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# Blocks of Ice: Newsletter Challenge (03/13/07)

Posted March 11, 2007 5:01 PM
Pathfinder Tags: challenge questions

The question as it appears in the 03/13 edition of Specs & Techs from GlobalSpec:

You have two blocks of ice with the same volume. One has a bubble of air inside, and the other one has an equivalent piece of iron inside. You put these blocks in two identical ponds. When the ice blocks melt, which pond will have a higher water level?

(Update: March 20 8:35 AM) And the Answer is...

When both blocks melt, the pond where you put the ice block with a bubble of air will have a higher water level. Let's consider both cases:

1) For the case of the ice block with the air bubble, the level of water after the block melts will be exactly the same as the level of water before the block melts because the displaced water is exactly the same as the volume of the water that came from the molten block.

2) For the case of the ice block with the pieces of iron, the level of water after the blocks melt is less than the level of water before the block melts because the volume of water displaced due to the iron piece exceeds the volume of the piece. According to the Archimedes' principle the amount of water displaced is proportional to its weight. Remember that an object sinks if it is heavier than the water it displaces.

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#1

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/12/2007 1:10 PM

Okay, the net amount of water in each block is the same, so they cancel out of the equation. All that is left after melting is air for one and iron for the other.

So the air (which turns out to be CO2) rises above the pond into the atmosphere. The iron settles into a deep dive and crashes a catfish party at the pond's bottom.

For the moment, the pond with the iron rises infinitesimally higher than its neighboring pond that received the ice with the air bubble. So the immediate answer is the iron laden pond is higher.

However, the released CO2 from the first block now causes a greenhouse effect and the mean temperature of the area rises 10°C and both ponds promptly evaporate in a puff of steam and Al Gore builds a new mansion on the mud caked remains.

Okay, I don't get this one, so what am I missing?

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#2

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/12/2007 3:26 PM

No, no, no. You have it all wrong. The extra CO2 melts the nearby glacier and the pond is now a lake.

Other than that, I thought along the same lines that you did. The iron raises the level.

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#5

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/12/2007 11:03 PM

Yikes! You are right! I should have checked Google Maps first. Nice catch!

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#4

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/12/2007 9:33 PM

"So the immediate answer is the iron laden pond is higher." Agreed.

"Okay, I don't get this one, so what am I missing?" Agreed.

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#7

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 12:26 AM

Love your answer, especially since the only person making out on this is the politician. Just like real life.

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#20

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 9:14 AM

But wait there's more

You forgot about the environmental impact study that will cost the taxpayers MILLIONS without doing anything but producing paper reports.

AND you don't even want to forget the department of natural resources and the army corps of engineers, who will spend even more to discover that a foreign material has been of loaded into the pond.

Then finally, what about the HAZMAT removal that will take YEARS to remove the now rusted out piece of iron.

Which brings us to the final question. When the iron finally rusts out. Will the pond return to it's natural water level?

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#21

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 9:37 AM

No, cos they used the water from both ponds to pulp the paper for their reports.

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#70

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 8:53 PM

Yes, and all the trees cut down to provide the paper reduced the size of the forest reducing the capaility to convert CO2 to O2.

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#64

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 6:25 PM

Why do we need one? Equal is equal.

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#77

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 1:25 AM

"The weight of the iron incased in the ice cube is pulled into the pond raising the level of the pond while the ice cube with the air floats and the level remains reletively the same."

I'm going to jump in here because I think this may be closest to the answer...

Consider that the ponds are full and that overflow is lost (neither condition is specified but what the... neither was global warming or glaciers, and it does affect the result)

As noted above, when floating, the cube with the iron will sink lower into the pond than the cube with the air (its density is higher). Hence it will displace more water, which overflows and is lost.

Now the ice melts. Since ice is less dense than water (it floats!) the volume due to the added water is less so the level drops, ie no more overflow. Ignoring the iron for the moment, it is clear that the level in the pond that had the iron ice cube will be lower due to more overflow. Now put in the iron. The volume will increase but less than the volume of water that was displaced when it was floating because iron is more dense than water (it sinks!)

The net result is that, given that the ponds are full and lose their overflow, the pond with iron ice cube will end up with a lower volume when they melt...

Whew!

Stephen

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#99

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 8:42 AM

Good as it goes but what happens in time when the iron starts to rust? I be interested to hear your chemical analyse's of the situation then.

john

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#107

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 9:55 AM

Assuming that the oxygen in the rust is derived from the water, the hydrogen floats away and the reduction in the volume of the water is greater than the increase in the volume of the iron->iron-oxide. But then iron-oxide encourages algal and other growth, so the volume already expands again.

Otherwise, otherwise.

Fyz

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#92

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 6:36 AM

You all are missing the bigger picture! What about the Catfish? They have rights!

Why are we dropping blocks of ice on them in the first place?

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#136

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/16/2007 2:28 AM

Laugh My Ass Off, man I wished I had thought of that one,,,,great thinking

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#122

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 4:51 PM

I wanted to retrieve the catfish (which got bonked on the head with the iron) for dinner but the game warden was right behind me with his tablet and pencil out. Oh Well....

Bill

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#166

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/20/2007 6:12 PM

The question says the ponds have the same volume BEFORE the ice cubes are put in. So, the displacement of the ice cubes before they melt doesn't matter. So basically, we can say we're adding equal amounts of water to each pond but adding steel balls to only one. Therefore the water displaced by the steel balls will make that one have higher level.

The "correct" answer is wrong by my estimation. Unless I'm missing something which is entirely possible. In fact, it's possible this is a meaningless question. Or perhaps an evil question in that it wasted 15 minutes of my time. But I'd only have been working so what the hell?

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#169

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/20/2007 8:01 PM

I just triuie id theea expoisiment witeh a ocupolc of iyc cubmvs 1 with aaaaaa ball bierring in it one witth bubbble werp in a tallllllllll glez of my favvorite scoch. NOOW wiaiting forr thatt dammn bball bearing to passs. Butt I zure feell a lottt betterr naouw. BUUT obzerved tha levvle of ths scotch keppt goingg down so had to refill mannny tmises

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#3

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/12/2007 3:33 PM

The one with the iron, as it's volume remains in the pond, thus adding to the total volume. dru-

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#6

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/12/2007 11:19 PM

It isn't much of a problem if the answers so far are so easy to come by!

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#8

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 2:42 AM

Unless...... the iron ball inexplicably bounces clean out of the pond?

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#9

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 5:30 AM

What is "equivalent" ? Mass or Volume ? This has to be a trick question , so we need to consider how could the iron laden pond end up with a lower level. Well an equivalent mass of air/iron would sort that one. Other thoughts - does the rusting of the iron come into this seemingly daft question ? Does the decrease in volume of water to ice have any relevence ( yeah I know the volume of ice MAY be the same ). Will somebody braver than me go and make big ice cubes in their partners freezer .

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#12

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 7:54 AM

this is probably a trick question as you have brought up. I was giving some thought to the aspect that both ponds would remain at the identical level. This is due to the fact that iron core would sink to the bottom of the pond and also sink into the mud layer at the bottom of the pond. The displacement of mud would be mostly if not all absorbed or become a horizontal shift and would represent no change what so ever. The air core of the other ice block would dissipate. Just a hunch.

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#14

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 8:05 AM

At first glance I thought your suggestion good , but mud at the bottom of the pond would be saturated - and compaction of the mud (by movement in any direction)would result from the iron weight forcing water out of it. Hence no change from compaction (I think !).Then again , it could be argued that rotting vegetation at the bottom would be trapping gasses that would be released by a weight.

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#24

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 10:10 AM

The temperature of both ponds are equivalent until the ice blocks melt, at which time the air bubble is released and that pond's temperature starts increasing. The iron drifts to the bottom but retains its thermal mass.

Would the block with the air bubble melt faster? If the ice blocks melt at the same rate, then the "iron" pond would be at a higher level at the instant the ice is melted and the air bubble is released since the water in the ponds would be at the same temperature. But, the air bubble will be released prior to the ice completely melting, and with water filling in the cavity of the air bubble, this block will melt quicker than the "iron" block of ice will due to the increased surface area. Thus I conclude that the ice with the iron melts slower than the ice with the air bubble.

So, it is possible that the water in the "air bubble" pond will be warmer than the "iron" pond at the point that all the ice is melted. If the volume of the water expansion is greater than the volume of the iron, the level of the "air bubble" pond will be higher.

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#102

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 9:36 AM

That will depend whether the "iron" is plugged in or not.

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#10

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 5:32 AM

The question does not mention what was in the ponds to start with.

So, assuming it was acid, the iron reacts, raising the temperature past the boiling point, and all evaporates to create havoc somewhere else, while in the other pond.....

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#11

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 5:45 AM

If the pond was in Vegas , the water in the air-bubble pond would evaporate quicker since the iron would slow down warming. What if it's a pond of something other than water ? OK I'm getting desperate !

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#13

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 8:04 AM

Although it isn't stated clearly ....... , it seems to me the "equivalent" piece of iron must mean "equivalent volume" of iron with the buble of air (nitrogen and oxygen).

So common sense tells us the iron block should initially float lower in the water than the "bubble block" and the "iron block" pond level should initially be higher.

After the blocks of ice have melted, the water volume of each pond remains the same (since the iron and air volumes have canceled each other out)...... however, the "iron" remains in its pond and the "air" floats to the surface of its pond. Therefore, the final pond level of the "iron" pond will remain higher as well.

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#15

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 8:18 AM

You could add to your reasoning; The 'air' block intially floats hence total surface area is higher, so total evaporation is greater.In addition the 'iron' pond is cooled longer and will loose its ice last , allowing longer evaporation time in the other pond.

It troubles me that the answer is 'obvious'.

If I offered to trade a bubble of air for an equivalent ammount of iron on e-bay I wander what I would be offered !

This thread could wind up as a lot of hot air

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#16

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 8:29 AM

What if equivalent applies for mass and not volume?

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#28

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 1:19 PM

Good, but that makes the iron cube pond even higher! There would be more water in the iron cube because air displaces what would be water in the air cube. Remember that the cubes have the same size and volume.

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#30

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 1:38 PM

I don't think so - the equal mass(iron=air) iron cube wold be lighter, but its total volume would be the same as for equal volumes(iron=air) before melting. Then the ice would shrink, so the total volume (water+iron) would be less than if the iron volume was the same as the air.

So, although the ponds with iron would be higher than the ponds with air in both cases, the additional volume increase for equal volume(iron=air) pond would be slightly greater than the volume of air before freezing (iron expands as it warms), whereas the additional volume for equal mass(iron=air) would be slightly less than the volume of air (ice contracts as it melts)

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#87

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 6:24 AM

The question states you have two cubes of equal volume.

The final state of the system is after the ice melts.

No matter how you shake it, the air, even if it is highly compressed into a massive bubble, will not contribute to the volume of the pond.

100% of the iron cubes volume contributes to the pond's level.

The air bubble cube can only contribute something less than 100% of its total volume.

Now, that being said, the only thing that could keep the iron pond's level lower is some trivial fact that was not revealed about the pond or cubes that will make everyone groan.

At this point I am only waiting to see if the answer is:

a) Something entirely stupid

b) Painfully simple (as in my first post) and belongs in a first grade quiz

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#113

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 11:51 AM

or C) see post 117.

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#80

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 2:50 AM

Yes. My earlier postings are about the answer being too obvious.Perhaps I was not clear enough -review all my comments. Maybe I'll stand back for a bit , since I jumped in earlier and I could end up spending my life replying replying to all repeat/obvious comments. No offence intended .

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#79

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 2:38 AM

look at my #9

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#17

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 8:30 AM

On another note, air could describe a variety of gases all of which everyone has assumed to be in equilibrium with the partial pressure between the lakes surface and the atmoosphere. Under those assumptions the iron ice cube wins everytime. what if pure radon is trapped in the ice cube which would eventually decay into daughter isotopes that would sink into the sediments and alter their chemistry. as well the iron dissolves, or reacts with the oxides in the water, all eventually taking up more volume than their trapped state in a frozen ice cube. I would suggest the iron ice cube would still win but the race between the tortois and the hair becomes suprisingly closer.

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#18

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 9:05 AM

presumably the one with the piece of iron which will displace its volume of water,whereas the air has gone and will not displace anything.

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#19

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 9:13 AM

The pond with the ice and iron

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#22

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 9:45 AM

and the pond is really a hot tub? then there'd definitely be more water in this one since i'd be jumping in too....:)

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#23

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 10:06 AM

Hmmm. Since the "volumn" of the two objects are equivalent, I suspect the water level won't rise or decrease. Instead, I suspect the density of the water will change, if anything.

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#25

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 10:28 AM

A possibility, maybe....

The challenge doesn't say if the ponds are frozen. If they are in fact frozen, when the blocks of ice are placed on the ponds, through sublimation, they will "melt", leaving the iron on top of the frozen ice, thereby leaving both ponds exactly the same height.

Then when the ponds unfreeze, (if they ever do) the one with the iron bar would become slightly higher.

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#117

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 12:42 PM

Yes the problem has too many variables

1. Size and temperature of the ponds.

they could be near the same volume as the ice cubes or massive.

2. Size and temperature of the ice and imbeded iron/air cubes.

they could be at 32deg F or near 0 deg K

3. Atmospheric temperature and humidity.

I think a piece of metal at -450 deg would become a much larger piece of ice in a small small pond giving a much longer time to melt, sublimate or evaporate and the atmospheric humidity would effect the colder and the warmer ponds differently.

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#26

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 11:45 AM

The bubble will join the atmosphere and not impact the level of the pond 1. The iron will add volume to pond 2 making it higher than pond 1

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#27

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 12:42 PM

Regarding "trick question*" - perhaps one crucial piece of information was omitted - the ponds become full (rain) at some point before the ice blocks melt. So they both overflow, but the one with the iron in the block loses more water, because the ice floats lower. When the ice melts, the the pond with the ice containing air stays full, but the level in the pond with the ice containing the iron becomes lower. Alternatively, it has been raining continuously and the ponds continue to oveflow, so the levels remain identical. In short, if it's a trick question, you can have any answer you like, depending on how you choose to define the conditions.

A slightly less trivial version of the question might compare placing blocks of ice in the ponds, with one containing a piece of iron, otherwise both blocks are solid ice, and both blocks are of the same external dimensions. What are the relative water levels both before and after the ice melts (assume neither pond overflows - and that any potential trickery is not deliberate)?

Fyz

*There is also the possibility that both blocks were placed in both ponds, sequentially - still unanswerable, and not worth the trouble.

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#29

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 1:37 PM

The iron wins again! At this point it is down to the coefficient of expansion of iron versus water when they warm up from thr freezing point to the STP or whatever.

Water expands when frozen, but contracts when unfrozen, then slowly expands. Iron does not undergo that reversal like water in its size.

Initially the iron cube also submerges more of its cube than the pure water cube, so the initial state and final states have the iron cube pond as the higher of the two.

Incidentally, the expansion rate really is splitting hairs when you consider it, but technically it exists, so ...

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#32

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 1:44 PM

I agree - the final difference is small, and the problem is only slightly less trivial.

I think we've already worked this "challenge" to "beyond death"

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#53

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 4:44 PM

I forgot to say - if the block with the iron still floats, the difference in levels will be about eight times the volume of the iron - not that trivial, perhaps?

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#31

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 1:42 PM

Hi Fyz, you wrote: "Regarding "trick question*" - perhaps one crucial piece of information was omitted - ..."

Yep, I also have an issue with questions that lack enough information...

Then, I presume that real life works like this - we never seem to have all the information at the start of any project! As such, this is a very good lesson for young engineers, for which I do not qualify, so I'll keep out of this one!

Regards, Jorrie

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#34

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 1:47 PM

Hi Jorrie

In real life, there needs to be the chance to aquire any critical information - or abandon the project. In this case, the rewards are insufficient in any event - so I'm abandoning (unless unexpected interest emerges)

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#83

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 4:38 AM

I agree with you , but as you say we never seem to have enough information at the start.This is after all a "Challenge" question , and Id like to give the editor benefit of the doubt for now (please God don't let this be the 'obvious' answer). Mind you , I thought the last Q was dodgy (an elastic ball bouncing up immediately it contacts the ground ? ).Like the ice I think I need to chill out on this one.

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#33

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 1:45 PM

I feel like Copernicus on this one. After all, he was wrong, too. I am from the midwest where we have many farm ponds. I have seen in almost all of them, a man-made dam with a spillway that maintains the pond water to a maximum level.

This is what happens to our model when put into the reality of a farm pond:

• Initially, the pond with the iron and ice reaches the level of the pond spillway, leveling it with a submerged ice cube. When it melts, a barely negligable change in volume occurs due to the temperature change in the iron.
• Conversely, when the ice cube filled with air floats on the water, it remains partially afloat above the water level of the pond. The pond spillway overflows and levels the pond to the level of the spillway. As the air-filled ice cube melts, more water fills the pond and it, too, is released over the spillway.

Eureka! The answer is that the ponds remain at the same water level beause of the spillway. However, if you measured the amount of water run over the spillway, the pond with the iron in the ice would have displaced a net volume greater equal to the volume of the iron.

This is where Copernicus was wrong. He mistakenly thought the displacement of the water was equal to the mass of the object instead of its volume.

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#37

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 2:06 PM

You said: "This is where Copernicus was wrong. He mistakenly thought the displacement of the water was equal to the mass of the object instead of its volume."

This statement needs a bit of clarification. A floating object does indeed displace its mass; a submerged object displaces its volume.

As for the original question, the word "equivalent" bothers me. How is equivalence defined? It could be volume, mass, cost, beauty, age, or any other measurement! I vote for air and iron with equal Quantum Strangeness numbers.

Anonymous Poster
#45

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 4:10 PM

Re your last paragraph - it doesn't matter what equivalence you use: the air will not contribute to the level of the pond, whereas any replacement material will, regardless whether it is iron or ice, and regardless of how little additional replacement material there is (other than zero).
Quantum strangeness numbers mere pretension here?

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#50

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 4:31 PM

Yup. Pretension, humor, take your pick.

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#57

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 5:16 PM

Perhaps it's a bit unkind, but: humor if right, both if not?

Anonymous Poster
#71

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 9:06 PM

I believe the statement should read "a floating object displaces a volume of water equivalent to the objects mass"

Anonymous Poster
#39

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 2:21 PM

I think the spillway holding the ponds at a maximum level is the key to the trick in this question. Assuming the density of ice is 0.917 kg/L and that each ice cube has a volume of 1 liter (for illustration), consisting of 0.6 liter of ice and the balance either iron or air.

When the 1 liter iron-laden cube is placed in the pond, it will sink, displacing 1 liter of water. When it melts, there will be (0.6*0.917)=0.55 liters of water plus 0.4 liters of iron. The pond level will have fallen by 0.05 liters from its maximum, initial level.

When the 1 liter air-laden cube is placed in the pond, it will displace a volume of water equal to its weight or 0.6*0.917=0.55 liters. When it melts, there will be 0.55 liters added, keeping the pond at the same height. Thus the pond with the air-laden cube will be at a higher level.

If the ponds are not at their maximum levels when the cubes are added, then the iron-laden cube will cause the level to rise higher.

Anonymous Poster
#48

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 4:19 PM

I think your measurements may need refining. When the ice cube containing the iron melts, its volume reduces, so the water level falls. It won't fall as far as it would if there was enough ice for the cube to float (and the same amount of iron), but fall it will. There will also be some fall in level due to the water in the pond being cooled by the ice - although other heat sources could cause a greater rise. The part of the change due to cooling of the other water in the pond will also be observed for the floating ice, of course.

Anonymous Poster
#35

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 1:56 PM

And what if the blocks of Ice were very big and very cold and the ponds were very small?

Then the block with the iron in it could have enough mass to freeze the pond it is in while the block of only ice and air will not.

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#36

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 2:04 PM

POND

Equivalent Piece-->volume equal

Water Level

Air bubble pressure greater than water + ambient pressure.

Ice+iron block have greater mass density than Ice+air bubble block.

The water level is greater in Ice+Iron pond due to buoyant force that displaces the liquid.

Archimedes' principle Physics. the explanation by Archimedes of the principle of buoyancy. He noted that an object placed in water apparently loses an amount of weight equal to the weight of the water displaced by the object; this led to the statement that a body immersed in a fluid is buoyed up by a force equal to the weight of the fluid it disperses.

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#38

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 2:13 PM

Neither.

Here's why:

1)It would be too facile a problem to post if it were the iron-block pond.

2) As ice floats, the water displaced by the ice of a floating block will be no more than the additional water of the melted block, but the pond's water level may temporarily lower until the ice's cooling effect has been neutralised. If the size of the ice blocks are not huge relative to the volume of the bubble/iron, then the iron-containing block will be submerged initially, and its volume will decrease as it melts (water being more dense than ice), making the pond's water level lower. Even if the iron-containing block floats initially the expansion of the warmed metal will be little significance compared to the contraction of the melted ice.

Anonymous Poster
#52

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 4:38 PM

2) Nothing is too easy to post here - look at some of the previous challenges. Then, forget the effect on the pond initially. Think only about the volume of the material you add after the ice has melted. The air will go away, the iron won't. So you always add more with the iron present.

As stated by Fyz the +iron-pond's level can fall if the pond levels are equal after the ice blocks are added. The levels can even be equal after settling is if there is a sluice at the correct height for exactly the correct volume of water to go over. That would be a water volume that is equal to the warmed-up volume of the iron

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#40

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 3:07 PM

I have a sneaking suspicion that they have left out an important piece of information.

The bit that I believe is missing is, the level of water in the ponds is identical after the ice cubes are added not before as everybody is calculating.

If this is the case the question becomes considerably more complex as the ice cube with the iron in it displaces more water than the ice cube with the air in it.

Yes I do realize that this is not strictly what the question says but it would make the question more complex than the simple one that it currently is.

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Anonymous Poster
#46

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 4:12 PM

But if the water level is the same after the cubes are added then the amount of water in the air cube is less to compensate for the volume of the iron in the 2nd block.

Anonymous Poster
#49

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 4:25 PM

Everybody? See post 27

Anonymous Poster
#98

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 8:24 AM

I think you are right. The true answer lies in what you call t=0 where the height is measured. If the height is measured immediately after adding the blocks of ice, the water levels will be identical after melting (Archimede's principle). If t=0 is before adding the blocks, then the iron ball will add it's volume to increase the level while the air will dissipate.

Chemist

Anonymous Poster
#103

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 9:38 AM

No, the extra weight of the iron means that if the block with the iron floats it will displace about eight times the volume of the iron (s.g. 7.86). If it sinks initially, the volume of the ice will be displaced. In the first case, the total volume will reduce 6.86x the volume of the iron; in the second case, the volume will reduce by the shrinkage of the ice. So for this interpretation of the question, the level sinks.

---------------------

"Some proofs command assent. Others woo and charm the intellect." John Strutt, Viscount Rayleigh

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#133

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/15/2007 7:17 PM

hi masu...agree with lacking informtion but answer may be in the statement: "one has a bubble of air inside, and the other one has an equivalent piece of iron inside"; note equivalent. does it mean volume, weight, or what? still would believe that mass of air versus mass of iron would have more water in the cube with iron, therefore with the added water volume and small iron mass, the water in the pond with the iron will rise.

ps..it is good to see that your government has the same specifications as we do...

Anonymous Poster
#41

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 3:13 PM

with a simple question shouldn't we assume there is no spill way that we only measure the water level after all ice has melted (think of the stagnant pond in your neighbors yard that poses as a decrotive addition to his landscaping) could any gas react in solution to produce a change in mass, greater than observed by the dissolving iron cube? Other factors may include the isotopic ratio in the iron cube...

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#42

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 3:33 PM

I wish I had the time to prove you all wrong and find specific conditions where the reactive gas exponentially increased in volume after the ice had melted... Did you know some gases would dissolve in the melting water and react spontaneously?...

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#43

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 3:43 PM

Obviously this is too easy without the trick. Some speculated on whether the word equivalent meant the air and iron were equivalent in volume or mass.

That would appear to be the trick. A large volume of air is required to weigh the "equivalent" of a small volume of iron (to use scientific terms). The block of ice with the iron of what ever size would have much more ice than the block with the air bubble and raise that pond to a higher level both before and after the ice melts.

If the trapped air and the imbedded iron weigh an equivalent amount those who are impatient for the answer can find out now by weighing the ice blocks. The one with the iron and greater volume of ice will weigh more.

"Every thing should be made as simple as possible but no simplier." Albert E.

Anonymous Poster
#54

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 4:57 PM

Not much of a trick if it leaves the answer unchanged from the obvious interpretation?

Anonymous Poster
#44

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 4:04 PM

That's an easy one: The pond with the cube that has the iron in it. As our beloved president would say ....." That's just commonsensical ". That's a real quote.......... Alan

Anonymous Poster
#47

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 4:14 PM

The iron will not expand at measurable level,I think the rate is 0.008 mm per 10 ft,per 10 degrees C.

My first instinct was to notice a trick question or.... is the trick question to; try to make it look to easy as to not look at the obvious.

Hmmmm..........

Is the air bubble under pressure ?

Anonymous Poster
#55

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 5:02 PM

Irrelevant unless there's a spillway, as the air will always depart. In any case, there's no way you could compress air to equal the density of iron - there's no known material that would take that sort of pressure without flowing.

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#51

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 4:34 PM

But the question states: "When the ice blocks melt, which pond will have a higher water level?" not when the blocks are placed in the pond.

I posted an alternative answer earlier (#24?) but I think it got lost being too close to the top so am reposting it here:

The temperature of both ponds are equivalent until the ice blocks melt, at which time the air bubble is released and that pond's temperature starts increasing. The iron drifts to the bottom but retains its thermal mass.

Would the block with the air bubble melt faster? If the ice blocks melt at the same rate, then the "iron" pond would be at a higher level at the instant the ice is melted and the air bubble is released since the water in the ponds would be at the same temperature. But, the air bubble will be released prior to the ice completely melting, and with water filling in the cavity of the air bubble, this block will melt quicker than the "iron" block of ice will due to the increased surface area. Thus I conclude that the ice with the iron melts slower than the ice with the air bubble.

So, it is possible that the water in the "air bubble" pond will be warmer than the "iron" pond at the point that all the ice is melted. If the volume of the water expansion is greater than the volume of the iron, the level of the "air bubble" pond will be higher.

-Erica

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#56

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 5:14 PM

I'm afraid I ignored it first time around - because it helps if you have an idea of the relative size of the effects. In this case, the volume specific heat of iron is lower than that of water. Below 30-degC, the TCE of liquid water is less than 0.03%/degC. So, even if the ice and the iron are initially at -70-degC, the additional contraction of the water will be less than 3% of the volume of the iron - a long way from the level needed for it to affect the relative change in surface heights.

Anonymous Poster
#58

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 5:44 PM

Hypotheticly, with the equality of the air and iron being "mass", then with the air bubble being of such a micro size as to be desolved into the the water as the ice melted, and the nano speck of iron of the same mass but less volume than the air and all other conditions perfict, one could determin with rigiorous calculations that the pond with the air/ice would have more volume.

Truly, Seth MM

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#61

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 5:57 PM

you would still need to know the solubility constant of the pond water and other chemical data that would help depict whether the pond water was saturated or deficient in the gases found in the micro size air bubble. And further mor, the size of the air bubble would be of grave importance as to make sure that the gas would remain in solution and not escape into the atmosphere. If we were dealing with a dense gas that was highly soluble in solution some of this info would be less important.

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#62

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 6:04 PM

The gas is air. So there is no reason to expect that total dissolved after melt will be significantly different between the two situations (the main difference is in the surface area of the molten surface of the ice at melt)

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#209

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

04/28/2007 6:46 AM

Seth , I don't recall where in this thread , but I made just such a calculation. In a 1m cube , the iron is a air size (for the 2 systems to balance ) .Which water level ends up higher could be made to happen quite easily.Kris

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#59

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 5:52 PM

This is why I am glad I am not an engineer. You spend way too much time trying to complicate a very simple question.

Anonymous Poster
#60

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 5:57 PM

Does anyone who reads the challenge ever just answer the question as written and not add conditions such as frozen ponds, spillways, CO2 gas, etc.?

I admit that sometimes the questions are not very clear, but this one is straightforward if you just deal with it as it is written and don't think about greenhouse gases, etc.

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#63

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 6:05 PM

I agree that that the puzzles are designed to promote dialog and thought, but come on. I mean an Apple is an Apple. We could discuss the difference between type of apples, and the difference between apples in the tree, apples on the ground or apples in plastic bags. But my 3 yr old says it best.

Anonymous Poster
#65

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 6:34 PM

What is the thermal density of the iron? The comment was made the air filled would melt faster than the iron filled.Would it? or....Will the iron retain it's own thermal abilty or will it adhere to the ice temp?

I would have to revise my earlier posted comment concerning the iron mass/expansion.We are working on a scale that may support the possible expansion of the iron do to the temp regulating factor....

hmmmmm.......

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#66

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 7:37 PM

I may have found the twist. There could be a cocktail called "Two Identical Ponds". This is a drink that MUST be made with two ice cubes. There is also a very similar cocktail called "Which pond" that differs only in that it has extra liquid water and a little piece of iron in place of the ice cubes. If we take the question mark away from the last sentence it becomes a true statement, because "Which pond" will indeed have a higher water level.

But come on guys, let's stop complaining. How many of you have come up with a challenge question?

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#67

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 8:05 PM

nursy says ...the one with the iron piece

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#68

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 8:07 PM

The pond with the iron ball.

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#69

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 8:40 PM

OK Here is a challenge question that requires lots of thought and with many variables

You are standing on a flat bed trailer travelling at 60 mph. You jump up as straight as humanly possible. do you land in the same place on the trailer??????

I feel this questions poses a lot more realistic dialog than the ice block query

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#78

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 2:32 AM

So far, every time I have jumped my initial upward velocity has been less than the earth's escape velocity so I did land on earth, just to rule out one option.

It sounds like the truck's velocity is constant (straight line and uniform speed). If you jump vertically (straight) with respect to the truck you will land in the same place relative to the truck, but the truck will be in a different place relative to the earth. This is ignoring wind resistance and my urge not to jump while travelling on the back of a truck. Wind resistance would reduce your velocity through the air, whereby increasing your velocity relative to the truck, causing you to land behind the place you jumped from.

If the truck was travelling at 60mph around a curve then you would land slightly to the outside of the point from which you jumped, providing you didn't jump from too close to the edge in which case you would land a bit lower than the point you jumped from a lot faster relative to the surface you land on.

If the truck was travelling down a slope then you would land slightly toward the back of the truck, and the opposite applies to travelling up a slope.

Since we are all different body shapes and therefore different wind resistances, and we are all tired of this question, I really think we all need to get out and do this experiment for ourselves.

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#114

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 11:54 AM

Yeah, let's do it!

You got a big truck? No, wait - let's use a TRAIN!

Do we have to compensate for possible low bridges? No? OK, then I'm in!

ANY excuse to get outside for a bit and call it "research"!

Anonymous Poster
#72

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 9:26 PM

the pond with the iron ball will have a higher level because of the displacement of the iron. The water addition from the melting ice is equal in this case. The air bubble will displace no water in the other pond.

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#73

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/13/2007 9:39 PM

The multiplicity of alternative replies is quite creative and entertaining!... until it gets repetative, and begs for an end to the confusion... which I can't resist.

So, to expand on my first reply #38...
and clarify the question:
"You have two blocks of ice with the same volume." Either the blocks have the same volume or the volume of ice in each is the same or both.

"One has a bubble of air inside, and the other one has an equivalent piece of iron inside". Only an equivalence in volume would be congruent with all meanings that one can interpret in the first sentence above (and plausible).

"You put these blocks in two identical ponds." ...and of course the water level becomes higher in both, more so in the the pond with the iron-containing ice block, but who cares?... as that question hasn't yet been asked!

"When the ice blocks melt, which pond will have a higher water level?" ... which can be read ambiguously as having various possible interpretations:

1. which of the two ponds will have a higher water level than the other?
2. which of the two ponds will have a higher water level than it had before its ice block melted (ie. immediately after the ice block was added)?
3. which of the two ponds will have a higher water level than it had originally (before the ice blocks were added)?

The answer to 1. would be the pond with the iron-containing ice block, (as already declared by several other contributors).... assuming that both ponds were kept at the same height/altitude from the outset, but since this important information has not been given it is probably an inappropriate and irrelevant interpretation.

The answer to 2. would be: Neither! as explained in #38

The answer to 3. would be: Both, of course!.... but this interpretation wouldn't make much of an issue for a discussion.

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#115

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 11:58 AM

Your #2 answer is true if the ice-with-iron block floats. But what if it sinks? Then the ice-with-air pond wins in #2, right?

Anonymous Poster
#118

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 12:44 PM

It's all in the Jesuitical wording: "which pond has the higher level after melting than (that pond had) immediately before melting". The answer is that, whether the ice with the iron initially floats or sinks, the level of the water will fall. If it falls, it is not higher - therefore, neither.

I think that PofM's 3 (both rising relative to their pre-ice condition) was intended to clarify this.

My attempt at clarification of the four possible interpretations:

Pond Air relative to pond Air and pond Iron relative to Pond Iron - ponds the same before adding ice, and no overflow => answer=both

Pond Air relative to pond Air and pond Iron relative to Pond Iron - ponds the same after adding ice => Air falls (water contracts on cooling) Iron falls => answer=neither

Pond Air relative to Pond Iron - ponds the same before adding ice, and no overflow => answer= Pond Iron

Pond Air relative to Pond Iron - ponds the same after adding ice => answer=air

So you can interpret the problem to give any of the four possible answers.

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#125

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/14/2007 10:26 PM

"...and begs for an end to the confusion... which I can't resist."

Ha! It takes more than a comprehensive, correct answer to stop these folks being confused!

Anyway, how can two blocks of ice simultaneously occupy the same volume. Equal volumes I could understand, but the same volume??

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#129

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/15/2007 5:58 AM

Nice one

Fyz

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#130

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/15/2007 6:08 AM

I can't resist a bit of confusion either.

ps - it's the copper coating that causes the lever to rotate.

Only joking , I couldn't resist.

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#146

### Re: Blocks of Ice: Newsletter Challenge (03/13/07)

03/18/2007 2:24 AM

"When the ice blocks melt, which pond will have a higher water level?"

There's another interpretation. Instead of reading this as "When the ice IN the blocks melts," I read it as "When the blocks WITH ice melt." In my reading, the block is not melted until everything in the block is melted; including the iron.

This interpretation comes with a new set of ambiguities. From a theoretical standpoint, the iron could be made molten instantaneously without appreciably affecting the temperature of water around it. The thermal expansion of iron would be the only new factor contributing to water level. If the temperature was brought up slowly, the entire pond would turn to steam and present a new dilemma: is the level higher because the volume of vapor is greater than liquid, or is the water level lower because it has all changed to steam?

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