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How long to melt all the polar ice?

The answers to this question say that the sea level will rise 66m if all the polar ice, etc, melts.

How long will this take?

Transporting incredible amounts of heat energy to the poles and injecting it into the ice, a good insulator, so that it melts must be very, very slow. The Netherlands, London, and all the rest will be long gone for other reasons, I imagine, long before it could be completed.

We need some numbers.

How much ice is there?

( Antartica contains 26.5 million cubic km of ice

http://en.wikipedia.org/wiki/Antarctic_ice_sheet

So: 2 * 10 ** 14 kg )

How much heat energy is needed to melt a unit of ice?

( 333 kJ/kg.

http://www.ask.com/question/how-many-joules-of-heat-are-required-to-melt-40-kg-of-ice-at-0-degress-c )

So we need 6 * 10 ** 16 kJ

How good an insulator is ice? ( Assume the ice is 1 km thick. How long does it take for the required energy to conduct through 1 km of ice? )