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Suppose ice and water (not necessarily of the same mass) are both at $0^{\circ}$C and placed into a perfectly insulated, sealed container so that it is filled completely. If we leave this system alone for some time, what happens?

I think this may be similar to what happens when ice melts or water freezes, as then there are different states of matter at the same temperature. Thus, my best guess is that both the amount of water and the amount of ice will remain constant, as there is no heat flowing into or out of the system to drive the phase change either way.

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    $\begingroup$ Your best guess is correct. $\endgroup$
    – David White
    Commented Aug 11, 2021 at 18:55

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As pointed out repeatedly in the comments above, the total amounts of water and ice will remain the same.

However, also as pointed out repeatedly in the comments above, "true nothing" does not exist.

In fact, during any time interval, molecules of water will constantly leave the ice to join the liquid water, while essentially the same number of molecules of the liquid will join the ice.

And if you wait long enough, you'll notice that any "peak" of ice will lose just a bit more molecules, while on any "trough" just a bit more molecules will get stuck. So the surface will get more regular. Also ice blocks initially separated will tend to stick to each other. This, however, will be very slow and you'd need to keep your system perfectly isolated for a long time before these changes become noticeable.

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As long as they are initially in thermal equilibrium (no temperature gradients in the mixture), nothing will happen.

Hope this helps

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    $\begingroup$ If the ice and water are in thermal equilibrium, ice molecules will enter the water and the same number per unit of time of water molecules will end up as ice. There's not net change in the masses of ice and water respectively. That's what equilibrium means. Whether that constitutes 'nothing will happen' could be a matter of debate. $\endgroup$
    – Gert
    Commented Aug 11, 2021 at 19:57
  • $\begingroup$ In my view if there’s no change in the amount of ice or water there is no net change. One can always argue that even in thermal equilibrium there is energy transfer at the molecular level from low temperature to high temperature ( higher KE molecules in the lower temperature substance transfers KE to the higher temperature substance), but the net effect is no transfer of energy. $\endgroup$
    – Bob D
    Commented Aug 11, 2021 at 20:07
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    $\begingroup$ There's no net change, agreed and as I also highlighted. But I'm not sure that what is happening can be characterised as 'nothing happens'. At the molecular level there are things happening. Thanks. $\endgroup$
    – Gert
    Commented Aug 11, 2021 at 20:11
  • $\begingroup$ I can’t think of anything where literarily “nothing happens”. Anyway, Cheerio! $\endgroup$
    – Bob D
    Commented Aug 11, 2021 at 20:19
  • $\begingroup$ I can't imagine 'nothing'! Tue nothing, that is... ;-) $\endgroup$
    – Gert
    Commented Aug 11, 2021 at 20:21

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