[math-fun] coldest place, CO2 retraction
Warren D Smith <warren.wds@gmail.com> wrote:
The interesting thing about this is that dry ice (froen carbon dioxide) forms at -78.5C (-109.3F) at Earth atmospheric pressures. Mars has a carbon dioxide seasonal "ice" cap. It would now appear that the Earth does too.
From: "Keith F. Lynch" <kfl@KeithLynch.net> No. That temperature is when CO2 frost will form with a partial pressure of CO2 of one atmosphere. But of course only about 1/2500th of the air is CO2. So if someone dropped a block of dry ice in that Antarctic valley, it would have sublimated, just like it would in your back yard. Well, okay, maybe more slowly, but it certainly wouldn't have grown, much less appeared spontaneously.
--aha yes, good point... BUT, what we need to know, then, is "what is the sublimation temperature of dry ice at 1/2500 atm CO2 gas pressure?" The phase diagram of CO2 is here http://www.teamonslaught.fsnet.co.uk/co2%20phase%20diagram.GIF and a better diagram for us since it uses a log scale for pressure, is http://www.cgenpower.com/images/other/pop-up/fasendiagram.jpg and it would appear from extrapolating the latter diagram, that to get stable solid CO2 at 1/2500 bar of vapor pressure, you'd need to be at temperature of about minus 150 celsius. The antarctic record of minus 94 C was not cold enough. So, sorry for my wrong claim; I now agree with Lynch.
Note that the partial pressure of CO2 on Mars is much higher than on Earth, since its atmosphere is 95% CO2.
--the atmospheric pressure on Mars allegedly is about 8.7% of Earth's so again I agree with Lynch.
It requires shielding and active refrigeration to cool something to a lower temperature than 2.7K.
No. An active object can also be *colder*. Adiabatic expansion can turn a megakelvin gas cloud from a supernova explosion into a microkelvin gas cloud. Atoms in the same vicinity within such a cloud started with the same speed and direction, so their relative speeds are much lower than in a 2.7 kelvin cloud. Of course the cloud will eventually absorb the microwaves and warm up, but that could take a very long time, as a thin neutral gas is very transparent to microwaves and to almost everything else.
--really? I mean, is there really a gas cloud from some supernova that is microkelvin? Or is this just a speculation? I agree with Lynch on the general principle that an active object could get below 2.7K, but does it actually happen someplace? For example, is that Finnish lab that got 100 picoKelvin, really the coldest place in the universe? To make a completely crazy scenario, let's say we have a neutron star that has planets orbiting it. (It is known from pulsar timings that such exist.) After a long time, the planet gets cold, approaching 2.7K. Now further suppose that the planet is totally magnetized by the enormous magnetic field of the neutron star, which far exceeds any magnetic field we can make on Earth. Now a rogue planet swoops in from outer space and gravitationally interacts with our planet, causing it to escape from neutron star. As a result, it experiences demagnetization cooling. Maybe in this way temperatures way below 2.7K could be reached naturally. I'm dubious, but it might be possible.
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Warren D Smith