optimum growth in the range of 12 to 18°C. The mesophilic group tolerates temperatures in the range of 20 to 50°C, with an optimum temperature between 25 and 40°C, while thermophilic bacteria survive in a temperature range of 35 to 75°C and have optimum growth at temperatures in the range of 55 to 65°C (Metcalf
and Eddy, Inc. 1991). In their respective classes, facultative thermophiles and facultative psychrophiles are bacteria that have optimum temperatures that extend into the mesophilic range. Optimum temperatures for obligate thermophiles and obligate psychrophiles are outside the mesophilic range.
The van't Hoff rule provides a generalization of the effect of temperature on enzyme reaction rates stating that the reaction rate doubles for a 10°C temperature increase. Also, according to Arrhenius, the following equation describes the relationship between reaction-rate constants and temperature:
K = the reaction-rate constant Ea = the activation energy, cal/mole R = the ideal gas constant (1.98 cal/mole-°K) T = the reaction temperature, °K
Integrating Equation 7.22(1) yields the following equation:
where B is an integration constant.
Equation 7.22(2) can be integrated between two temperature boundaries T2 and T1 to yield the following relationship that estimates the effect of temperature over a limited range:
In biological treatment, the activation energy Ea can range from 2000 to 20,000 cal/mole. For most biological treatment cases, the term (Ea/R)/(T2T1) is constant; therefore, the following equation applies:
where O is the temperature coefficient.
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