________________________________ From: Keith F. Lynch <kfl@KeithLynch.net> To: math-fun@mailman.xmission.com Sent: Tuesday, December 10, 2013 5:46 PM Subject: Re: [math-fun] coldest place on earth
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.
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.
Note that the partial pressure of CO2 on Mars is much higher than on Earth, since its atmosphere is 95% CO2. In fact, if you neglected to pump the Mars air out of a room on Mars before filling it with Earth air, it would exceed the OSHA limit for human CO2 exposure. If you teleported Mars's CO2 ice cap to Earth, keeping its temperature unchanged, it would quickly disappear.
Eugene Salamin <gene_salamin@yahoo.com> wrote:
All of space is filled with the 2.7 K cosmic microwave background.?
True. That means an inactive object in space far from any other source of heat will (eventually) be at that temperature. An active object can of course be warmer.
It requires shielding and active refrigeration to cool something to a lower temperature.
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.
Spin temperatures, color temperatures, and information temperatures are metaphorical when taken out of context. As Eugene Salamin pointed out, flipping a magnetic field can result in spin temperatures which are either negative or hotter than infinity, depending on your perspective. But I don't think they can be used to heat or cool your home. Nor can a microwave oven be used to freeze food, even though its radiation has a color temperature of less than one kelvin. Nor can you start a fire with an x-ray machine even though its radiation has a color temperature of millions of kelvins.
As for information temperature, would you get more heat by burning a deck of punched cards containing the first million digits of pi or by burning a deck of punched cards containing a million random digits? (This is actually a surprisingly subtle question if you analyze it in enough detail. Can Maxwell's Demon calculate pi? And does it have a Szilard engine to play with?)
Answer: You get the same amount of heat, since each digit on a punch card (in IBM format) removes 1 chad. -- Gene