Answer :
Final answer:
The mass of the iceberg is approximately 1.4672 x 10^15 kg, with a heat transfer of 4.900608 x 10^20 J needed to melt it. Using sunlight at 100 W/m^2 for 12 hours a day, it would take roughly 48.5 years to melt the iceberg.
Explanation:
To calculate the mass of the iceberg, we need to use the volume and the density of ice. First, let's convert all measurements to meters to be consistent with the density unit:
- Length: 160 km = 160,000 m
- Width: 40 km = 40,000 m
- Thickness: 250 m
The volume V is therefore:
V = Length × Width × Thickness = 160,000 m × 40,000 m × 250 m = 1.6 x 1012 m³.
The mass m can be calculated using the density ρ of ice (917 kg/m³):
m = V × ρ = 1.6 x 1012 m³ × 917 kg/m³ = 1.4672 x 1015 kg.
To calculate the heat transfer needed to melt the iceberg, we need the latent heat of fusion for ice, which is about 334,000 J/kg:
Heat Q = mass × latent heat of fusion = 1.4672 x 1015 kg × 334,000 J/kg = 4.900608 x 1020 J.
For the amount of time it would take sunlight to melt the iceberg, assuming an absorption of 100 W/m² and 12 hours of sunlight per day, first calculate the total power absorbed by the iceberg:
Total Area Absorbing Sunlight = Length × Width = 160,000 m × 40,000 m = 6.4 x 109 m².
Power P = Total Area × Absorption Rate = 6.4 x 109 m² × 100 W/m² = 6.4 x 1011 W.
The daily energy absorption is Power × Time:
Energy per day = 6.4 x 1011 W × 12 h × 3600 s/h = 2.7648 x 1016 J/day.
Finally, to find the years it would take:
Years = Total Heat Required / (Energy per day × Days per year)
= 4.900608 x 1020 J / (2.7648 x 1016 J/day × 365 days/year)
≈ 48.5 years.
