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?

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!!!)

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.

If the water is pretty cold, the volume may shrink. Remember, water has max density (aka, lowest volume for a given mass) at 4 ^oC.

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 ρ_w and the volume of the submerged portion of the ice cube V_s. Now call the density of the ice ρ_i
and the volume of the ice cube V_i.

Then by Archimedes' principle

ρ_wV_sg = ρ_iV_ig

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

Now, by re-arrangement

ρ_w/ρ_i = V_i/V_s

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.

... 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

... 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....

(*have overlooked your note)

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)

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!

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 :eek:

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?

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?

Originally posted by AD1
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.

Originally posted by AD1
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

Originally posted by AD1
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

Originally posted by John Connellan
Originally posted by AD1
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.

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!

"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.

Hi AD1

Originally posted by AD1
"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.:D

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.

Hi AD1:

Originally posted by AD1
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.

1-I was not talking about the buoyancy force, I was talking about the relative proportion of the cubes submberged.

I may be wrong about this, but my logic is as follows consider a cube of sides x the force compressing the water underneath a point on the bottom of a cube as x units. The distance the cube will sink into the water is directly related to that force in a given density of water.

Now consider a cube of sides 2x, the force compressing the water underneath each point on the bottom of the cube is 2x units, and the cube must sink twice as deep to have the same proportion of itself submerged as its cousin. Now, perhaps, it can be established that the distance a cube of x is submerged is exactly 1/2 that of a cube 2x, but the logic escapes me.

2.If you have doubts about different shaped pieces of ice having different portions submerged, please check out links on icebergs.

Cheers!

I was not talking about the buoyancy force

My apologies. You did say, however:

"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." [Emphasis my own.]

I may be wrong about this, but my logic is as follows consider a cube of sides x the force compressing the water underneath a point on the bottom of a cube as x units. The distance the cube will sink into the water is directly related to that force in a given density of water.

Now consider a cube of sides 2x, the force compressing the water underneath each point on the bottom of the cube is 2x units, and the cube must sink twice as deep to have the same proportion of itself submerged as its cousin.

Are the masses of the two cubes equivalent? Are their densities equivalent?

As I understand it, the proportion of an object submerged in the water is proportional to the density of the object and irrespective of its volume and shape. This is Archimedes' Principle (http://scienceworld.wolfram.com/physics/ArchimedesPrinciple.html). The force exerted on a body immersed in a fluid is equivalent to the weight of the displaced fluid. It follows from this that the proportion of an object kept above the water level is dependent only upon the relative densities of the fluid and the body.

That's how I understand it, anyway.

My apologies to AD1:

After careful reading of Archimedes principle, I find that I am wrong, the density is the principle which guides the proportion of a cube which is submerged.(In my defense, I hadn't taken this since junior high).

I was neglecting to consider that icebergs whose submerged portions do vary could also vary substantially in density.

As such, it follows that the height of the water after melting of the ice cube is unchanged in a closed system, anyway.

Cheers!

added in edit: In practise, the ice cube melting will serve to cool the water it is floating in which will slight alter the water level.

In practise, the ice cube melting will serve to cool the water it is floating in which will slight alter the water level.

Yes. But imagine performing the experiment with a glass of room temperature water and measuring the initial water level before an appreciable volume of ice has melted. Then allow the ice to melt and the water to once again rise to room temperature. Pretending none of the water evaporated, has the water level changed from the initial water level?

I found the following information.One important property of ice is that it expands upon freezing. At zero degrees Celsius, it has specific gravity 0.9168 as compared to specific gravity 0.9998 of water at the same temperature. As a result, ice floats in water.Using the above, I calculated that the water level would be the same after the ice melted. Obviously my intuition (see my previous post) was incorrect.

Perhaps one of you could check my logic and my arithmetic. I assumed the following. 10,000cc of water in a container with a 4X5 base and a height of 500cc One cc of ice put into container. Temperature zero Celsius so that the above densities could be used for calculations.IceWeight = .9168 grams

VolumeDisplaced = 0.916983396679336 — ( This is .9168 / .9998 )

NewHeight = 500.045849169834 — ( 500 + 0.916983396679336 / 20 )

MeltedIceVolume = 0.916983396679336 — ( .9168 / .9998 )

The volume of the melted ice is the same as the volume of water it displaced. The amount above the water is a misleading issue.

FinalHeight = 500.045849169834 ---- ( 500 + .9168 / .9998 )

I hope there are no typo's above.

I am guessing that the same conclusion would result if different amounts of water & ice were used and/or the sahpe of the contaner was changed.

With some logic, it looks as though the above could be proven as a general theorem, making suitable assumptions about temperature.

Someone mentioned that if the ice caps melted the sea level would not rise.. thats kinda right.

If the north pole melted the sea level would not rise; the amount above sea level is balanced out by the difference in greater space occupied by frozen water. This is possible because the north pole is just a floating chunk of ice.

However, if the south pole were to melt the sea level would rise. That's because the ice of the south pole lies on an actual land mass (or a lot of it at least). Since it would be unlikely that the north pole would melt without the south pole also melting polar ice melting = bad.

Originally posted by Dinosaur
The volume of the melted ice is the same as the volume of water it displaced. The amount above the water is a misleading issue.


Absolutely coz the more seen above the water, the more unseen under the water! They both cancel out and it is the SAME proportion above the water always (contrary to some peoples opinion on this thread!).

With some logic, it looks as though the above could be proven as a general theorem, making suitable assumptions about temperature.

Call the Volume of the ice cube V₁ and its volume once it has melted V₂ and the densities of the respective states ρ₁ and ρ₂. Its mass is constant, so

ρ₁V₁ = ρ₂V₂ (1)

The proportional change in the water's volume (V₂/V₁) as it changes from solid to liquid is (ρ₁/ρ₂). And

V₂ = V₁(ρ₁/ρ₂) (2)

Calling the volume of the submerged portion of the ice cube V_s, the buoyancy force acting on the ice cube as it floats in the water is

F_b = ρ₂V_sg (3)

This is equal to the weight of the ice cube, so

ρ₂V_sg = ρ₁V₁g (4)

Both sides multiply by g, so

ρ₁V_s = ρ₁V₁ (5)

What is the volume of the submerged portion of the ice? It is:

V_s = V₁(ρ₁/ρ₂) (6)

The righthand side is identical to equation (2). Therefore

V₂ = V_s (7)

And that means that when the ice melts, it shrinks to a volume equal to that of its submerged portion.

How's that for an attempt?

I wonder about icebergs in the ocean. I think they are almost pure water, while the ocean is salty and more dense than ordinary water.

The arithmetic might not work out the same for fresh water ice floating in salt water. The ice would float higher in a more dense liquid.

Will a saturated solution of salt water freeze out and produce salt crystals at a temperature well below zero?

I thought that salt water froze with the salt still in solution. I am not sure of this.

Originally posted by Dinosaur
I thought that salt water froze with the salt still in solution. I am not sure of this.

What, u mean ice will form in one part of the container and salt will remain in solution in liquid water in another part? In that case I am right, the salt will have to precipitate out coz the water is already saturated.

Correct me:
Solid water reaches it's minimum density at a few degs below freezing point, and liquid water reaches its maximum density at 4 deg C, provided that for both cases the pressure is constant.

Originally posted by curioucity
Correct me:
Solid water reaches it's minimum density at a few degs below freezing point, and liquid water reaches its maximum density at 4 deg C, provided that for both cases the pressure is constant.

OK I would have thought that like most solids, the minimum density of ice would be just below its melting point. In other words as u cool ice, it becomes more and more dense. Im not sure about this. Whats ur point anyway?

Just wanting to know. Nothing yet in particular...

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?

Water is unique in the fact that it expands when frozen. Considering this I would assume that the water level drops after the ice has melted given the ice cube displaces more water than its liquid state. Of course a certain percentage of the ice cube would be above the water level before melting. The difference in the volume of the frozen water below the water level and the volume of the entire "iceberg" as liquid should determine your answer.

Right??

Azcool, there are posts in this thread between yours and the original post. Are you aware of that?

Yes I am aware, thank you.

John Connellan: I have no ideas about freezing a saturated salt water solution water, other than the common knowledge that the salt water freezing point is below the fresh water freezing point.

I thought that the salt froze along with the water rather than precipitating out of the solution. Id est: I expect that freezing salt water would result in salty ice cubes, but I would not bet money on my opinion.

Originally posted by Dinosaur
I thought that the salt froze along with the water rather than precipitating out of the solution. Id est: I expect that freezing salt water would result in salty ice cubes, but I would not bet money on my opinion.

Yes that was my first thought too, that the salt would get caught up in the crystal lattice but an experienced colleague (and physics teacher) said that the water would freeze without salt in it!

So, to make salty ice, can we keep some salty water in a perfectly closed contained and freeze it suddenly? Or would it still result in pure ice separated from now even saltier water? Or perhaps the water freezes, leaving ALL the salt solid?

Like I said, apparently at a low enough temperature, all the water will freeze precipitating out the salt!

Which means the salt will be left as solid?
A bit related to that: I heard that some solutions can be frozen without separating the water and the solluble materials. Is this true?

Originally posted by curioucity
Which means the salt will be left as solid?
A bit related to that: I heard that some solutions can be frozen without separating the water and the solluble materials. Is this true?

Like I said, thats what I believed until my esteemed colleage said otherwise but I have often proved him wrong in arguments so if u could find out about that experiment (maybe provide a link) then I would love to know!

Assuming that the salt precipitates out as the salty water freezes, I wonder what the resulting mixture would be if a container of salty water were frozen. Possibilities: All the salt at the bottom of the container, assuming a salt more dense than water/ice. All the salt on top of the ice, assuming a salt less dense than water/ice. Chunks or small grains of salt interspersed as impurities in the ice.It would be difficult to freeze every small volume of the solution at the same time (or at very close to the same instant). If the solution froze first near the container walls, top, & bottom first and at the center last, I would expect some salt interior to a large block of ice.

Actually, I would expect regions of salt interspersed with ice, but would not bet money on this intuition without doing an experiment. Perhaps a region of salt would cause ice above/below it to melt slightly, allowing the salt to gradually sink/rise to the bottom/top of the container, depending on the density of the salt.

Note that water (and/or other substances) freezing, melting, boiling have a latent heat of fusion/evaporation. As a substance is cooled/heated and reaches a transition temperature, removing/adding heat does not change the temperature until all of the substance is frozen, melted, boiled. This is a local approximation to reality, but is a reasonably accurate description of global effects if the cooling/heating is uniform or if a substance being cooled/heated is stirred. Even motion at the molecular level fights an attempt to get part of the substance at a temperature different from the transition temperature before all the substance is in one state.

Id est: It is difficult to get a large amount of ice below the freezing point until all the water has frozen; It is difficult to get a large amount of water above the freezing point until all the ice has melted. In a large container with the cooling/heating device acting at small surface area of the container, you can get effects counter to this principle, but the principle works hard to keep all of the substance at the transition temperature while freezing, melting, boiling is still occurring.

Assuming that the salt precipitates out as the salty water freezes, the heat of fusion effect might cause complete separation of the salt and the ice.

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?

You are all mother fucking nerds and should be stabbed. who gives a fuch about an ice cube melting in water, just drink the fucking shit before i piss in it.

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?

You are all mother fucking nerds and should be stabbed. who gives a fuck about an ice cube melting in water, just drink the fucking shit before i piss in it.

fuck you nerdy ass mother fuckers arguing over fucking ice in a cup. have any of you ever been laid? you should geta fucking girlfriend and just drink the water before i piss in it

smoke sum :m:

penis

i dont live in an egg

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