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Astronomy and Cosmology
Astronomy and Astrophysics
Ice in space, sublimation time
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[QUOTE="snorkack, post: 6866768, member: 436348"] I believe the article is much better than the equation. I independently came up with basically the same reasoning. Consider the following reasoning: In vacuum, a vapour will escape an evaporating surface at a speed at the order of the speed of sound, within a modest factor. At 0 C, assume that it is 400 m/s for water vapour. Then at 0 C, 1 square metre of ice will give off 400 cubic m of water vapour per second. But it is water vapour at the vapour pressure - 6,1 mbar. So if you compress it to STP - which won´t be stable, but I´m doing it for accounting reason to track the gas law - you would get 2,44 cubic m of steam. Avogadro´s law states that 22,4 l is 1 mole at STP, so 2440 l at STP is about 110 mol. Which is 2000 g of water. One square m of ice at 0 c will lose 2,2 mm per second, 8 m per hour. But ice´s latent heat of evaporation at 0 C is around 2830 J/g. Which means that keeping ice at 0 C in vacuum will take 5,6 MJ/m[SUP]2[/SUP]*s Sun at 1 AU will provide only under 1400 J/m[SUP]2[/SUP]*s. You will need to approach 60 times closer, to within 2 400 000 km of Sun´s centre, that is, 1 700 000 km of Sun´s surface, to melt ice! Alternatively, the ice would cool until its vapour pressure falls 4000 times or so compared to the vapour pressure at 0 C, and the speed of evaporation and loss of heat to evaporation decreases to below the heat input. My estimate is that at 1 AU, this would happen around -80 C or so. Now, if the heat input is lower... There will be two ways for heat to get out of the snowball. One is evaporation. This is close to proportional to vapour pressure, which falls close to exponentially with 1/T. The second is radiation, which falls with T[SUP]4[/SUP]. So with sufficiently low T, the radiation becomes the main heat loss. For high heat inputs, most of the heat is spent on evaporation and speed of the evaporation will be proportional to heat input. For low input, most of it is radiated away and speed of evaporation falls exponentially. Would you like more trying the details? [/QUOTE]
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Ice in space, sublimation time
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