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where Dobsref is the decimal reduction time at Pref, Pref the reference pressure, and zP the z-value at a certain temperature. Also the zP-value can be estimated using two different regression approaches: plotting the 10-based logarithm of D in function of pressure, the zP-value at a certain temperature can be derived from the slope of the regression line, or the zP-value can be estimated using nonlinear regression analysis (see below).

Analogous to the validity evaluation of a first-order kinetic model, the appropriateness of the coefficient models to describe the temperature or pressure dependency of the inactivation rate constant can be evaluated by determination of the goodness of fit of ln k vs. 1/T (Arrhenius model), log D versus T (TDT model), ln k vs. P (Eyring model), or log D vs. P (PDT model).

3. Combined Pressure-Temperature Dependence

Based on experimentally determined inactivation rate constants for an elaborated set of pressure-temperature combinations, an iso-rate contour plot, connecting pressure-temperature combinations resulting in the same inactivation rate constant can be constructed. Iso-rate contour diagrams for pressure-temperature inactivation of enzymes as well as of microorganisms are often elliptically shaped. These elliptical pressure-temperature kinetic diagrams can be modeled on a thermodynamic basis.

The basic thermodynamic equation governing the behavior of a system during a pressure and a temperature change can be represented as Eq. (18).

Since the entropy change (AS) and the volume change (AV) vary with pressure and temperature [Eqs. (19) and (20), respectively], Eq. (18) can be reformulated as Eq. (21) (20, 21).

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