Occasionally, huge icebergs are found floating on the ocean's currents. Suppose one such iceberg is 114 km long, 31.3 km wide, and 194 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 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?

Question

Occasionally, huge icebergs are found floating on the ocean's currents. Suppose one such iceberg is 114 km long, 31.3 km wide, and 194 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 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?

Need help please.

Answer 1

To solve this problem, we need to calculate the heat required to melt the iceberg and then determine how many years it would take to deliver the equivalent energy to the iceberg.

(a) To find the heat required to melt the iceberg, we can use the formula:

Heat = mass * specific heat * temperature change

The mass of the iceberg can be calculated by multiplying its volume by its density:

Mass = volume * density

The volume of the iceberg is given by:

Volume = length * width * thickness

The specific heat of ice is 2.09 J/g°C, and the temperature change is from 0°C (ice) to 0°C (water).

First, let's convert the given dimensions into the appropriate units:
Length = 114 km * 1000 m/km = 114,000 m
Width = 31.3 km * 1000 m/km = 31,300 m
Thickness = 194 m

Now let's calculate the mass of the iceberg:
Volume = 114,000 m * 31,300 m * 194 m = 694,439,200,000 m^3
Mass = 694,439,200,000 m^3 * 917 kg/m^3 = 6.36 * 10^14 kg

Next, let's calculate the heat required to melt the iceberg:
Heat = mass * specific heat * temperature change
= 6.36 * 10^14 kg * 2.09 J/g°C * 0°C
= 1.33 * 10^15 J

So, the heat required to melt the iceberg is 1.33 * 10^15 J.

(b) To determine how many years it would take to deliver the energy equivalent to the iceberg, we divide the annual energy consumption of the United States by the heat required to melt the iceberg:

Years = Energy consumption / Heat required

Given that the annual energy consumption of the United States is 9.3 x 10^19 J, we can calculate the number of years:

Years = (9.3 * 10^19 J) / (1.33 * 10^15 J)
Years = 6.99 * 10^4 years

Therefore, it would take approximately 69,900 years to deliver the energy equivalent to the iceberg and melt it.

Note: This calculation assumes that energy is evenly delivered to the iceberg over time. In reality, the actual time required may be longer due to various factors like heat dissipation and loss.