Fluids Question- bouyancy

[Perkins]

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In a passage on global warming from the AAMC guide to the MCAT sample problem book, the question asked whether a melting iceberg would increase sea level.

The answer was that it would not, because the melted iceberg displaces its weight of water.

I don't understand why the floating iceberg displaces the same amount of water as the melted iceberg, since part of the floating iceberg is above the water (thus not displacing volume) while ALL of the melted iceberg- the part that used to be above water and the part that was below water- now get added to the sea volume.

thanks!

 

[ModusProbandi]

The floating iceberg and the melted ice berg weigh the same do they not? (contain the same amount of water) The melted iceberg and the floating iceberg would have to displace the same amount of water.

Imagine it like this....the top of the ice berg floats above water level because the iceberg as a whole is less dense than water. As it melts, the density is increasing to that equal to the water so the iceberg must now occupy the same amount of weight per volume as the water. In essence, the volume of the melted iceberg is less than that of the floating but you have the same amount of water in the melted iceberg as you had in the floating iceberg.

Water level would go up IFFF density didn't increase for the iceberg to melted-iceberg transition. The way you're imagining it is that you merely add the volume of the top of the iceberg to the water. Well, that volume is actually lost due to the decrease in volume occupied by the same amount of iceberg (aka increased density by melting).

Now what if we had dry ice floating on liquid CO2?

 

[Perkins]

Thanks ModusProbandi.

If we have dry ice floating on liquid CO2, I would assume that melting the dry ice would increase the overall volume of liquid CO2 since dry ice (which is really solid CO2) does not hydrogen bond like water and is thus more dense as a solid than as a liquid (typical). So if you melt it, then it displaces more volume than before, so overall liquid CO2 volume rises.

 

[ModusProbandi]

Thanks ModusProbandi.

If we have dry ice floating on liquid CO2, I would assume that melting the dry ice would increase the overall volume of liquid CO2 since dry ice (which is really solid CO2) does not hydrogen bond like water and is thus more dense as a solid than as a liquid (typical). So if you melt it, then it displaces more volume than before, so overall liquid CO2 volume rises.

Yea, trick question , it doesn't float! but you're right, it will increase the volume.