Occasionally, huge icebergs are found floating on the ocean\'s currents. Suppose

Question

Occasionally, huge icebergs are found floating on the ocean's currents. Suppose one such iceberg is 137 km long, 27.1 km wide, and 203 m thick. (a) How much heat in joules would be required to melt this iceberg (assumed to be at degree C) into liquid water at 0 degree C? The density of ice is 917 kg/m^3. (b) The annual energy consumption by the United States in 1994 was 9.3 times 10^19 J. If this energy were delivered to the iceberg every year, how many years would it take before the ice melted?

Explanation / Answer

Latent heat of water at 0 degree is 333.55 kJ for 1 kg of ice to melt.

Mass of iceberg = density*volume = 917*137*103*27.1*103*203 = 691122817.7*106 Kg

Heat require to melt the ice at 0 degree = (latent heat to melt 1 Kg)*(Total mass of ice)

= 333.55*103*691122817.7*106

= 230524015843.835*109 J =2.30524015843835*1020

b) Year require to melt all ice = (2.30524015843835*1020) / (9.3*1019) = 2.47875 year

nearly 2.5 years

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