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
) 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 02/06/10)