Temperature excursion: difference between revisions
Diff·revision 36 → 37·01:14, 19 Sep 2025
Difference between revision 36 and revision 37 of Temperature excursion. 4 lines changed; the page grew by 1,332 bytes.
| Revision 36 — 10:35, 14 Sep 2025 SurpassSunniva (talk) fix unit 15,979 bytes +1,719 | Revision 37 — 01:14, 19 Sep 2025 NPOV_Nadia (talk) lead should summarise the body, not add to it 17,311 bytes +1,332 | ||
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| 91 | The mean kinetic temperature is 10.2 °C, above the 8 °C upper limit, while the arithmetic mean is 7.3 °C and comfortably inside it. The two statistics reach opposite conclusions about the same record. This is not an artefact: the arithmetic mean treats an hour at 22 °C as equivalent to an hour at 5 °C when for degradation purposes it is roughly eight times as costly.{{r|haynes1971}} | 91 | The mean kinetic temperature is 10.2 °C, above the 8 °C upper limit, while the arithmetic mean is 7.3 °C and comfortably inside it. The two statistics reach opposite conclusions about the same record. This is not an artefact: the arithmetic mean treats an hour at 22 °C as equivalent to an hour at 5 °C when for degradation purposes it is roughly eight times as costly.{{r|haynes1971}} |
| 92 | 92 | ||
| + | 93 | The calculation's limits are as important as its result. It presumes a single degradation pathway obeying the Arrhenius relationship with the assumed activation energy; a real product has several pathways with different activation energies, and where the dominant pathway has an activation energy far from 83 kJ·mol⁻¹ the statistic misrepresents the exposure in a direction that cannot be signed without knowing which pathway dominates. It also compresses the profile, so it cannot answer whether a threshold — a freezing point, a glass transition — was crossed.{{r|usp1079,waterman2005}} | |
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| 93 | === Why the two means diverge === | 95 | === Why the two means diverge === |
| 94 | 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. | 96 | 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. |
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| 102 | 104 | ||
| 103 | so approximately a threefold acceleration per 10 K. This is the origin of the informal expectation that degradation roughly triples for each 10 °C, and it is the reason a short warm interval can outweigh a long cold one.{{r|waterman2005}} | 105 | so approximately a threefold acceleration per 10 K. This is the origin of the informal expectation that degradation roughly triples for each 10 °C, and it is the reason a short warm interval can outweigh a long cold one.{{r|waterman2005}} |
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| + | 107 | Real products depart from the single-pathway model in documented ways. Peptide degradation proceeds by several routes with different temperature dependences — [[deamidation]] of asparagine, [[Methionine oxidation|oxidation]] of methionine, backbone hydrolysis, disulfide exchange, and physical [[Peptide aggregation|aggregation]] — so the apparent activation energy of total degradation changes with temperature as the dominant route changes. Extrapolation from accelerated conditions to real storage is therefore reliable only over a limited range, which is why ICH stability programmes require long-term data at the labelled condition and treat accelerated data as supporting rather than substituting.{{r|ich_q1a,manning2010}} | |
| 104 | 108 | ||
| 105 | === Freezing and interfacial damage === | 109 | === Freezing and interfacial damage === |