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

(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

To calculate how many years it would take sunlight alone to melt ice of a given thickness, use the formula:

Time = Energy / (Power x Area)

Where:
- Time is the duration in seconds
- Energy is the energy required to melt the ice
- Power is the average power absorbed by each square meter of ice
- Area is the total surface area of the ice to be melted

Let's calculate it step by step:

1. Calculate the area of the ice:
The area of the rectangular iceberg can be found by multiplying its length and width:

Area = Length x Width

Area = 160 km x 45 km
Note: Convert kilometers to meters for consistent units.

Area = 160,000 m x 45,000 m

2. Calculate the total energy required to melt the iceberg:
The energy required to melt the ice can be calculated by multiplying the mass of the ice by the latent heat of fusion of ice.

Energy = Mass x Latent Heat of Fusion

To find the mass, we can use the density of ice and the volume of the iceberg:

Mass = Density x Volume

Volume = Length x Width x Thickness

Volume = 160,000 m x 45,000 m x 250 m

Now, calculate the mass:

Mass = Density x (Length x Width x Thickness)

3. Calculate the time required to melt the ice using sunlight:
Now, plug in the values obtained from the previous calculations:

Time = Energy / (Power x Area)

Power = 100 W/m² (Given)
Area = (Length x Width)

Time = Energy / (100 W/m² x (Length x Width))

However, we need to convert the time from seconds to years. Here's how:

Time (in years) = Time (in seconds) / (365.25 days/year x 24 hours/day x 60 minutes/hour x 60 seconds/minute)

Plug in the values to calculate the time required in years.

This will give you the answer to part (d) of the question.

To solve part (d), we need to calculate the total amount of energy that the iceberg receives from the 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 surface area of the iceberg:

Surface Area = length × width
Surface Area = 160 km × 45.0 km
Surface Area = 7200 km²

Next, we need to convert the surface area to square meters:

1 km² = (1000 m)² = 1,000,000 m²
Surface Area = 7200 km² × (1,000,000 m²/km²)
Surface Area = 7200 × 1,000,000 m²
Surface Area = 7.2 × 10^9 m²

Now, let's calculate the total energy received by the iceberg each day:

Energy = power × time
Energy = 100 W/m² × 7.2 × 10^9 m² × 13.00 h

Note: We need to convert hours to seconds to have consistent units.

1 h = 3600 s
Total energy = 100 W/m² × 7.2 × 10^9 m² × (13.00 h × 3600 s/h)

Now, let's calculate the number of days it would take to accumulate enough energy to melt the iceberg:

Energy required to melt the iceberg (b) = 5.51 × 10^20 J

Number of days = Energy required to melt the iceberg / Total energy per day

Number of days = (5.51 × 10^20 J) / (100 W/m² × 7.2 × 10^9 m² × (13.00 h × 3600 s/h))

Calculating this expression will give us the answer:

Number of days ≈ 44.8 years

Therefore, it would take approximately 44.8 years for sunlight alone to melt the ice with the given conditions.