Editing Openai/680a25f8-9f18-8004-a42d-cd36374ba000 (section)

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This is the biggest error. The absorbed solar energy doesn’t go into raising the temperature much—it goes overwhelmingly into overcoming the latent heat of sublimation, not just “heating up ice.”

Ice sublimation happens well below melting (direct solid → vapor), and most energy is spent turning solid into vapor, not changing its temperature.
* Latent heat of sublimation for ice: ~2.83×10⁶ J/kg (vs. specific heat: 2100 J/kg·K)

So:

: 

Sam is using the wrong energy equation for the wrong process.

===== Contrail ice crystals are typically ~20 µm in diameter, not 1 mm² in area (which is 1000× too big in linear scale). =====
* Actual radius: 10⁻⁵ m
* Cross-sectional area: πr² ≈ 3.14×10⁻¹⁰ m²
* Mass: ~3.84×10⁻¹² kg, not 0.001 g (= 10⁻⁶ kg)

That’s a 1,000,000× overestimate of mass!

So Sam is:
* Overestimating the energy required to raise T (by using wrong mass)
* Underestimating the temperature rise and sublimation rate

===== You did it properly: =====
* Start with the actual absorbed power: ~2.97×10⁻⁷ W = 2.97×10⁻⁷ J/s
* Compare to mass-transfer-limited sublimation rate, driven by vapor pressure difference
* Result: Crystal vanishes in ~1 second, not 6 days