4 ms·

So it would overflow, right, dependent on how much of the cubes extend above the surface?

dredmorbius 13y ago
What is Archimedes' principle? How does it relate to density? What is the association of density to volume? What happens to ice as it melts (or water as it freezes)?
- webspekt 13y ago
  The puzzle had me fooled twice (after 2 seconds: water level sinks, after the article: solution cant be determined), but thanks to your hint it finally dawned on me
- Unosolo 13y ago
  Since water reaches its peak density at about 4 °C, the actual outcome will vary slightly depending on the initial and the final temperature of the water once the ice has melted.
  - spindritf 13y ago
    The final temperature of water right after the ice melts will be ~0°C.
    - dredmorbius 13y ago
      Not necessarily. _Melted_ ice is 0°C. The result of ice + water depends on the quantities and starting temperatures of both. You could have very cold ice in water resulting in freezing the entire volume. Or small amounts of warm ice in water resulting in water well above the freezing point.
  - typon 13y ago
    No it wouldn't. The outcome will be the same regardless of the temperature, given the context of this problem. And the context is that the ice cubes are FLOATING, and that the temperature is hot enough for the ice to melt.
  - Unosolo 13y ago
    spindritf, not necessarily, we don't know the initial temperature of the water and on a hot day (as per the problem statement) the ice-water system will be absorbing some of the external energy. In practical world, more likely that water will start at around 20-25°C mark and will be considerably cooler once the ice has melted but still above 4°C. So the water volume is likely to shrink a tiny bit due to the rising density and then some more due to ice and water evaporation. But the effect might be barely noticeable and for some time water will stay level with the edges after ice melted.
  - dredmorbius 13y ago
    I think that the standard form of this question assumes that the water+ice is initially at 0°C, so that there's no net warming of the water, only latent heat of melting. Conversely, one could compute what relative volumes of ice and water would be required to arrive at a final temperature above 0°C. It's also possible (actually: likely) for ice to start at some temperature below 0°C, typically around -12°C for home refrigerator/freezer units. So let's say we're starting with room-temperature water at 22°C, ice at -12°C, and a ratio of 50-50 water to ice, 100g total. Latent heat of fusion for water is 80 cal/g, and latent heat is 1 cal/g. We're heating 50g of ice by 12°C and then melting it. Additional heat, if necessary, is drawn from the environment. The ice absorbs 200,000 calories. Subtracting 200,000 calories from the 50g of water would cool it by 4000°C, not counting heat of fusion, or would pretty much freeze all of it solid, if we do. Or conversely, the water can release at most 1100 calories of heat energy before freezing. Working backwards, we find that our 50g of water would require only 12g of ice to cool it to 0°C, or a ratio of roughly 1g ice to 4.2g water.
nkoren 13y ago
It's a trick question. The question creates doubt because it asks you to choose between two wrong options. [Edit: no, it gives all three possibilities; I speed-read through that. Thanks to others for pointing that out. However it then does predominantly focus on the question of "up or down?", which isn't the right question.] Ice is lower density than water, which is why it floats. As the ice melts, the runoff from the above-surface ice will raise the water level -- but the shrinkage from the below-surface ice will lower the water level. Assuming the above-surface and below-surface ice melts at the same rate, the water level will remain unchanged. (Note that if this were a glass of hot water in a cold room, then you'd get non-uniform heating of the ice. The subsurface ice would melt first, causing the level of the water to lower, until the above-surface ice melted, at which point the water level would return to its original level. On the other hand, a glass of cold water in a hot room would initially overflow while the above-surface ice melted, and then its water level would lower when the subsurface ice melted. So the answer to the original question is, depending on context, either "neither" or "both".)
- kaybe 13y ago
  The ice is floating, it would just lie higher or lower in the water depending on what melted first. No change of water level.
- jessriedel 13y ago
  > The question creates doubt because it asks you to choose between two wrong options. I think you misread the post: > Does it rise and over-flow the glass, remain constant throughout the melting process, or go down? Also, > Assuming the above-surface and below-surface ice melts at the same rate You don't have to assume anything about ice melting rates. All the info necessary to solve the problem is provided.
- croddin 13y ago
  It isn't a trick question. The article gives all three possibilities.
  - nkoren 13y ago

What is Archimedes' principle? How does it relate to density? What is the association of density to volume? What happens to ice as it melts (or water as it freezes)?

webspekt 13y ago
The puzzle had me fooled twice (after 2 seconds: water level sinks, after the article: solution cant be determined), but thanks to your hint it finally dawned on me
Unosolo 13y ago
Since water reaches its peak density at about 4 °C, the actual outcome will vary slightly depending on the initial and the final temperature of the water once the ice has melted.
- spindritf 13y ago
  The final temperature of water right after the ice melts will be ~0°C.
  - dredmorbius 13y ago
    Not necessarily. _Melted_ ice is 0°C. The result of ice + water depends on the quantities and starting temperatures of both. You could have very cold ice in water resulting in freezing the entire volume. Or small amounts of warm ice in water resulting in water well above the freezing point.
- typon 13y ago
  No it wouldn't. The outcome will be the same regardless of the temperature, given the context of this problem. And the context is that the ice cubes are FLOATING, and that the temperature is hot enough for the ice to melt.
- Unosolo 13y ago
  spindritf, not necessarily, we don't know the initial temperature of the water and on a hot day (as per the problem statement) the ice-water system will be absorbing some of the external energy. In practical world, more likely that water will start at around 20-25°C mark and will be considerably cooler once the ice has melted but still above 4°C. So the water volume is likely to shrink a tiny bit due to the rising density and then some more due to ice and water evaporation. But the effect might be barely noticeable and for some time water will stay level with the edges after ice melted.
- dredmorbius 13y ago
  I think that the standard form of this question assumes that the water+ice is initially at 0°C, so that there's no net warming of the water, only latent heat of melting. Conversely, one could compute what relative volumes of ice and water would be required to arrive at a final temperature above 0°C. It's also possible (actually: likely) for ice to start at some temperature below 0°C, typically around -12°C for home refrigerator/freezer units. So let's say we're starting with room-temperature water at 22°C, ice at -12°C, and a ratio of 50-50 water to ice, 100g total. Latent heat of fusion for water is 80 cal/g, and latent heat is 1 cal/g. We're heating 50g of ice by 12°C and then melting it. Additional heat, if necessary, is drawn from the environment. The ice absorbs 200,000 calories. Subtracting 200,000 calories from the 50g of water would cool it by 4000°C, not counting heat of fusion, or would pretty much freeze all of it solid, if we do. Or conversely, the water can release at most 1100 calories of heat energy before freezing. Working backwards, we find that our 50g of water would require only 12g of ice to cool it to 0°C, or a ratio of roughly 1g ice to 4.2g water.

nkoren 13y ago

It's a trick question. The question creates doubt because it asks you to choose between two wrong options. [Edit: no, it gives all three possibilities; I speed-read through that. Thanks to others for pointing that out. However it then does predominantly focus on the question of "up or down?", which isn't the right question.] Ice is lower density than water, which is why it floats. As the ice melts, the runoff from the above-surface ice will raise the water level -- but the shrinkage from the below-surface ice will lower the water level. Assuming the above-surface and below-surface ice melts at the same rate, the water level will remain unchanged. (Note that if this were a glass of hot water in a cold room, then you'd get non-uniform heating of the ice. The subsurface ice would melt first, causing the level of the water to lower, until the above-surface ice melted, at which point the water level would return to its original level. On the other hand, a glass of cold water in a hot room would initially overflow while the above-surface ice melted, and then its water level would lower when the subsurface ice melted. So the answer to the original question is, depending on context, either "neither" or "both".)

kaybe 13y ago
The ice is floating, it would just lie higher or lower in the water depending on what melted first. No change of water level.
jessriedel 13y ago
> The question creates doubt because it asks you to choose between two wrong options. I think you misread the post: > Does it rise and over-flow the glass, remain constant throughout the melting process, or go down? Also, > Assuming the above-surface and below-surface ice melts at the same rate You don't have to assume anything about ice melting rates. All the info necessary to solve the problem is provided.
croddin 13y ago
It isn't a trick question. The article gives all three possibilities.
- nkoren 13y ago