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The Melting of the Arctic Ice Cap

 

If the entire Arctic ice cap melts, by how much will the sea level rise?

If the entire Arctic ice cap melts, by how much will the sea level rise?    

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An ice cube melting in pure water will not cause the water level to rise at all.

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It will hardly rise at all.

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Firstly we can show that an ice cube that melts in a glass of water will not cause the water level to rise at all.

Ice cubes do not rest on the surface of the water, but float at the water line. Roughly 90% of the ice cube is beneath the surface. This is because ice has a density about 90% of water.

The mass of the ice cube is fixed, so as it turns to water, increasing it's density as it does so, the volume taken up by the molecules that were ice will shrink. In fact it will shrink to 90% of its origional size and will therefore 'fit' into the space left by the ice cube that was under the water line. In this way, the water line will not move upwards.

To help visualise this, look at the diagram below. currently the ice cube is floating with 10% of its volume out of the water. As the ice cube melts, it will lose 10% of its volume (as its density increases). If we imagine that the10% it loses is the same 10% that is above the surface we can see that the water level will not change with the melting.

 

 

The arctic ice cap is resting on sea water. Sea water has a higher density than pure water so the above analysis does not work exactly and there will be a slight increase in sea level. (If you've gone further than this, e-mail your answer to WebMaster@IntellectualLoafing.com)

 

Sadly, even with only a little rise in sea level melting the arctic ice cap will be catastrophic as the huge excess of pure water will upset the Gulf Stream, so we cannot be complacent about Global Warming.

 

Follow up question:

Also, the melting of the Artic ice cap is likely to coincide with the melting of the Antarctic ice cap which is resting on a land mass and not sea water. What difference does this make? 

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