Temperature excursion: difference between revisions
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| 83 | The colder term is smaller by a factor of e<sup>−2.0707</sup> = 0.1261. The weighted sum is therefore | 83 | The colder term is smaller by a factor of e<sup>−2.0707</sup> = 0.1261. The weighted sum is therefore |
| 84 | 84 | ||
| + | 85 | {{math|e^{−33.8811} × (96 + 624 × 0.1261) ÷ 720 = e^{−33.8811} × 174.7 ÷ 720 = e^{−33.8811} × 0.2426}} | |
| + | 86 | ||
| 85 | === Why the two means diverge === | 87 | === Why the two means diverge === |
| 86 | The divergence is a direct consequence of convexity. Degradation rate is a convex function of temperature, so the average of the rates at two temperatures exceeds the rate at their average temperature. Mean kinetic temperature is defined as the temperature whose rate equals the average rate, and therefore always lies at or above the time-weighted arithmetic mean, with equality only for a constant profile. | 88 | The divergence is a direct consequence of convexity. Degradation rate is a convex function of temperature, so the average of the rates at two temperatures exceeds the rate at their average temperature. Mean kinetic temperature is defined as the temperature whose rate equals the average rate, and therefore always lies at or above the time-weighted arithmetic mean, with equality only for a constant profile. |
| 87 | 89 | ||
| 88 | The gap widens with the spread of the profile. For the 30-day case above, a spread of 17 °C produced a gap of 2.9 °C. For the extreme cycle worked at [[Cold chain]], a spread of 28 °C produced a gap of 8.1 °C. A record with a narrow spread can be summarised by its arithmetic mean with little error; a record with a wide spread cannot, and it is precisely the wide-spread records that arise from excursions.{{r|haynes1971}} | 90 | The gap widens with the spread of the profile. For the 30-day case above, a spread of 17 °C produced a gap of 2.9 °C. For the extreme cycle worked at [[Cold chain]], a spread of 28 °C produced a gap of 8.1 °C. A record with a narrow spread can be summarised by its arithmetic mean with little error; a record with a wide spread cannot, and it is precisely the wide-spread records that arise from excursions.{{r|haynes1971}} |
| + | 91 | ||
| + | 92 | == Degradation kinetics == | |
| + | 93 | The rate constant for a chemical degradation pathway is conventionally described by the Arrhenius equation, in which rate rises exponentially with the reciprocal of absolute temperature. With the compendial activation energy, the multiplier for a 10 K rise near 25 °C is | |
| + | 94 | ||
| + | 95 | {{math|exp[10000 × (1/298.15 − 1/308.15)] = exp(1.0884) = 2.97}} | |
| 89 | 96 | ||
| 90 | == References == | 97 | == References == |