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Aug17-06, 10:50 AM
P: 185
Quote Quote by fargoth
I did a little experiment, to see if it makes any sense... i took a measuring cup, filled it with about 5cc, and put it in the fridge (about 269K). the water had a surface area of about 15cm^2.
it took the water about 8 minutes to freeze, and not all of it froze.

so, the assumption that the water's temperature is homogenous isn't correct, because it has less then ideal heat conductivity - thats why the "deeper" water didn't freeze yet.
First I'll acknowledge that Boltzmann's Law does tend to yield slightly shorter cooling times than actual observation would measure; but not drastically so.

That said, I embarked on this study of Radiative Cooling for the very reason that you rightly pointed out that the "experiment" creates a near vacuum, therefore radiative was the only realistic scenario for cooling; notwithstanding whatever you come up with for the evaporative cooling.

Also, your experiment has some significant deviations from the original. For one thing, the container (measuring cup) would have a much greater capacity to hold heat than the container in the original; a very shallow metal dish about 1mm thick. Your container provided insulation.
in my experiment there was atmosphere, which means that in your experiment these water would cool slower, the lack of atmosphere slows the cooling process because the heat conduction is done only by radiation and not with the help of the surrounding gas.
You use the presence of gasses in your freezer to argue they were assisting cooling; I should think a vacuum would be ideal for the transmission of photons, however, so would not Radiative Cooling be more efficient then?
and ignoring the ambient temperature is true for the sun for example, but you can't do it if the ambient and "hot" temperatures are close, as it is in this case. in our case, there is radiation from the outside that gets absorbed in the water, its not only the water which radiates.
My calculations do in fact include the ambient. I'll post separately to show the full math...
i'll continue to develop the formula for heat loss due to boiling just out of curiousity, but i think the conclusions can be made right now...
I'm very curious to see what you come up with.