If you (hypothetically) had an infinitely cold ice cube (an ice cube that stays at absolute zero no matter how much heat it absorbs), how long would it take for the Universe to cool down to absolute zero?
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$\begingroup$ How big is the ice cube? That will make all the difference (kind of, the technical answer would be infinite time regardless of the size as long as it wasn't the size of the entire universe). $\endgroup$– JMacCommented May 29, 2017 at 17:54
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$\begingroup$ Wouldn't have an effect on anything outside of Earth's atmosphere - diffusion doesn't really work through a vacuum $\endgroup$– Señor OCommented May 29, 2017 at 18:01
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$\begingroup$ @SeñorO Good thing diffusion isn't the only way to transfer heat then... $\endgroup$– JMacCommented May 29, 2017 at 18:04
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1$\begingroup$ @JMac Yeah good thing lmao! But also good thing it's the only relevant transfer method in his scenario $\endgroup$– Señor OCommented May 29, 2017 at 18:08
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$\begingroup$ I'm pretty sure radiation would have a huge effect. We basically have an infinite heat sink. $\endgroup$– JMacCommented May 29, 2017 at 18:17
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2 Answers
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There is no such thing as a infinity cold ice cube.
The closest scenario I can think of is a system with a heat sink; a system coupled to a very large heat reservoir. You can them solve a heat equation.
You should also take into account that only at $$t\rightarrow \infty $$
will the temperature of the system equal that of the reservoir, so there is no definite period of time thats answers the equation.
Instead you can ask what the characteristic time of cooling is (i.e. when it will equal 1/e of the initial temperature) or you can ask when it will reach some threshold temperature (i.e. 0.001 of the initial temp).
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$\begingroup$ And to determine that characteristic timescale we would need the size of the cube; but this is essentially what it would boil down to. $\endgroup$– JMacCommented May 29, 2017 at 18:29
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$\begingroup$ @JMac I agree that to get an exact answer you would need that information, but if you treat is as an "infinite" reservoir them you're actually saying that that the exact size of the cube doesn't matter. $\endgroup$– YoACommented May 29, 2017 at 18:32
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$\begingroup$ It matters for the timescale. The larger the sink the faster you can remove thermal energy and therefore the faster you approach equilibrium. It actually matters quite a bit for the spirit of the question (it just doesn't invalidate anything in this answer). $\endgroup$– JMacCommented May 29, 2017 at 18:37
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Absolute zero means that the particles aren't moving at all. Any thermal energy will be absorbed by the cube. If we assume diffusion as the only method of heat transfer, there must be a direct chain of mass from the cube to all other objects in the universe for it to absorb energy from all of them. The second there is vacuum, diffusion can no longer occur. Hence assuming an ideal heat sink, it would just reduce everything in Earth to absolute zero.
It's also true that diffusion isn't the only method of heat transfer. Electromagnetic waves and radiation can travel through vacuum and can transfer heat, but this would have little to no effect. These forms of energy are reaching us already, and the amount of energy from other objects in the universe that reaches Earth is miniscule. The ice cube would not increase what arrives.
Hence, it would only have an effect on Earth.
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$\begingroup$ I disagree highly. There is no infinite heat source in the universe, yet this would be an infinite heat sink. It would be a very slow start, but eventually all heat would be radiated to this sink and lost through the magical handwave. $\endgroup$– JMacCommented May 29, 2017 at 18:20
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$\begingroup$ This assumes that over a long enough timespan, all energy from the universe would somehow find its way to Earth in a spontaneous manner. This seems highly unlikely to me. The heat sink certainly won't do anything to attract it. $\endgroup$– SteveCommented May 29, 2017 at 18:21
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$\begingroup$ See heat death of the universe where theoretically the universe would reach an equilibrium temperature. If you add an infinite sink, you will eventually lower the temperature of the system. It's not intuitive; but essentially you would be providing somewhere for heat to go to. If the universe is all approaching an average equilibrium temperature, a constant sink will ruin that. Essentially by saying "we can indefinitely keep this at absolute zero" what you really say is "we can remove infinite energy". $\endgroup$– JMacCommented May 29, 2017 at 18:28
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$\begingroup$ The notion of heat death is that the universe will expand until it has no thermal energy anymore. Assuming an utterly static universe where nothing else happens, it is plausible to think that all energy would eventually find its way to Earth. However, there are many things going on everywhere else. The expansion of the universe itself would have a far greater impact. $\endgroup$– SteveCommented May 29, 2017 at 18:33
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$\begingroup$ Heat death of the universe concerns the uniform spread of the energy in the universe resulting in everything at essentially equilibrium conditions. This occurs because the net energy of the universe is 0. By adding the cube, that relationship no longer holds. You now can have negative net energy through your magic heat sink. The timescales involved may be insane, but theoretically all of the heat energy will eventually approach that equilibrium at absolute 0. $\endgroup$– JMacCommented May 29, 2017 at 18:36