In the summer of 2010 a huge piece of ice roughly four times the area of Manhattan and 500 m thick caved off the Greenland mainland. Required:
a. How much heat would be required to melt this iceberg (assumed to be at 0°C) into liquid water at 0°C?
b. The annual U. S. energy consumption is 1.2 x 10^20 J. If all the U. S. energy was used to melt the ice, how many days would it take to do so?

a

b

Explanation:

From the question we are told that

     The  area of  Manhattan is  

      The area of the ice is

        The  thickness is  

Generally the volume of the ice is mathematically represented is

substituting value

Generally the mass of the ice is

Here is the density of ice the value is  

=>  

=>    

Generally the energy needed for the ice to melt is mathematically represented as

Where is the latent heat of fusion of ice and the value is  

=>    

=>    

Considering part b

  We are told that the annual energy consumption is  

So  the time taken to melt the ice is

converting to days

because it says use -2,0,and 2 for x, we can plug those numbers into the equation. y/4=3/4(-2)+2   y/4= -1 1/2 +2 now to get x by itself, we can multiply each side by 4. y=-6+8 which equals y=2 when x=-2. now you can do the same thing with 0 and 2 as x. you get y=8 when x=0 and y=14 when x=2.

x   |   y

-2 |   2

0   |   8

2   |   14