Puzzle

Suppose you have a glass of water, with ice cubes floating in it.  As everybody knows, when ice floats, about 10% of it pokes out of the water.  When the ice melts, will the level of the water go up (because the ice which pokes above the surface turns into water) or down (because the majority of ice below the surface takes up less volume in a liquid state)?

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14 Responses

  1. 10% of the ice cube will be converted to gas as it melts. It’s a push, the water displacement is not measurable.

  2. “It’s a push”? I don’t understand that expression. Water displacement is measurable, and I guess I need to say “assume no water enters or leaves the system in any phase (solid, liquid, or gas). I.e. put a lid on the glass. There is an answer, or at least I have one, and it might even be right!

  3. Push = no change.

    I believe that this glass of water will end up overflowing the coastlines of every land mass on earth, when its ice melts.

    And we need to do something about it now.

  4. Bruce,

    We should be evacuating NYC as we speak…

    Assuming there aren’t any air bubbles or anything like that in the ice, the water level should stay the same. Water expands by the same “about 10%” when it freezes, which is why ice floats to begin with, so the freely floating cubes only displace the same amount of water that they’ll contribute when they eventually melt.

    zrim

  5. An ice cube is floating in a glass of water. When the ice melts, what will happen to the water level? Would the same thing apply if the ice was cooling a glass of whisky? Well some 2300 years ago Archimedes discovered in his bathtub that a floating body displaces its own weight of liquid. So the ice, even though it floats partially above the water line, has left a hole equal to the weight of the water it is made out of. So as it melts, it simply fills in the hole and the water level stays the same. When the ice is in a glass of whisky however, it is a different story. As any drinker of Scotch-on-the-rocks will tell you, ice does not in fact float in the alcohol, Ice is heavier bu volume than whisky, and so it remains in the bottom of the glass. But water expands when it freezes and so, as the ice melts its volume decreases and therefore the liquid level in the glass goes down. So the next time you’re in a pub, if you go the washroom and return only to find that your whisky appears to have evaporated, your friends are innocent. It’s Archimedes’ fault.

    …so saith Dr Amanda Bewsher, of the National Research Council in Ottawa.

    zrim

  6. We have a winner! Others may have gotten the right answer, but zrim had the right explanation:

    So the ice, even though it floats partially above the water line, has left a hole equal to the weight of the water it is made out of. So as it melts, it simply fills in the hole and the water level stays the same.

    As for this inconvenient nontruth:

    I believe that this glass of water will end up overflowing the coastlines of every land mass on earth, when its ice melts.

    As we have seen, if the only ice in the world was already in the ocean, there would be no worry about rising ocean levels. Rising ocean levels would be a result of melting polar land-ice. Which makes me wonder: since we know that the north-polar ice cap is just ice, not land, is it all just floating up there, or has it frozen solid down to the polar ocean floor, so that it has become an ice-island, that supports more than 10% of its ice above sea level?

  7. I don’t think the polar Ice has frozen all the way down to the ocean floor. In fact I believe this is the reason that there isn’t a permanent research facility, because the ice is constantly moving around (though slightly). If I’m not mistaken I think we’ve sent submarines to the north pole.

  8. Hmmm, Wikipedia confirms that “Earth’s north pole is covered by floating pack ice”. I guess fear of rising ocean levels must be from Antarctica only.

  9. Evidently the Russians are really happy about global warming since it provides them the opportunity to place a flag at the north pole… 15,000 feet under water! What the heck kind of whiskey are they putting their ice cubes into?

    http://www.msnbc.msn.com/id/19952934/

  10. This is some pretty interesting stuff about antarctica in case you were really curious rube.
    http://www.msnbc.msn.com/id/15850535/

    But listening to this guy trying to explain whether or not the ice shelves breaking off can be attributed to global warming makes me doubt the scam even more. He talks about a HUGE piece the size of Rhode Island that broke off in 2002… of course I didn’t notice the ocean getting any higher in 02 did you?

  11. Hey Reuben, don’t tell me you saw the movie “An Inconvenient Truth”, I didn’t think you could sink that low. Anyway, the ice cube in the glass thing was a part of the movie and the point was made that only some of the ice masses are floating on the oceans. I forget the percentage that are not in his “scam”, but it is considerable.

  12. rube,

    1) my vocation (standardized student assessments) finally paid off! truth be told, i had to tap into a math/science colleague, who himself had to do a little tapping; we both knew this had come up at some point. i told him that, just like me, he’d be a really bad neo-con, since the first rule seems to be “admit nothing.” he admitted he gave up on that rule in his 20’s. i’ll let you draw the lines for political commentary on that one!

    2) speaking of neo-cons, something tells me your pop had his tongue firmly in his cheek…as for me, i have stopped trying to make sense of the whole global warming bit, shortly before trying to figure out gas prices. all i know is that it’s a hot one this summer as i stand there filling and filling and filling and filling and filling…

    zrim

  13. don’t tell me you saw the movie “An Inconvenient Truth”

    Actually, I haven’t seen it. I’m still operating under the assumption that Al Gore is as much of a liar as Michael Moore. (BTW, Fahrenheit 9/11 and Fahrenhype 9/11 make a great double-header!) Note back in #8 I did say that ocean levels could rise due to non-floating Antarctic ice melt.

  14. MM has an annual film festival in my hometown up north in the summer. that guy lives the dream i have: a place in NYC and one in antrim county. i can take or leave his politics (though i am no neo-con). perceiving a latent agenda, the local righties inaugerated their own propaganda effort thinly veiled as a film festival…oy.

    zrim

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