6. Temperature Effects. The Z Value.  (TOC)

Thus far, we have been discussing phenomena occurring at constant temperature. We know, however, that the thermal death constant, K, varies with temperature. The assumption was made implicitly, since the kinetics of thermal death of microorganisms was modeled as a first order reaction, that there is a key chemical reaction, perhaps inactivation of an enzyme, that controls the death process. Extend the analogy further, and think of the thermal death constant K as a pseudo-chemical rate constant. Discussion of the theory of chemical reaction rates is well beyond the limits of this short tutorial, but we can guess that K will vary with temperature in a way similar to many chemical reaction rate constants. One of the oldest formulations, admittedly a simplification, was originally devised by Arrhenius. Molecules which have absorbed quantum energy of sufficient magnitude are activated and thus in an energy state wherein they will react chemically in some way. The energy required is termed the activation energy, E. The proportion of molecules with thermal energy of E or greater is proportional to exp(-E/RT), where R is the universal gas constant, and T is the absolute temperature. By analogy, then, the thermal death constant K may be expressed as

A is the Arrhenius factor for the activation under consideration, and for our purposes may be considered as constant. This equation may be differentiated to yield

Ignoring pressure and temperature effects

and

or

Rearranging

A plot of lnD vs T is linear with intercept on the lnD axis at ln(2.303/A) and slope R/E. This value R/E is usually called the Z value for the organism, and is expressed entirely equivalently as

The Z value is thus just another way of expressing the activation energy. However, a caveat. Although this derivation of the Z value is more or less rigorous, much of the literature expresses the Z value using the Fahrenheit temperature scale instead of the Kelvin or Centigrade scale, and uses common logarithms instead of natural logarithms. This particularly unfortunate practice can lead to no end of confusion, and to serious misinterpretation of published data. Be sure you know how the Z value is defined before you use a particular instance.

Another confusing term in some use is Q₁₀, which can be defined as the ratio of the thermal death constant at temperature T and the thermal death constant at (T + 10)^oC. With this definition, it can be shown that the product of the Z value and Q₁₀ is a constant. The Q₁₀ ratio is based on the assumption that D = aexp(bT) where a and b are empirical constants.