JamesTKierkegaard t1_j3qru2w wrote on January 10, 2023 at 12:58 PM

There is no right answer without knowing more about the system. All the previous answers hit on most of the salient details. One of the biggest factors will probably be surface area exposed to air. If the container is a poor conductor (e.g. glass) then the water filling the container might reduce that surface area and slow the system. If it's a metal container that would be less of a factor. Another factor to take into account is evaporation which will remove heat from the system, but how big a factor this will be depends on the temperature and humidity of the air. The ice can sublimate as well, but this is a much slower process than evaporation and I don't believe it's exothermic, but I could be wrong.

kilotesla t1_j3tz1rk wrote on January 11, 2023 at 1:22 AM

That's good advice that the specifics matter. Since there will be heat transfer by radiation as well as convection, the emissivity of the surface of the container also matters, and if it's polished metal, the low emissivity would retard melting. Also, if the thermal mass of the container is significant, its starting temperature would matter.

When considered in comparison to air, glass is not a poor conductor of heat. It's conductivity is 33 times higher than that of air, and it's likely pretty thin, such that the heat transfer through the air will be the dominant thermal resistance. Air of course has the advantage that it is moving and so carrying heat by convection, not just conduction but it's still going to be the dominant thermal resistance.

JamesTKierkegaard t1_j3ueydg wrote on January 11, 2023 at 3:14 AM

It's not glass compared to air that's the issue so much as compared to water or ice. The air is the environment in this situation so if the system is in a glass container the heat transfer to the air will be negligible compared to the surface area of the water and ice (which again depends on the shape of the container greatly). If it's a thin metal container then water remaining will probably win in most configurations simply because it will act as a convective exchange surface. Realistically, radiation is going to be a meager source of heat loss, even hot water radiators to heat houses only supply about 5% of their heat contribution through actual radiation, and that's at higher temperatures.

kilotesla t1_j3uolby wrote on January 11, 2023 at 4:27 AM

>It's not glass compared to air that's the issue so much as compared to water or ice. The air is the environment in this situation so if the system is in a glass container the heat transfer to the air will be negligible compared to the surface area of the water and ice (which again depends on the shape of the container greatly).

In a series circuit with a very low resistance resistor, a medium value resistor, and a large resistor, fed by a voltage source, the voltage drop across the medium value resistor is affected a lot more by the large resistor than by the smallest resistor. If we have 1 ohm, 33 ohms, and 1000 ohms in series, the drop across the 33 ohm resistor is 3% of the source value, even if we drop the 1 ohm resistor to 0.1 ohms. We can't conclude that the 33 ohm resistor will have a lot of voltage drop because it is huge compared to 0.1 ohms. That doesn't work.

The glass outer surface will be very close to the same temperature as the water. The heat flow per unit area is determined by the temperature difference between the water and ambient. If the outer glass surface were at 1 C instead of zero, the temperature difference with respect to ambient would not change significantly. And the surface temperature wouldn't even be that high.

>Realistically, radiation is going to be a meager source of heat loss, even hot water radiators to heat houses only supply about 5% of their heat contribution through actual radiation, and that's at higher temperatures.

5% is way too low. Modern "radiators" have fins which enhance convection but not radiation, so convention is typically larger, but radiation is still about 25%, even just counting the outward facing surface.
In the range of temperatures we are talking about, radiation is reasonably approximated by a linear function of temperature difference. Yes I know, that's counterintuitive with that fourth power, but it's T1^4 - T2^4 , not (T1-T2)^4. On the other hand, natural convection is nonlinear enough that it drops as a fraction of overall heat transfer when the temperature difference gets smaller.