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Q & A: Who wins the hot potato race?

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Most recent answer: 02/07/2010
Q:
You're in deep space. You put two potatos in the oven, heat 'em to 300 F. Place one on the table in your capsule at 70F and eject the other into space. Which one will cool from 300F to 100F faster? (Disregard any explosion, etc caused by decompression. If you need to, substitute a rock for the potato, though it doesn't have the same ring to it) Thanks I've been wondering about this for about 15 years
- Michael (age 57)
Las Vegas, NV
A:
Great question Michael,
Three methods of transferring heat from a warm body are conduction, convection,  and radiation. Convection basically shuts down  inside the microgravity environment of the space capsule. Conduction pretty much shuts down outside the capsule, because there are so few gas molecules around.    The radiation rate follows the
Stefan–Boltzmann law and is proportional to  σ(T14 - T24) where T1 is the temperature of the body and T2  the temperature of the surrounding environment.  Inside the capsule, the ambient temperature is room temperature, about 300 Kelvin.  Outside the capsule, the ambient temperature is that of the cosmic microwave background,  2.7 Kelvin.  The heat conduction by air inside the capsule isn't enough to make up the difference for a potato-sized object. So the hot potato in space will cool much faster then the one in the comfy space capsule, unless the potato is sitting on a nice metal table, which can conduct the heat away fast. However, in microgravity, the potato is unlikely to stay in good contact with the table.

I have neglected the fact that if you are not in deep space but in a low earth orbit the sun might be shining on the space potato.  If you want to take that into consideration you have to know the reflectivity of the potato skin and what the detailed shape is and what fraction of the time the potato is in the shadow of the earth.  The amount of power from solar radiation in low earth orbit is about one kilowatt per square meter.  I haven't made a detailed estimate but my guess is that solar heating might make a it a much closer race. 

LeeH (w. Mike W)

Actually, it will be a close race. The potato is more or less similar to a little earth, partially reflective. The earth, exposed to solar radiation, has a balance of incoming and outgoing radiation, Therefore we know that the average solar input is about the same as the output for a typical earth surface T, say 280K. That means that the average solar input radiation is about the same as the average thermal radiation the potato in the capsule picks up from its surroundings. So, with the help of a little conduction, I bet the potato in the capsule cools just a little faster.  Mike W.


As I said at the beginning, 'A great question'.   When you can get two physics professors into a lively discussion of who wins a hot potato race, it must be good.
I still vote for the space potato.  LeeH

(published on 02/04/2010)

Follow-Up #1: Hot potato race revisited

Q:
Okay now suppose you were able to pick up all the electromagnetic radiation emitted by the heat of the potato in the capsule and transfer it into the outerspace one without any loss (ceteris paribus) Would that be correct to say that the potaton inside the capsule will cool faster that the one in space? Or if the two would cool down at the same rate? (There's no Sun also to heat up the potato in space, perfectly dark)
- Anonymous
A:
No, because any device for picking up the radiation from the potato has to completely surround it.  It will be at a certain temperature and will radiate back at the potato at its own temperature.  Most likely the device is at room temperature so you don't win.   If you artificially cool the device you would have to cool it to the outer space temperature, 2.7o Kelvin, or below.  Then you might as well be back in deep space.

LeeH

(published on 02/07/2010)

Follow-up on this answer.