Question

Occasionally, huge icebergs are found floating on the ocean's currents. Suppose one such iceberg is 140km long, 32.9 km wide, and 152 m thick. (a) How much heat in joules would be required to melt this iceberg (assumed to be at 0 degrees Celsius) into liquid water at 0 degrees Celsius? The density of the ice is 917kg/m³. (b) The annual energy consumption by the United States in 1994 was 9.3 x 10¹⁹ J. If this energy were delivered to the iceberg every year, how many years would it take before the ice melted?

Answer 1

To find how much heat is required to melt an iceberg, calculate the iceberg's mass using its volume and the density of ice, then multiply the mass by the heat of fusion for water. For the time estimate, divide the total energy required by the annual energy consumption.

Step-by-step explanation:

To calculate how much heat would be required to melt an iceberg measuring 140 km long, 32.9 km wide, and 152 m thick, we must perform two steps:

1. First, we calculate the mass of the iceberg. Given that the density of ice is 917 kg/m³, we use the volume formula for a rectangular prism (Volume = length × width × height) and convert all measurements to meters. Therefore, the volume is (140000 m × 32900 m × 152 m) and the mass (m) can be found by multiplying this volume (V) by the density (ρ) of ice, m = ρ × V.
2. Second, we use the heat of fusion for water, which describes the amount of energy needed to melt one kilogram of ice, to find the total energy required. The heat of fusion for water is approximately 334 kJ/kg, so the total energy (E) needed in joules is E = mass × 334000 J/kg.

For part (b), assuming the annual energy consumption of the United States is 9.3 x 10¹¹ J, we divide the total energy needed to melt the iceberg by this annual consumption to estimate the number of years it would take to melt the iceberg using this amount of energy.

The actual calculations for the mass and the heat required would need numerical solving, which isn't presented here.