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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?

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    $\begingroup$ The energy loss in the vacuum of space will be due entirely to thermal radiation, using the equation $P=\epsilon \sigma AT^4$. $\endgroup$
    – NeutronStar
    Jul 24 '13 at 23:05
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    $\begingroup$ I think there is not enough information to answer it, we need to know how close the container material to black body to know how much it really radiate, and in the same time absorb sun's, earth's, and moon's radiation, also it's thickness and heat conductivity will play important role. $\endgroup$
    – TMS
    Jul 24 '13 at 23:38
  • $\begingroup$ Are you asking which container will cool to its environment's temperature the fastest, or which will cool the fastest at the beginning, at the temperatures you've give us? Also, what metal are we using for the container? Thermal conductivities and emissivities can vary greatly between materials. $\endgroup$
    – NeutronStar
    Jul 24 '13 at 23:40
  • $\begingroup$ I thought I posted a comment here but it isn't showing up. @Joshua-I want to know which one cools faster initially. I have modified the question to reflect this. I don't think the metal matters since it's the same metal for both. But just for the sake of the question let's just say it's iron. $\endgroup$
    – cspirou
    Jul 24 '13 at 23:58
  • $\begingroup$ @TMS-The container is in deep space so any other radiative bodies are negligible to the the answer. My main focus is on the container in a vacuum vs the container in a regular atmosphere. You could use STP for the atmospheric conditions. $\endgroup$
    – cspirou
    Jul 24 '13 at 23:59
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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.

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  • $\begingroup$ i assume this should read 2.7K? $\endgroup$
    – kutschkem
    Jul 29 '14 at 10:58
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I'd say the container in air will cool faster initially - convection (and thermal conductivity) will cool more efficiently at this temperature than radiation.

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There are 3 methods of thermal energy transfer!!! [radiation, convection and conduction] Given that energy always obeys the law of entropy and is always moving towards lower levels. Left alone hot things cool. As space is an ideal insulator, the only means of cooling is radiation. On earth the atmosphere serves to wick away thermal energy from the can and earth itself. The air molecules in contact with the can conduct heat from the can the heated air around the can, now at a lower density than the air around it, begins to gravitationally displaced as convection sets in to add to the radiative and conductive cooling already and independently in progress. The gas mix of the atmosphere is significant with the three states of water working on a global scale. No special rules, 3 methods

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