In 1986 a gargantuan iceberg broke away from the Ross Ice Shelf in Antarctica. It was approximately a rectangle 160 km long, 45.0 km wide, and 250 m thick.
(a) What is the mass of this iceberg, given that the density of ice is 917 kg/m3?
(b) How much heat is required to melt it?
(c) Compare this amount of energy with the annual U.S. energy use of 8 multiplied by 1019 J by taking a ratio.
(d) How many years (365.25 days) would it take sunlight alone to melt ice this thick, if the ice absorbs an average of 100 W/m2, 13.00 h per day?
I know the answers and how to do the a,b,c, but I can't figure out the last one?
a.1.65e15; b.5.51e20; c.6.89; d.44.8Years
To solve part (d), we need to calculate the amount of energy received from sunlight each day and then determine how many days it would take to accumulate enough energy to melt the entire iceberg.
First, let's calculate the total surface area of the iceberg. The surface area can be obtained by multiplying the length and width of the rectangle:
Area = Length × Width = 160 km × 45.0 km
However, we need to convert the units to meters, so:
Area = (160 km × 1000 m/km) × (45.0 km × 1000 m/km)
Next, let's calculate the total energy received from the Sun each day. The average power absorption per unit area is given as 100 W/m^2. Considering that the iceberg will receive sunlight for 13.00 hours per day, the energy received per day is:
Energy per day = (100 W/m^2) × (Area) × (13.00 h)
Now, let's convert the units of the area to square meters:
Area = (160 km × 1000 m/km) × (45.0 km × 1000 m/km) = (160 × 1000 m) × (45.0 × 1000 m)
After substituting the value of the area, we can calculate the total energy received per day:
Energy per day = (100 W/m^2) × [(160 × 1000 m) × (45.0 × 1000 m)] × (13.00 h)
Finally, we can calculate the number of days it would take to accumulate enough energy to melt the entire iceberg by dividing the mass (given mass from part (a)) by the energy received per day:
Number of days = (Mass of iceberg) / (Energy per day)
Note: Here, we need to convert the mass of the iceberg to energy units by multiplying it with the heat of fusion for ice, which is 3.33 × 10^5 J/kg.
Number of days = [(Mass of iceberg) × (3.33 × 10^5 J/kg)] / (Energy per day)
Now, you can substitute the given values to get the answer in years.
Answer: It would take approximately 44.8 years for sunlight alone to melt ice this thick.
(a) m=ρ•V= ρ•L•W•H=917•160000•45000•250=1.65•10¹⁵ kg
(b) Q=mL=1.65•10¹⁵•334000=5.51•10²º J
(c) Q/Q(US) =5.51•10²º/8•10¹⁹=6.89
(d) Q/q= 5.51•10²º/100•160000•45000•13•3600 •365.25 =44.8yr