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Homework Help: Fluid Mechanics : Ice cube melting and Surface Energy Que.

  1. May 26, 2010 #1
    Q. 1. if a ice cube is placed in a container containing liq on which it is floating.
    then is it possible that after ice melts, water level rises in vessel in any particular case.

    2.Does heat evolves when water rises in a capillary. and how much heat is evolved in height of liq in capillary is h.

    These are just conceptual que in which i m confused.
  2. jcsd
  3. May 26, 2010 #2
    1. The Archimedes principle says that when an object is completely or partially immersed in a fluid, the fluid exerts an upward force on the object equal to the weight of the fluid displaced by the object.

    Therefore the weight of the ice is exactly equal to the amount of water displaced. So after it melts the level remains the same.

    Note this only holds if the ice and the water are the same liquid, i.e this will not hold with salt water and fresh water ice, in that case the water level will rise as salt water is more dense that fresh water.

    2. I don't understand what you mean.
  4. May 27, 2010 #3
    Last edited: May 27, 2010
  5. May 27, 2010 #4
    You're forgetting that some of the ice is above the water level.

    edit: didn't notice you had deleted your post
  6. May 28, 2010 #5
    I don't really get this concept. Can you explain it more thoroughly, preferably with calculations if possible?

  7. May 28, 2010 #6
    Essentially when an object floats, it sits in the water. How deep it sits in the water depends on its weight. The heavier it is the deeper it sits in the water, until eventually it will sink.

    The Archimedes property says that the object will displace a weight of water EQUAL to the weight of the object. (This is why some things sink, they have a density greater than water and so effectively displace more water than their volume.)

    Now lets say the ice block weighs 10kg. It will displace 10kg of water. We know that ice is less dense than water so some of it will still be above the surface. When the ice melts to 9kg, it will displace 9kg of water, 1kg of ice has become water. The water level hasn't changed because 1kg less of water is being displaced but there is an extra 1kg of water in the container. Therefore when the ice has completely melted, the surface level of the water hasn't been effected.

    Is that clear enough or is there something you'd like me to elaborate on further. I can provide calculations if you want but I think that will just make it more complicated.
  8. May 28, 2010 #7
    Thanks for the response, I think I get the gist of what's going on. I would appreciate some calculations if it's not too much trouble.

    Thanks again!

    Edit: Is this neglecting heat transfer? Because wouldn't the ice cube decrease the temperature of the liquid changing its density?
  9. May 28, 2010 #8
    Yes it ignores heat transfer, but if the container is in a room of constant temperature it will go back to equilbrium anyway. (It also ignores Mass-energy effects etc, but I'm guessing these aren't relevant)

    http://en.wikipedia.org/wiki/Buoyancy has the calculations I would have written at the top of the page. It goes into more detail but you can ignore that.
  10. May 31, 2010 #9

    I got myself confused again. I know I have a logic flaw but I don't know what it is. What I'm wondering is, if one kg of ice melts, how does new 1kg of the water account for the volume of the 1kg less of ice and the volume of 1kg less of water?

  11. May 31, 2010 #10
    The new 1kg of water takes up the volume of the icecube that was previously below the surface of the water.
  12. May 31, 2010 #11
    But then wouldn't the water take up less volume than the ice cube since it is denser?
  13. Jun 1, 2010 #12
    It does take up less volume, but remember some of the ice was above the surface of the water.

    The volume of ice below the water surface is equal to the volume of 1kg of water.
  14. Jun 1, 2010 #13
    Okay I understand the second part, the volume of the melted ice is equal to the volume of the ice under water.

    But what I'm wondering is, if I have 10 kg of ice in equal volume of water, is the water level the same as if I put 9 kg of ice and 1 kg of water into the same volume of water; like during the melting process, does the water level stay constant. I would think it is but somehow I'm not understanding why it is?
  15. Jun 2, 2010 #14
    Providing the ice is floating then during the melting process the level of the water will always stay the same.

    If you put 10kg of ice in 1000kg of water then the water level is the same as if you put 9kg of ice into 1001kg of water.
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