Occasionally, huge icebergs are found floating on the ocean's currents. Suppose one such iceberg is 125 km long, 37.9 km wide, and 180 m thick.

(a) How much heat in joules would be required to melt this iceberg (assumed to be at 0°C) into liquid water at 0°C? The density of ice is 917 kg/m³.

(b) The annual energy consumption by the United States in 1994 was [tex]9.3 \times 10^{19} \text{ J}[/tex]. If this energy were delivered to the iceberg every year, how many years would it take before the ice melted?

(a) Number Units .

(b) Number Units ____.

To solve this problem, we need to find the mass of the iceberg and then calculate the amount of heat required to melt it, considering the latent heat of fusion of ice.

(a) Heat required to melt the iceberg:

Step 1: Calculate the volume of the iceberg.

Volume = Length × Width × Thickness

Volume = 125,000 m × 37,900 m × 180 m

Volume = 8.5725 × 10¹² m³

Step 2: Calculate the mass of the iceberg.

Mass = Density × Volume

Mass = 917 kg/m³ × 8.5725 × 10¹² m³

Mass = 7.8589 × 10¹⁵ kg

Step 3: Calculate the heat required to melt the iceberg.

Heat required = Mass × Latent heat of fusion of ice

Heat required = 7.8589 × 10¹⁵ kg × 334 kJ/kg

Heat required = 2.6244 × 10¹⁸ kJ

Heat required = 2.6244 × 10²¹ J

Therefore, the heat required to melt the iceberg into liquid water at 0°C is 2.6244 × 10²¹ J.

(b) Years required to melt the iceberg with the annual energy consumption:

Step 1: Calculate the number of years required.

Number of years = Heat required to melt the iceberg / Annual energy consumption

Number of years = (2.6244 × 10²¹ J) / (9.3 × 10¹⁹ J/year)

Number of years = 28.22 years

Therefore, if the annual energy consumption by the United States in 1994 were delivered to the iceberg every year, it would take approximately 28.22 years to melt the iceberg.

(a) Number: 2.6244 × 10²¹ Units: Joules

(b) Number: 28.22 Units: Years