Temperature excursion: difference between revisions
Diff·revision 28 → 29·02:12, 3 Aug 2025
Difference between revision 28 and revision 29 of Temperature excursion. 2 lines changed; the page grew by 105 bytes.
| Revision 28 — 05:35, 29 Jul 2025 RepackRadek (talk) ce 13,309 bytes +873 | Revision 29 — 02:12, 3 Aug 2025 Ref_Desk_Ron (talk) expand §Definition and framing 13,414 bytes +105 | ||
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| 81 | {{math|e^{−10000/295.15} = e^{−33.8811}}} and {{math|e^{−10000/278.15} = e^{−35.9518}}} | 81 | {{math|e^{−10000/295.15} = e^{−33.8811}}} and {{math|e^{−10000/278.15} = e^{−35.9518}}} |
| 82 | 82 | ||
| + | 83 | The colder term is smaller by a factor of e<sup>−2.0707</sup> = 0.1261. The weighted sum is therefore | |
| + | 84 | ||
| 83 | === Why the two means diverge === | 85 | === Why the two means diverge === |
| 84 | 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. | 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. |