Water Level Changes in a Beaker with Melting Ice: Exploring Pressure and Density

[RAHIL008]

What happens to the level of water in a beaker when a block of ice floating in it, melts?
Does it go up, down or remains same?
What is the reason?

 

[Doc Al]

What happens to the level of water in a beaker when a block of ice floating in it, melts?
Does it go up, down or remains same?

What do you think and why?

 

[RAHIL008]

Sir first thought that comes in my mind is that level should remain intact as volume displaced by ice cube will be compensated by the water in it(Archimedes principle).
But at second thought, i heard that ice is lesser dense than water, in that case level should come down.
But why ice is lesser dense as solids are denser than liquids?
Sir you only answer please.

 

[Doc Al]

Sir first thought that comes in my mind is that level should remain intact as volume displaced by ice cube will be compensated by the water in it(Archimedes principle).

Good.

But at second thought, i heard that ice is lesser dense than water, in that case level should come down.

If ice wasn't less dense than water it wouldn't float, would it? But how does that change your conclusion from Archimedes' principle?

 

[RAHIL008]

Ok,I got it, if ice would have been denser than water(like a stone or something), it would have sunk.
But do you want to say that that virtue of ice being lesser dense does not affect the fact of Archimedes principle?
But I think that Archimedes principle applies only to an object of particular volume being submerged or taken out of liquid, but here, the object taken out is also releasing some liquid as well.
So, in that way, level should rise, shoudn't it?

 

[Doc Al]

But do you want to say that that virtue of ice being lesser dense does not affect the fact of Archimedes principle?

I do.

But I think that Archimedes principle applies only to an object of particular volume being submerged or taken out of liquid, but here, the object taken out is also releasing some liquid as well.

Archimedes' principle states that the buoyant force experienced by a submerged object will equal the weight of the displaced fluid. Since the ice is floating, the buoyant force must exactly equal the weight of the ice.

So, in that way, level should rise, shoudn't it?

No. Note that a given amount of ice will melt to an equal weight of water.

 

[Studiot]

Instead of talking around the subject, draw yourself a picture.

It's obvious then.

Think of icebergs.

 

[Grimstone]

Ok,I got it, if ice would have been denser than water(like a stone or something), it would have sunk.
But do you want to say that that virtue of ice being lesser dense does not affect the fact of Archimedes principle?
But I think that Archimedes principle applies only to an object of particular volume being submerged or taken out of liquid, but here, the object taken out is also releasing some liquid as well.
So, in that way, level should rise, shoudn't it?

displacement value of the liquid vs the displacement value of the solid.

the water level would go down.

The ice has a larger displacement value than the liquid it is made of.

 

[Doc Al]

displacement value of the liquid vs the displacement value of the solid.

the water level would go down.

The ice has a larger displacement value than the liquid it is made of.

Untrue, and that's the entire point. The amount of water displaced by the floating ice is equal to the volume of water obtained from melting that ice. (Note that only part of the ice is displacing fluid--the part under the water surface.)

 

[fillipeano]

The ice is displacing water equal to the volume that is submerged.
When the ice melts, the displaced water is replaced with the water from the melted ice (As Doc Al said, only the ice under water is displacing the water). Therefore, the water level will remain the same.

 

[sophiecentaur]

Archimedes talks of Weight causing the displacement. The weight of the ice / melted ice stays the same on melting and so will the displacement.
I have heard a number of smartypants alternative answers involving considerations like the transfer of latent heat from water to melting ice and the consequent change of the density of the original water in the bath as it cools down.
Also, the ice is dropped overboard from a boat. Does that make a difference?
OR, a lead weight is dropped overboard etc. etc.

The most interesting discussion, however, is about the simplest (original) scenario

 

[Studiot]

simplest (original) scenario

I too like the title.
After all what is molten ice?

:rofl:

 

[JaredJames]

After all what is molten ice?

Yet, for some reason when I picture the 'scenario' I see it glowing red hot and flowing like treacle. :uhh:

I worry myself at times.

Interesting question though, particularly when you consider whole issue around the arctic melting and how doesn't affect sea levels as much as people believe it will.

 

[Grimstone]

Untrue, and that's the entire point. The amount of water displaced by the floating ice is equal to the volume of water obtained from melting that ice. (Note that only part of the ice is displacing fluid--the part under the water surface.)

Water freezes and it expands. this is why your Pepsi can explodes.
this is also why your water bottle can and often will break.
want to test this? take a mason jar, fill it to the lip. cap it and freeze it. be ready for the clean up.
I don't have to know the formula's to know that water expands as it freezes, thus its displacement value is greater than it started.
Thus the water level would drop.

 

[Born2bwire]

The water in the ice tray is up to the top of each "cube".
Water freezes and it expands. this is why your Pepsi can explodes.
this is also why your water bottle can and often will break.
want to test this? take a mason jar, fill it to the lip. cap it and freeze it. be ready for the clean up.
I don't have to know the formula's to know that water expands as it freezes, thus its displacement value is greater than it started.
Thus the water level would drop.

The fact that water expands when it freezes is why a block of ice is not submerged when it is placed in water. Only the volume of the ice that is equivalent to its volume when liquid is submerged in the water. Hence, when the ice melts, the volume that it was displacing will be replaced by the resulting water.

Again, take note of the fact that not all of the ice is submerged when it is placed in water. Thus, the volume displaced by the ice is not as large as the volume of the ice itself.

 

[Phrak]

That a floating object displaces it's weight in fluid, whether ice or otherwise, is no obvious intuitively. As I understand it, many physical science teachers find it very mysterious and come up with all kinds of peculiar and sometimes erroneous answers to explain it, as well as textbook errors.

That buoyancy is independent of shape isn't really not as simple as it appears. It's a variety of Stoke's theorem in disguise.

$$\int_{\partial\partial\Sigma}F =\int_{\partial\Sigma} P = \int_\Sigma \rho = M$$

F is the dual vector weight, $F=F_\mu dx^\mu$. P is a two form, $P=P_{\mu\nu}dx^\mu \wedge dx^\nu$, whose bases is a directed area. Rho is the density difference as a function generalized coordinates, $\rho = \rho_{\mu\nu\sigma} dx^\mu \wedge dx^\nu \wedge dx^\sigma$. So already Archimedes principle is restricted to incompressible fluids. M is the scalar mass difference.

This is enough to send a man streaking a major metropolis. Even in Cartesian coordinates it only simplifies to vector calculus for arbitrary shapes.

 

[Grimstone]

we are still talking about a beaker and a ice cube.
If a iceberg was used, I would nod in agreement with you.
But place a ice cube in your tea, and all but a smidgen is under the surface.

 

[Born2bwire]

we are still talking about a beaker and a ice cube.
If a iceberg was used, I would nod in agreement with you.
But place a ice cube in your tea, and all but a smidgen is under the surface.

That is because there is only a slight difference in the density between ice and water. Salt water has a higher density than pure water and thus the relative difference between the density of salt water and ice is greater. Regardless, the fact that a smidgen is above the surface is enough here. As long as some of it is above the surface then we know that the water level will not change upon melting. If the ice cube did not float but sank then we could not make the same assumption (or if the liquid was not the same substance as the cube).

 

[sophiecentaur]

At the end of the day, which parts of the wate in the beaker are ex-ice and which bits are original?
The compressibility of water is a few magnitudes removed from this effect and its explanation, I think. The anomalous expansion of water is what it's all about. Without it, the ice wouldn't float and there would be no question.
Imagine a block of sub-zero ice, nearly as big as the beaker. If the water didn't actually freeze, the level (after thermal equilibrium with thr room) would be less in the end.
Too complicated and not what the man who penned this question way back in history intended, I think.

 

[S_Happens]

Water freezes and it expands. this is why your Pepsi can explodes.
this is also why your water bottle can and often will break.
want to test this? take a mason jar, fill it to the lip. cap it and freeze it. be ready for the clean up.
I don't have to know the formula's to know that water expands as it freezes, thus its displacement value is greater than it started.
Thus the water level would drop.

I think the point that you are missing, which born2bwire has already stated and that I will try to restate, is that that you are only considering the ice that is level with the water or below. There IS indeed ice above the water level. You cannot claim that ice is less dense than water, will cause mason jars to explode, and then also say that the amount of ice above the water level in your glass of tea (how about just water) is negligable. Ice is either less dense than water, can cause jars to explode, does indeed stick up above the water level, or it is/does none of these.

If you were to melt only the volume of ice that is originally equal to the water line or below and remove the original volume of ice that stuck out of the water level, then yes the water level would drop. But you'd still have extra ice. If you account for all the ice that is both above and below the water level, then the level will not change as has been repeatedly stated.

 

[Studiot]

All too often, and especially in elementary texts, the floating of ice is attributed to the anomalous density v temperature curve for water.

This is true in fresh water.

It is generally untrue in water containing a significant quantity of dissolved material.

For example the density v temperature curve for seawater decreases monotonically to the freezing point.

Icebergs float because ice in the sea contains a significant quantity of entrained air. This is why they are less dense.

 

[kchikage]

But isn't the density of an ice and liquid water differs because of the chemical structure where they are bonded?

The water-molecule in solid ice is hydrogen-bonded to 4 other molecules; while the water-molecule in liquid is hydrogen-bonded to 3.4 other molecules. Noticed that there are more empty spaces in a solid ice structure than liquid water structure, so, there are actually fewer molecules in the solid ice compared to liquid water of a same volume. Thus, the slight difference in density.

So, even if ice floats 10% in liquid water, the weight it displaced in the water is still equal to the weight it is and will has when it melts to liquid.

 

[Grimstone]

That is because there is only a slight difference in the density between ice and water. Salt water has a higher density than pure water and thus the relative difference between the density of salt water and ice is greater. Regardless, the fact that a smidgen is above the surface is enough here. As long as some of it is above the surface then we know that the water level will not change upon melting. If the ice cube did not float but sank then we could not make the same assumption (or if the liquid was not the same substance as the cube).

What happens to the level of water in a beaker when a block of ice floating in it, melts?
Does it go up, down or remains same?
What is the reason?

Then we have a lack of information.
A. Rahil did not say if the water was salty.
B. he did not state that the water had been taken from the beaker, then frozen.
C. I myself did not say that the density of the ice is what breaks the jar. it is the expansion of the ice as if freezes.
D. I would have to say the test is invalid due to lack of founding facts.
E. Also it was not stated if the water was marked before or after the ice was added.
before. then its going to go up. (you added water).
After it will go down. (due to displacement. or lack there of)

I am just a guy with 2 brain cell's more than the average joe, who thinks he has 4.
I don't know about the molecular bonding. I just know that ice has a higher displacement value than water its self.

Unless...
Unless the ice's density is higher than water, with a higher displacement value.
of which case the water level would go up, based on more water being added to the beaker.

 

[Grimstone]

So, even if ice floats 10% in liquid water, the weight it displaced in the water is still equal to the weight it is and will has when it melts to liquid.

I'm not debating this for the fun of it. I am actually trying to learn as well. If I am in error, I like to know so. and learn from my mistakes.

As i understand, the displacement value of a object is more about the volume it takes up. not its mass.
a 1inch cube of steel and a 1 inch cube of lead would displace the same amount.
right?

 

[JaredJames]

Then we have a lack of information.

No, we have all we need.

A. Rahil did not say if the water was salty.

That has no bearing on the particulars of the problem.

B. he did not state that the water had been taken from the beaker, then frozen.

Either way, the water level once the ice is put in will remain constant even when ice has melted.

C. I myself did not say that the density of the ice is what breaks the jar. it is the expansion of the ice as if freezes.

I'm not sure anyone said you did or claimed that (I'm not reading back through now).

D. I would have to say the test is invalid due to lack of founding facts.

Nope, again we have all we need.

E. Also it was not stated if the water was marked before or after the ice was added.before. then its going to go up. (you added water).

If you added water then the level will increase on insertion of the ice - but that level will remain constant as it melts.

After it will go down. (due to displacement. or lack there of)

What are you talking about? The level won't drop. See above.

Unless the ice's density is higher than water, with a higher displacement value.
of which case the water level would go up, based on more water being added to the beaker.

Correct, but ice has a density less than water so it's an irrelevant issue.

 

[JaredJames]

I'm not debating this for the fun of it. I am actually trying to learn as well. If I am in error, I like to know so. and learn from my mistakes.

As i understand, the displacement value of a object is more about the volume it takes up. not its mass.
a 1inch cube of steel and a 1 inch cube of lead would displace the same amount.
right?

Correct. Both would displace the same amount. It's only when you bring buoyancy into the equation you introduce the mass. At which point the displacement value can change.

For example: A ship will displace a volume of water with equal mass to itself - but the volume displaced does not equal the volume of the object. This is true for anything less dense than the fluid (in this case water) that is floating on that fluid.

 

[sophiecentaur]

When it sinks it will displace its volume. When it floats it will displace its weight- once it has displaced tht amount of water, the upthrust will equal its weight.

Once you know the exact conditions of the water and the ice (temperature, salinity, actual volume / mass of each etc. etc) you could determine the level of the water in the beaker at the time of immersion and then you could say what would be the final level, after the beaker an everything reached room temperature.
I would have said that the 'obvious' and assumed conditions would be distilled water at normal room temperature and pure ice that is just below 0C. The answer to that would be "no change" in level. If more, smartypants conditions apply then the answer can get smartypants too! Without limit, possibly.

 

[Doc Al]

I just know that ice has a higher displacement value than water its self.

An ice cube has a higher volume than an equal mass of liquid water. But the amount of water that a floating ice cube displaces is the amount of its volume under the water surface. That turns out to be exactly equal to the volume of water that will be created when that ice cube melts.

 

[sophiecentaur]

I'm off for a bath. If I displace more than the available freeboard of the bath, it may overflow. I shall then leap out and run naked down the street shouting Eureka. I shall call all of you in my defence to the Magistrate.

 

[Grimstone]

I'm off for a bath. If I displace more than the available freeboard of the bath, it may overflow. I shall then leap out and run naked down the street shouting Eureka. I shall call all of you in my defence to the Magistrate.

Do make sure its a WARM bath.

 

[Grimstone]

An ice cube has a higher volume than an equal mass of liquid water. But the amount of water that a floating ice cube displaces is the amount of its volume under the water surface. That turns out to be exactly equal to the volume of water that will be created when that ice cube melts.

So then the water level will not change in the least bit. assuming tht hte icecube flaots with as much as itself under the surface. (wich it will do).


How many can agrea with Doc Al?

 

[JaredJames]

How many can agrea with Doc Al?

There's nothing to disagree with. If anyone disagrees they don't understand the basic physics behind it.

 

[turbo]

Time for a simple science-fair-level experiment. Put water in a clear container, like a drinking glass, add ice, and use a sharpie to mark the water level. Come back later when some or all of the ice has melted, and check the water level vs the ink-mark. This would be a SLOW demonstration and would be a bit tedious. The best way to make this experiment fun for a science fair would be to use a web-cam to record the level as the ice melts, then speed up the loop on a laptop so people viewing the science-fair projects can see the process in its entirety.

 

[Studiot]

Like I said, draw a diagram then it's obvious.

 

[S_Happens]

I think you can just go back and read the posts to see that everyone agrees with Doc Al. It was stated and restated many times.