Question

Antarctica is covered by glacial ice and surrounded by floating shelf ice (and icebergs). The density of ice is 917 kg/m3, of fresh water is 1000 kg/m3, and of ocean water is 1025 kg/m3 . Use g = 10 m/s2.

a) A particular floating iceberg has a mass of 106 kg. Calculate the buoyant force FB acting on that iceberg.

b) Suppose that a volume 3.5 x 1016 m3 of glacial ice on land melts. [This is all the ice on Antarctica.] Estimate the increase of sea level Δh that would be caused by adding the resulting volume of water to the oceans. The surface area of the Earth is approximately 5 x 1014 m2, and 70% of the surface is covered by oceans.

c) Suppose that the same volume of ice was already floating, the way it is at the North Pole. Estimate the resulting change of sea level as it melted. Explain your reasoning in words, or by calculations.

d) The present mass of ocean water Moceans = 40 mA where mA is the mass of ice in Antarctica. (Don’t find mA; it should cancel out.) Suppose that the average temperature of Antarctic ice is Tice = −40 ºC, and that it all might melt because of global warming. (Do this calculation as if all the ice slides off the land into the water, and then melts.) What would be the resulting average temperature TF of the ocean water? Assume that if the ocean were thoroughly mixed, its average temperature just before Antarctica catastrophically melts would be Tocean = 8 ºC. [Use specific heats of 2 kJ/(kg ºC) for ice and 4 kJ/(kg ºC) for water, and approximate the latent heat of fusion as 300

kJ/(kg) for the melting of ice.]

Answer 1