1. ## Riddle

You have glass of water, with an ice cube floating in it. you mark the water level.
After the ice cube melts, will the level of the water go up, down or will it stay the same?

2. the weight of water displaced by the cube is equal to the weight of the icecube. If u take the ice cube out, the volume of water decreases by an amount of water whose weight is equal to the weight of the cube. Leaving the cube in, it will melt producing an amount of water which will have the same volume as the fraction of ice submerged under the water.

Therefore it will stay the same (I think!!!)

3. The water level will go up slightly, but less than what you would expect if you measured the volume of the part of the ice cube which is above the original water level.

4. If the water is pretty cold, the volume may shrink. Remember, water has max density (aka, lowest volume for a given mass) at 4 <sup>o</sup>C.

5. I think John is right. The water level will not change.

I hope this isn't all a load of cack, but here we go:

Call the density of the water &rho;<sub>w</sub> and the volume of the submerged portion of the ice cube V<sub>s</sub>. Now call the density of the ice &rho;<sub>i</sub>
and the volume of the ice cube V<sub>i</sub>.

Then by Archimedes' principle

&rho;<sub>w</sub>V<sub>s</sub>g = &rho;<sub>i</sub>V<sub>i</sub>g

The weight of the ice cube is equal to the weight of the displaced water.

Now, by re-arrangement

&rho;<sub>w</sub>/&rho;<sub>i</sub> = V<sub>i</sub>/V<sub>s</sub>

Now when the ice melts, the density of the frozen water becomes equal to that of the rest of the water in the cup, so the left side of the equation is equal to 1. Therefore the right side must also equal 1. So the volume of the water from the ice cube is then equal to the submerged portion of the ice cube.

I think that's valid.

6. ... so if the polar caps(*) melt, there is no need to worry! The water level will not rise

Bye!

Crisp

(*) at least the north pole, south pole might be different because it is land covered with ice, and not floating ice

7. ## re crisp

... so if the polar caps(*) melt, there is no need to worry! The water level will not rise
Are the polar caps floating on the oceans? Than it must be the rotation what keeps them stable. Strange they didn't move in the direction of the meridian. Possibly they are very symetric/centered in the middle....

8. Originally posted by Crisp
... so if the polar caps(*) melt, there is no need to worry! The water level will not rise
No that is different coz the icecaps are floating in water which is more dense than the water produced from the ice. This means that the sea level will rise (but not as much as u might think at first)

9. Hi!

I think the answer depends on the portion of the ice cube which is above the level of the water.

If one was able to mechanically submerge the ice cube, measure the water level, allow it to melt and re-measure the level, it would have gone down, based on the chemical properties of H2O.

However, different ice cubes will have different portions above the water level. I did a very little research into this idea many years ago, using icebergs, and if memory serves the average increase in water level from the melting of an average iceberg was very close to zero. I don't know if the situation for ice cubes is similar to that of icebergs, but I assume that it is.

Cheers!

10. Originally posted by John Connellan
No that is different coz the icecaps are floating in water which is more dense than the water produced from the ice. This means that the sea level will rise (but not as much as u might think at first)
I calculated 215 feet the sea level will rise... but I did this calculation in preperation for world domination. Correct me if my plan is flawed

11. No that is different coz the icecaps are floating in water which is more dense than the water produced from the ice.

Isn't the Northern polar ice cap frozen seawater?

12. If one was able to mechanically submerge the ice cube, measure the water level, allow it to melt and re-measure the level, it would have gone down, based on the chemical properties of H2O.

How so?

However, different ice cubes will have different portions above the water level.

How so?

Isn't the Northern polar ice cap frozen seawater?
All ice caps or glaciers are made of snow that has turned to ice. If the northern ice cap would melt, the effect on sea level would be minor because it's floating in water.

The southern ice caps and most glaciers, on the other hand, are formed above the sea level on dry land, meaning that if they melted, the sea levels would rise.

No that is different coz the icecaps are floating in water which is more dense than the water produced from the ice.

Isn't the Northern polar ice cap frozen seawater?
No, its freshwater

If one was able to mechanically submerge the ice cube, measure the water level, allow it to melt and re-measure the level, it would have gone down, based on the chemical properties of H2O.

yes but the ice cube in the original problem nor the icebergs in questoin are being mechanically 'kept' submerged.

However, different ice cubes will have different portions above the water level.

no they won't unless the property of the water (e.g. salinity) changed

16. Originally posted by John Connellan
If one was able to mechanically submerge the ice cube, measure the water level, allow it to melt and re-measure the level, it would have gone down, based on the chemical properties of H2O.

However, different ice cubes will have different portions above the water level.
You're misattributing Contrarian's comments to me.

17. Hi Guys! Couple of quick clarifications.

If one was able to mechanically submerge the ice cube, measure the water level, allow it to melt and re-measure the level, it would have gone down, based on the chemical properties of H2O.
Water is one of the few substances whose solid form is less dense than its liquid form(at least as it appears on Earth)

However, different ice cubes will have different portions above the water level.
I was assuming that an ice cube is not a uniform quantity. I have had drinks where the ice cubes are cylinders. Changes in these quantities will affect how much of the cube is above the water.

Consider two pieces of ice one 10ft high by 10ft wide by 10 ft deep and the other is 1ft high by a 100 ft wide by 10ft deep. The two pieces have the same weight and density but different portions of the piece of ice will be above the water level and as such the melting of these pieces of ice will raise or lower the water level by different amounts.

Cheers!

18. "Water is one of the few substances whose solid form is less dense than its liquid form."

I know this. But I think I get what you mean now. When you say "mechanically submerge" I suppose you mean to force the whole of the ice cube underneath the surface of the water, right?

"I have had drinks where the ice cubes are cylinders"

cube

n.

A regular solid having six congruent square faces.

"Consider two pieces of ice one 10ft high by 10ft wide by 10 ft deep and the other is 1ft high by a 100 ft wide by 10ft deep. The two pieces have the same weight and density but different portions of the piece of ice will be above the water level and as such the melting of these pieces of ice will raise or lower the water level by different amounts."

Well, you're just heaping more complexity onto the problem than the problem requires. Provided that it is not bobbing up and down, there should be the same proportion above the surface of the water regardless of the shape of the piece of ice. Assume that it is a perfect cube. Assume that it is floating still.

"Water is one of the few substances whose solid form is less dense than its liquid form."

I know this. But I think I get what you mean now. When you say "mechanically submerge" I suppose you mean to force the whole of the ice cube underneath the surface of the water, right?

"I have had drinks where the ice cubes are cylinders"

cube

n.

A regular solid having six congruent square faces.

"Consider two pieces of ice one 10ft high by 10ft wide by 10 ft deep and the other is 1ft high by a 100 ft wide by 10ft deep. The two pieces have the same weight and density but different portions of the piece of ice will be above the water level and as such the melting of these pieces of ice will raise or lower the water level by different amounts."

Well, you're just heaping more complexity onto the problem than the problem requires. Provided that it is not bobbing up and down, there should be the same proportion above the surface of the water regardless of the shape of the piece of ice. Assume that it is a perfect cube. Assume that it is floating still.
1. Yes, obviously you would have to force the cube underneath the water in the first case, I can see that that is confusing.

2. Yeah, I know the definition of a cube However, If you asked the average person to measure the "ice cubes" in their freezer you'd find they weren't cubes after all.

Also, I am pretty sure that a cube with sides of 2x in length will have different proportion of itself above the water than a cube with side of length x, based on things like buoyance etc..., but the math is too complicated for me to do right now.

More to the point, the queston of whether or not a melting ice cube will raise the water level depends on the amount of of the cube above water.

change in volume due to melting of the cube=decrease in volume of water from melting of submerged portion of "cube" plus increase in volume from melting of non-submerged portion of cube.

Hopefully, that makes more sense.

20. Also, I am pretty sure that a cube with sides of 2x in length will have different proportion of itself above the water than a cube with side of length x, based on things like buoyance etc..., but the math is too complicated for me to do right now.

Could you perhaps point me toward some references rather than just handwave? I have consulted several and they all say that bouyancy force is equal to the weight of fluid displaced, full stop. There is no mention of the shape of the object.

More to the point, the queston of whether or not a melting ice cube will raise the water level depends on the amount of of the cube above water.

Which is dependent on the relative densities of the water and the ice and the volume of the ice cube. We've already established that. Only you contend that this is also dependent upon the shape of the ice cube. Although, you have yet to substantiate that.

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