The total amount of ice in the Greenland ice sheet is estimated to be 2.85 million cubic km.
Assume the Earth's surface is 70% covered by ocean, and that the Earth's radius is 6300 km. How many meters would sea level rise if the entire Greenland ice sheet were to melt?
(You may further assume that the density of ice is 916.9 kg/m^3 , and that once melted it attains the density of fresh water at 0 C, 1000 kg/m^3.)
To determine the sea level rise if the entire Greenland ice sheet were to melt, we need to calculate the volume of water that would be released. We can then convert this volume into a change in sea level.
1. Calculate the volume of ice in Greenland:
The given total amount of ice in the Greenland ice sheet is 2.85 million cubic km. We need to convert this to cubic meters for further calculations.
1 million cubic km = 1 x 10^12 cubic meters
So, the volume of ice in Greenland is 2.85 million x 10^12 cubic meters.
2. Calculate the volume of water released when the ice sheet melts:
Since ice has a lower density than water, we need to take into account the change in density when the ice melts. The density of ice is given as 916.9 kg/m^3, and the density of water is 1000 kg/m^3.
To find the volume of water released, we multiply the volume of ice by the ratio of densities:
Volume of water released = Volume of ice × (Density of water / Density of ice)
Volume of water released = (2.85 million x 10^12 cubic meters) × (1000 kg/m^3 / 916.9 kg/m^3)
3. Convert the volume of water to a change in sea level:
Knowing the Earth's surface is about 70% covered by oceans, we need to multiply the volume of water released by the fraction of the Earth's surface covered by oceans.
Change in sea level = Volume of water released × Fraction of Earth's surface covered by oceans
Change in sea level = Volume of water released × 0.7
4. Finally, convert the change in sea level from meters to the desired unit:
The radius of the Earth is given as 6300 km. We will convert it to meters by multiplying by 1000.
Change in sea level (in meters) = Change in sea level × 6300 km × 1000 m/km
By plugging in the calculated values, we can determine the sea level rise if the entire Greenland ice sheet were to melt.