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Volume of Frozen water

  1. May 15, 2007 #1

    I have been having a debate with someone that is driving me insane...
    Here is the problem

    Lets say we have 20,000m^3 of water like the image above.

    If we were to freeze a quarter of it. what will happen to the level of the water, eg, will it rise, drop or will it stay the same?

    The information I have looked up states that on freezing water it expands by
    9% and also that floating ice on water will be 89.5% underwater.


    Here we have frozen a quarter which would then become....

    with 89.5% underwater and 10.5% above the surface of the water.
    so now I can say that 89.5% of 5450m^3 = 4877.75m^3 is under the surface of the water.

    so now if you add the remaining 3 quarters of water 15,000m^3 to the frozen quarter thats underwater 4877.75m^3 you get:

    15,000m^3 + 4877.75m^3 = 19877.75m^3 total

    originally before freezing a quarter there was 20,000m^3, and now after freezing there is 19877.75m^3 so this must mean that the water level will drop slightly.

    However, the person I am having a debate with seems to think differently, she believes that if you freeze a quarter like we have done the level of the water will not rise or fall, it will stay exactly the same.

    PLEASE will someone clarify this.

    Thanks very much
    Last edited by a moderator: Apr 22, 2017
  2. jcsd
  3. May 15, 2007 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Do you have a reference for these values? They are not consistent. If you freeze a block of pure water such that it floats, it will displace a volume of water equal to its original volume. If the original volume is 1 unit, and it expands by 9% when frozen, it's new volume will be 1.09 units. 1/1.09 = 91.7% will be underwater.
    She is correct. Just like an ice cube floating in a glass of water--when it melts, does the water level change?
  4. May 16, 2007 #3
    But your friend is correct.the ice cube floats ie a bit of it is outside water. Now definetly the volume increases of the whole system but the amount by which the volume increases is exactly equal to the volume of ice outside water. now try to push the icecube in the water and definitely the water level would arise
    Last edited by a moderator: Apr 22, 2017
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