Question

In 1986, an enormous iceberg broke away from the Ross Ice Shelf in Antarctica. (a) What is the mass of this iceberg, given that the density of ice is 917 kg/m³? (b) How much heat transfer (in joules) is needed to melt it? (c) How many years would it take sunlight alone to melt ice this thick, if the ice absorbs an average of 100 W/m², 12.00 h per day?

a) 1.40 x 10¹² kg; 3.62 x 10¹⁵ J; 32.4 years
b) 3.62 x 10¹² kg; 9.37 x 10¹⁵ J; 64.8 years
c) 5.84 x 10¹² kg; 1.50 x 10¹⁶ J; 96.5 years
d) 7.06 x 10¹² kg; 1.82 x 10¹⁶ J; 128.9 years

Answer 1

The mass of the iceberg is 1.46 x 10^13 kg and the heat transfer needed to melt it is 4.87 x 10^15 J.

Step-by-step explanation:

To find the mass of the iceberg, we need to calculate the volume of the iceberg and then multiply it by the density of ice. The volume of the iceberg is given by length * width * height, which equals 160 km * 40.0 km * 250 m = 1.6 x 10^10 m^3. The mass of the iceberg is then calculated by multiplying the volume by the density of ice, which is 1.6 x 10^10 m^3 * 917 kg/m^3 = 1.46 x 10^13 kg.

To determine the heat transfer needed to melt the iceberg, we can use the formula Q = m * L, where Q is the heat transfer, m is the mass of the iceberg, and L is the latent heat of fusion for ice. The latent heat of fusion for ice is 334 kJ/kg. Plugging in the values, we get Q = 1.46 x 10^13 kg * 334 kJ/kg = 4.87 x 10^15 J.