If I have two containers filled with very hot water(~210°F) with one in outer space and one on earth, which one has a higher rate of cooling initially? Imagine the containers are single wall metal containers that are able to withstand any pressure.
Intuitively I would assume the one in space would cool faster because the average temperature of space is 3°K. However a vacuum flask is an extremely good insulator since the only way heat can transfer is through radiation. Space is an even more extreme vacuum then any flask so would that mean that it "insulates" even better?
If allowed to come to thermal equilibrium, the space container would certainly lose more energy overall, but is the rate affected by the temperature difference a la Newton's Law of Cooling or does it lose energy at the same rate no matter what?
Best Answer
The container on Earth will be cooled by convection currents i.e. it transfers heat to the air around it, and also by black body radiation. By contrast the container in space can only cool by black body radiation, and obviously it will cool down more slowly. You can calculate the cooling in space using the Stefan-Boltzmann law assuming you know the emissivity (if you paint the container black the emissivity will be close to unity). Calculating the cooling in air is harder; typically you'd use Newton's law with empirically derived constants.
The final temperature in air is obviously just the temperature of the air around your container. The final temperature in space depends on where your container is. Just as the container can lose heat by emitting radiation it can gain heat by absorbing radiation, and space is full of radiation. For example the Moon is just a lump of inert rock with little or no internal generation of heat, however by absorbing sunlight the daytime temperature can rise to over 100ºC. However at night, when there is no sunlight the temperature can fall to -150ºC. So the final temperature of your container would be different during the lunar night and day, even though it's in a vacuum in both cases. If you took your container into intergalactic space, well away from any radiation sources, then it would indeed cool to the 2.7K of the cosmic microwave background.