Answer :
a. Number: 2.6244 × 10²¹ Units: Joules
b. Number: 28.22 Units: Years
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
