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

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The Stefan–Boltzmann law says radiative emission increases rapidly with temperature:

Pemit=σAT4P_{\text{emit}} = \sigma A T^4Pemit=σAT4
So he argues that as the particle warms, emission increases rapidly and instantly balances absorption.

===== - This only describes radiative output, not how fast a particle actually warms up. =====
* To know how fast temperature rises, you must include heat capacity and mass:

dTdt=PnetmCp\frac{dT}{dt} = \frac{P_{\text{net}}}{m C_p}dtdT=mCpPnet
Where:
* PnetP_{\text{net}}Pnet = absorbed power – emitted power – latent loss
* CpC_pCp = specific heat capacity of ice (~2100 J/kg·K)

A 20 µm particle has:
* Mass ≈3.84×10−12 kg\approx 3.84 \times 10^{-12} \, \text{kg}≈3.84×10−12kg
* So even if Pnet∼1×10−7 WP_{\text{net}} \sim 1 \times 10^{-7} \, \text{W}Pnet∼1×10−7W, the rate of temperature rise is: dTdt≈1×10−73.84×10−12⋅2100≈12.4 K/s\frac{dT}{dt} \approx \frac{1 \times 10^{-7}}{3.84 \times 10^{-12} \cdot 2100} \approx 12.4 \, \text{K/s}dtdT≈3.84×10−12⋅21001×10−7≈12.4K/s

🔥 That’s not milliseconds — it takes multiple seconds to reach a new equilibrium temperature, even under sustained solar absorption.

✅ Stephen’s assumption of “instant thermal equilibrium in milliseconds” is physically false — he ignores the particle's thermal inertia.