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Problem: melting ice

  1. Dec 17, 2003 #1
    Ok, so you've got a glass of water with some ice (the ice is floating).

    After the ice melts, does the water's surface level
    a) rise?
    b) lower?
    c) stay the same?

    (and why?)
  2. jcsd
  3. Dec 17, 2003 #2
    Surface level will drop. H20 expands when frozen - so when it turns to liquid H20 the volume will drop - dropping the surface level.

  4. Dec 17, 2003 #3
    But wouldn't a substantial part of the ice cube's volume be above the surface level? Could this compensate for the decrease in volume as the ice melts?
  5. Dec 17, 2003 #4


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    Staff: Mentor

    No, the level stays the same. Since the ice is floating, the water level is lower than the level of the top of the ice. The difference is due to the expansion of the ice.

    When ice expands, it expands by something like 10%. Where is this extra 10% of volume? Its above the water level. All of it. As the ice melts, (lets say from top to bottom) the melted ice adds to the volume of water, but the ice also floats higher, cancelling out the added water level.

    edit: Posted before moose. You are correct, moose.
  6. Dec 17, 2003 #5
    ok i think i agree with you, russ_watters.

    here's how i just figured it out:

    we know that: the weight of the water displaced by the ice is equal to the weight of the ice cube (because it is floating).

    thus, when the ice melts, the weight (of what was the ice) is still the same, so the volume displaced is the same.

    hmm, does that make sense?
  7. Dec 17, 2003 #6
    Sounds good, and I suppose the the change in temperature is so minor that its affectations on volume are minimal enough that saying "It remains the same" is safe enough as 'a truth'.
  8. Dec 17, 2003 #7


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    Staff: Mentor

    There is no change in temperature while the ice is melting.
  9. Dec 17, 2003 #8
    I'm guessing that you mean that the ice cube's temperature remains constant while melting: not the liquid's. The liquid in the glass will surely cool as the ice cube melts. If the ice cube and the entire glass of liquid are exactly at the freezing point, no melting will occur until one of them recieves heat from somwhere in the surroundings.

    There will be a miniscule volume change due to some liquid state temperature changes which may happen "if" the initial liquid is signifcantly above freezing when the process starts. The liquid state expansion/contraction of the water masses represented by he cube and he liquid respectively will be different since the intial liquid had a "head start" heat transfer (and liquid state contraction) to the ice while the cube was melting. This is assuming that liquid water expands linearly with temperature, which is a common assumption. So basically, the liquid state contraction of what was initially liquid will outweigh the liquid state expansion of what was ice. So the final level is ever so slightly lower.

    Throwing that petty stuff aside I think russ nailed it on the head.
    Last edited: Dec 17, 2003
  10. Dec 18, 2003 #9


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    Staff: Mentor

    I was operating on the assumption that the water was at 32F when the ice was put in. Your right that for heat to flow there must be a temperature gradient in the water, but it won't be measurable unless the surroundings are significantly warmer or the volume of water is much higher than the volume of ice.

    I made a lot of simplifying assumptions in the absence of given information.
  11. Dec 18, 2003 #10
    Actually, thought about this (a little) last night, the fact of water reaching its maximiun density at 4° C tells us that even if there is an increasing temp. gradient, it is following/pushing a shrinking volume with temp increase above 0° C, till it hits its max density at 4° C, then it starts expanding, so in actuallity, as the temperature of the water increases above 0° C, its volume is actually decreasing, so it "remains the same" till all of the ice melts, then the volume gets smaller! (Neat eh?!!)
  12. Dec 20, 2003 #11
    Which explains why my coca-cola can expands when I freeze it. :smile:
  13. Dec 20, 2003 #12


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    Staff: Mentor

    Yeah, its a real pain to clean the coke out of your freezer. Trust me, I know.
  14. Dec 21, 2003 #13
    Assumptions can be made either way. This point could be argued either way. Put a piece of ice in a cup and one time you will see the level rise, the next you will not - depends on the piece of ice and exactly what you mean by "floating". But, if you explain your answer - you will not be wrong either way.

  15. Dec 21, 2003 #14
    Humm this is a science forum, testing can be done! results checked! accuracy! and accurate answers! are achievable! therefore A-S-S-U-M-P-T-I-O-N-S need NOT be made! at all!
  16. Dec 21, 2003 #15
    I agree, I put a piece of ice in water and when melted, the water level rose - but I was told that was wrong. The reason I was told I was wrong is b/c the assumption was made that the ice was floating at the appropriate level to keep it from rising when melted.

    I only made that statement to make a point that the right answer would be based on experimentation and your results can say one thing or another.

  17. Dec 21, 2003 #16


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    Staff: Mentor

    Sorry, MRP, but no. Even in an experiment, the same assumptions we talked about before are made in the experimental setup.
  18. Dec 22, 2003 #17
    Agreed russ, my 'rant'(!!!) was about the conclusion, not the premise, 'assumptions' are often made in the premise, it is one of those "slippery slopes" in experimentation, but after the experiment, we can measure all, and know, for the now un-assumed conditions, (now known from the experiment) such and such an outcome...right?
  19. Dec 26, 2003 #18


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    Is the ice amphoric?

    The water level will remain the same, Mr. Arch's principle, when water freezes air gets caught in it and makes teeny tiny little bubbles in the ice. Filling up more space
  20. Dec 26, 2003 #19


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    Homework Helper

    Clearly if the ice and the water are both pure, the water level stays the same.

    However, if the water is salt water, while the ice cube is pure water, then the level will rise slightly. This is also true for popular carbonated beverages.

    If the ice is resting on the bottom of the glass, then the water level will rise.

    If the ice is trapped beneath the surface of the water then the water level will drop.

    If a tiny elf is sitting on top of the ice throwing rocks that had been on the ice into the water, then the water level will drop.
  21. Dec 28, 2003 #20
    The water level would indeed stay the same because although the ice water has expanded when ice was formed, it still has the same mass as before. The ice before and after will still have the same mass unless evaporation occurs. I say c. the level will stay the same
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