supersix2

I'm studying for my physics final and my prof gave us a practice test to take. I'm unsure about a question on it and the reasoning behind the answer.
The question asks:
A waiter in a restaurant fills a pitcher full of water and ice so that water would spill out if any more ice was added. As the ice starts to melt:
a. The water level in hte pitcher falls
b. the water level in the pitcher remains the same
c. water starts to flow out the spout of the pitcher
d. the pressure on the bottom of the pitcher decreases
e. the pressure on the bottom of the picther increases

I think the answer is (a) because ice expands when it freezes, its volume increases, and therefore when it starts to melt it takes up less volume and therefore the water level falls. The only basis for this conclusion is my personal observation of frozen water and the fact that ice is less dense than water indicating that its volume is slightly bigger since denisity is mass/volume.

Yakk

Note: he said water level.

Place a battleship in water, how much water does it displace?

Place an icecube in water, how much water does it displace?

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Last edited by JHVH : 10-29-4004 BC at 09:00 PM. Reason: Time for a rest.

KnifeMissile

It's hard to tell what your question. It sounds like you do understand the question and even your reasoning behind your answer is good...

Peetster

You are correct if you assume that some or most of the ice is forced under water by the weight of the ice above it. It will then displace more water than it weighs. a is correct.

As the ice melts, the volume will decrease, but you will still have the same mass of water. Therefore d and e are right out.

b would be correct if there was a small amount of ice floating freely in the water, as Yakk suggested with his ship analogy.

supersix2

I think I understand the question but my professor is tricky I was just wondering if my logic is correct and if it is not what is the proper logic.

Peetster

You would get bonus points for pointing out that the question does not give you enough information to choose between a and b.

supersix2

I hate questions like this. Its stuff like this that makes me hate physics which is bad since I am an engineering student. I have have resolved to try it experimentally.
BTW
Peetster sweet avatar I actually used that picture in a presentation about nuclear disarmament.

KnifeMissile

Damn it! I didn't think of that. Knowing this, I think the actual answer is b.

What's going on is that, yes, ice is less dense than water and, thus, it floats. If it floats, how much of it is floating above the water? Well, just enough so that the "virtual density," that is the mass of the ice divided by the volume of ice that's still submerged in water, is the same as water! You can figure the rest out...

Yakk

How much of the ice at the surface of the water would be pushed out of the water by the boyency of the ice under the water?

If the ice was fused into one solid chunk, would this change? If you broke it into two pieces, with a gap between them, would this change? 500 pieces?

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Last edited by JHVH : 10-29-4004 BC at 09:00 PM. Reason: Time for a rest.

Redlemon

I was just coming back to this thread to say essentially the same thing. I vote (b).

supersix2

So far the results of my experiment is showing that B is the right answer.

KnifeMissile

Of course it would. While the backbone of physics (and engineering) is experimental verification, I feel safe in saying that you could have just figured that out, yourself. Then again, I come from a mathematical background...

supersix2

Well I'm mathematical too but the simple concepts always mess me up.

Sapper

My cat's breath smells like cat food.

What we know:

1) the question deals with volume

2) by definition, density deals with volume

3) the density of water is 1.00 g/cm^3 @ 4'C and its density decreases as you increase or decrease temperature

of interest: as the water becomes warmer or cooler, its volume will increase by definition

4) according to Archimedes principle, the mass of water displaced by the submerged portion of the ice equals the volume of the ice displacing the water times its density

of interest: this means that as the ice melts (becomes more dense) it will displace less water but its volume also decreases proportionately

Ok - with what we know, the ice cubes will become more dense and thus have a lower volume (by definition) as they melt. We also know that the ice cubes displace a certain amount of water (raising the water level) due to the difference in density. We also know that the amount of water displaced by ice is proportionate to the volume of ice.

Sadly, not enough information is given to choose between a or b as was noted by Peetster.

You see, as the ice attains standard conditions, the volume will increase somewhere in the 3rd decimal place. We also lack knowledge of the initial water temperature - had it been at 4'C the volume would increase as the water attains standard conditions.

Consider this. Put a known mass of ice in the water and measure the water level (volume). Next, add the exact same mass of water as ice to the container. What happens? What would you expect?

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KnifeMissile

Volume times density is mass. Your first sentence has been greatly obfuscated by you saying "volume of the ice displacing the water times its density" when you could simply have said "mass."

I disagree with your (and Peetster's) assessment that there is not enough information to choose an answer. I believe that there is, as I have already stated in an earlier post. You are looking so hard for more information to help you with this problem that you have included too much of it. Not everything that you mentioned is relevant to this problem and much of it is too specific.

Then again, this is the mathematician in me talking.

Let's work backwards because I find it easier to think that way.
Say, you have a pitcher of water. The water level will be at some height. Now, suppose that we freeze a portion of the water. This will be our "icecube." This portion of water will expand and the water level will rise as a result.
However, because the icecube is now going to float to the top, a portion of it's volume, that was previously displacing the water and causing the water level to rise, will be floating above the water. Obviously, this portion is not displacing the water and, so, the water level will go down, again.
The question now becomes, by how much will it go down? This is the difficulty that Peetster was mentioning and the both of you are convinced that we don't have enough information to know.

I think we do.

According to Archimedes, the mass of water displaced by the submerged portion of the icecube equals the mass of the icecube (as paraphrased by Sapper).
So, what is the mass of the icecube? Well, it's the same as the portion of water it was made from! I mean, just because you froze some water doesn't mean you changed its mass, does it?
Since the mass is the same, we can safely conclude that the volume of water displaced by the icecube is the same as the volume of the ice cube when it was water!
Therefore, the water level will not change.
QED. (oh, there's that math, again!)

Sapper

Well, freezing the ice does not change the mass - it does change the density.

The portion of the ice cube not submerged is a fraction of the portion that is. This "undisplaced" mass is essentially negligible.

As it turns out, the volume of water displaced by the ice cube is proportionate to the differences in density between liquid water and ice. This turns out to be a very small ratio and as such, no difference in water level will be observed. Purely from a numbers perspective, the water level would however decrease at the point of final thaw (or at approximately 4'C).

Man .. studying for my physics final (which is tomorrow). I'm at equation #160 or so now ... yikes !

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stingc

No. Its not negligible unless you ignore the difference in densities between ice and water (which is the whole point of this problem).

The mass of water displaced by the ice is equal to the mass of ice.

So the volume of water displaced is (m_ice)/(density_water).

When all the ice has melted, its mass stays the same, so it contributes a volume (m_ice)/(density_water).

The volume is the same before and after.

KnifeMissile

I think you missed the point of the question. The interesting and, thus, important thing about the problem is that the water level will not change regardless of how much, or little, the density of water changes. So, even if ice was half as dense as water, it still wouldn't change the water level. Now, that's cool (mind the pun)!

It's analgous to why bodies fall at the same rate, regardless of their mass. Good luck with your physics homework...

rsl12

yeah knifemissile, i'm with you.

the only way that the answer would be other than B is if the ice were really really big and hollow and holding a significant quantity of heavy gas or something. or if you're talking about a situation where the cup sides are not perfectly vertical and the cup is bearing some of the downward force of the ice cubes instead of the water. (actually, since the problem says that the pitcher is filled to the brim, the issue is if the pitcher is concave and the pitcher is bearing some of the *upward* force of the ice cubes trying to float.) the density of ice does not come into play at all, just as long as it's less than the density of water (so that it can float).

knifemissile explained it well. i have nothing more to add other than sapper, you really need to work on seeing the difference between negligible and significant factors in a given situation.

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Yakk

How can the water itself increase in volume?

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Last edited by JHVH : 10-29-4004 BC at 09:00 PM. Reason: Time for a rest.

Peetster

Water increases volume when it freezes into ice. That's why ice floats. It's less dense.

Fill a pitcher with ice and water. If some of the ice is forced to completely submerge due to the weight of more ice above it, then those cubes will displace more water than the water needed to make the ice in the first place. When they melt, they no longer displace a greater volume.

a is correct in this case.

Redlemon

I disagree; while what you said is true for the individual cube that is submerged completely, there is another cube that is floating/exposed more than it would have.

I still say (b).

rsl12

the buoyant force must equal the weight of the ice. even if some of the ice cubes are completely submerged, you can add up the forces acting on each individual cube (ie, buoyant and weight). Or, alternatively, pretend that all the cubes are a funky-shaped single block of ice. it all leads to the same conclusion--the mass of water displaced = the mass of water in the ice. B is the answer, let's move on already.

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Yakk

Take a volume of water at 4 degrees celcius. This is the tempurature that water has maximium density (roughly).

Add in an ice cube that is -200 degrees celcius.

Note the water level.

The ice warms up, and the water cools down. Any size change in the ice cube won't change the water level. The water, however, will expand as it cools from 4 degrees towards 0 degrees.

The ice melting simularly won't change the water level.

Hence, if the water was 4 degrees at the start of the experiment, the jug would overflow.

If the water was higher than 4 degrees, and in melting the ice it didn't get colder than 4 degrees, the level of the water would drop.

If the water crossed 4 degrees, the result is indeterminate without more information.

If the ice melted without changing the tempurature of the water (say, the water was 0 degrees to start with, and the ice got the warmth out of the surroundings), then the level of the water would not change.

I believe the pressure comments are also equally indeterminate. The source of the pressure would be from the change in atmosphere above the jug or some other utterly neglidgable source.

However, on a physics test, the answer is b, unless you like including essays attached to multiple joice exams, or pointing out flaws in tests tot he prof during the exam.

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Last edited by JHVH : 10-29-4004 BC at 09:00 PM. Reason: Time for a rest.

rsl12

yakk: the difference in density between water at 4 degrees and water at 0 degrees celsius is about 0.01%. even if you were to fill up a pitcher PAST the brim, so that it looks like a souflee held together by surface tension, chances are that, by the time the ice melts and the temperature lowers to 0, 0.01% of the water will have evaporated.

you're argument is like answering the question "do you walk across the street on the red light or the white light" with the answer "it depends on the amount of traffic, which light you're talking about, what country you're in." all that's true, but geez...

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Yakk

Good point RSL.
Density chart for water:
http://www.ucdsb.on.ca/tiss/stretton/chem2/data19.htm

About the only reasonable one would be near boiling water cooled down by ice, thus lowering the water level.

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Last edited by JHVH : 10-29-4004 BC at 09:00 PM. Reason: Time for a rest.

Sapper

Oh me oh my .. practice what you preach.

What you are quoting is exactly what I had said when you told me I "really need to work on seeing the difference between negligible and significant factors in a given situation."

So then according to your holiness, what does this fall under? negligible or significant?

While you continue to argue symentics I will be off actually practicing science.

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rsl12

sapper, you were correct about the density of water being negligible. you were incorrect about the amount of ice above the water level being negligible. it would be more appropriate to say that the amount that is above the water level doesn't matter, because even if ice were very fluffy and most of it floated above the surface, it's still true that mass of water displaced = mass of object floating. There's a difference between a factor being negligible and a factor making no difference.

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Sapper

lol .. as I said .. continue debating your definitions of negligible and significant.

IF you believe in math/science, the significant portion refers to any difference beyond your least accurate measurement. Even in a volumetric flask your accuracy is only +-0.02mL which is less significant than the difference in density of water.

But again, I encourage you to continue your attrition of verbatim.

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KnifeMissile

There is no hypocrisy here, holy or otherwise. The both of you agree that the change in water volume is negligible (although, I have a feeling it's not negligible across a phase change).

All that rsl12 was trying to say was that not only is the change in volume between ice and water negligible bit it isn't even significant in the sense that it didn't matter if it was not negligible, it still would not have affected the outcome.


Besides, I think it was clear that an assumption of the question was that the water volume didn't change according to it's temperature and that a volume change only occured when the ice melted. This is reasonable if you were to assume that the question was to be, both, answerable and interesting...

KnifeMissile

And while all of you argue... I will be off actually practicing engineering and whatever else I do when I'm not posting to TFP about what I do when I'm not on TFP and causing other people to wonder why I'd even bring these things up on this forum in the first place...

rsl12

sapper: my apologies--i thought you were the one who said that the density change of water with temperature was negligible for the situation. you didn't say that, so you weren't correct about that either. you just said that other comment about the amount of ice above the water level being negligible, which is wrong. sorry to prolong this silliness.

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supersix2

Ok well I talked to my physics prof. He said the answer is that the water stays the same. I pointed out that if there was a lot of ice compared to water that the level would drop and he agreed. However in this case the amount of ice compared to water was not enough to change the water level when the ice started to melt.

Peetster

I won't tolerate this. I never thought I'd have to warn a knowledge thread, but here you go.

Warned.

Sapper

Internet forums lack tone - I believe that you are taking my post to be to poignant.

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GM2

Seems to me the water runs over the brim of the pitcher. Here's why:

If even one more drop of water goes into the pitcher, it spills. But when the ice is cold, some of it pokes up above the surface of the water (and hence it also goes above the brim) because ice floats in water. Therefore, when the ice is completely melted, that water that was frozen and in a position above the brim initially, is now in the liquid part of the water below the brim. Thus, the water spills because it can't hold that extra amount.

Yakk

GM2, you are wrong. The amount of water displaced by the ice is equal to the amount of water displaced by the ice once it melts.

The only reason why the pitcher would overflow/go down is because of tempurature changes in the water itself. And that change is too small to detect in a real life situation, unless your pitcher of water contained near boiling water. ;-)

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Last edited by JHVH : 10-29-4004 BC at 09:00 PM. Reason: Time for a rest.

crow_daw

Even though this has been covered up and down, I still feel inclined to throw my two cents in. In the simplest way possible (Occam's Razor style).

The amount of space that is equal to the displacement of the ice cubes will be filled by the liquid produced by the melting of the ice. Therefore there will be no change in water level. The answer is B.

That is ONLY my opinion, I am not claiming to be 100% correct by any means.

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