Question 12 of 12 Incorrect Map Openstax College Physics Openstax presented by S

Question

Question 12 of 12 Incorrect Map Openstax College Physics Openstax presented by Sapling Leaming In 2002, a gargantuan iceberg broke away from the Ross Ice Sheet in Antarctica. It was approximately a rectangle 218 km long, 25.0 km wide, and 250.0 m thick. What is the mass of this iceberg. given that the density of ice is 917 kg/m? Number 1249x 1012 kg How much heat transfer (in joules) is needed to melt the iceberg? Number How many years would it take sunlight alone to melt ice this thick, if the ice absorbs an average of 113 Wim2, 12.0 hours per day? Number years O Previous O Check Answer 0 NextExit Submit Assianmen Hint

Explanation / Answer

a)
Volume of iceberg, V = lbh
= (218 x 103) x (25 x 103) x 250
= 1.3625 x 1012 m3.

Mass = density x volume
m = 917 x (1.3625 x 1012)
= 1.249 x 1015 kg.

b)
We assume that the temperaure of ice is zero degree.
Latent heat of fusion of ice, L = 334 kJ/kg
Heat required = mL
= (1.249 x 1015) x (334 x 103 J/kg)
= 4.173 x 1020 J

c)
Area of iceberg = lb
= (218 x 103) x (25 x 103)
= 5.45 x 109 m2.

Power received on the surface of iceberg = 113 W/m2 x Area
= 113 x (5.45 x 109)
= 6.1585 x 1011 W

Time taken to melt ice = Energy / Power
= (4.173 x 1020) / (6.1585 x 1011)
= 6.78 x 108 s
= (6.78 x 108) / (3600) Hr
= 18.82 x 104 Hr

Number of hours in a year where the sunlight is received = 12 x 365 = 4380 Hrs
Number of years needed = (18.82 x 104) / 4380
= 42.97 years.

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