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Water Level when Ice Cube Melts

Discussion in 'MCAT Study Question Q&A' started by nfg05, Jun 15, 2008.

  1. nfg05

    2+ Year Member

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    So the question that is tripping me up basically states

    A cube of ice is floating in water. After the ice melts, the water level:
    a. rises
    b. falls
    c. stays the same

    Now the answer reasons that the ice cube displaces a volume of water equal to its own volume and that when it melts the water will "perfectly fill in" and thus the water level will stay constant.

    Now I may be overthinking here, but isn't the ice LESS dense than the water so it actually takes up more volume in the ice form than it will in its water form after melting, thus meaning that the most correct answer to the question is that the water level falls after melting?

    P.S. It isn't even true that the ice cube displaces a volume of water equal to its own volume right. It displaces a volume of water whose weight is equal to the weight of the ice cube, which is not the same thing since again the ice is less dense than water. Not sure how this plays into answering the question though...
     
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  3. cwfergus

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    Haha i was actually curious about this! so i checked it out online:

    Imagine a perfect cube of ice whose dimensions are 1 cm by 1 cm by 1 cm. Since the density of ice at 0ºC is 0.9167 g/cm³, the mass of this cube would be 0.9167 grams. Placed in water, whose density at 0ºC is 0.9998 g/cm³, it will float. Since the density of ice is 0.9169 that of water, about 92% of its volume will float below the surface and about 8% above. The volume of the cube below water is therefore 1 cm x 1 cm x 0.9169 cm = 0.9169 cm³, which is also the volume of displaced water.

    When the ice cube melts, it will add 0.9167 grams of water to the glass. The volume of this added water would be 0.9169 cm³. So the volume of water added by the melting ice is exactly the same as the volume of water displaced by the cube previously. Hence, the water level would be the same.
     
  4. 161927

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    this is just something you have to know in life, so when people try to tell you "No! The water level will increase!" you can correct them.

    It has to do with the buoyant force and the fact that a floating ice cube is not 100% suspended above the surface of the water. Some of it is submerged.
     
  5. Vihsadas

    Vihsadas No summer
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    The trick here is to realize the interplay between density, buoyant force and water level (All of which are MCAT relevant!).

    Basically, because the ice is less dense, it will displace a volume of water smaller than its own volume because some of the ice cube will be above the surface of the liquid due to the buoyant forces.
    But what will happen when the ice melts??
    Well, the density will increase, and this leads us to believe that after melting the ice should take up less total volume than it was before. The question becomes how much less volume will it take up? If you think about this long and hard, you might intuitively see that the water from the melted ice must take up exactly the volume of ice that is under the surface of the liquid.

    As per above, you can do the math to prove it to yourself, but its definitely important to see if you can have that 'Aha!' moment where you understand it intuitively.
     

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