Ross Ice Shelf in Antarctica. It was an approximately rectangular prism 160 km long, 40.0 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 transfer (in joules) is needed to melt it?
(c) How many years would it take sunlight alone to melt ice this thi

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Answer:

Ross Ice Shelf in Antarctica. It was an approximately rectangular prism 160 km long, 40.0 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 transfer (in joules) is needed to melt it?

(c) How many years would it take sunlight alone to melt ice this thick, if the ice absorbs an average of 100W/m², 12.00 h per day

The answers to the questions are as follows

(a) The mass of this iceberg is 1467200000000000 kg

(b) The heat required to melt the ice shelf is 4.93 × 10²⁰ J

(c) It would  take sunlight approximately 49 years to melt the ice if the ice absorbs an average of 100 W/m² for 12.00 hours per day

Explanation:

(a) Given the dimensions as

160 km long,

40.0 km wide

250 m thick

We have the volume as volume = length × breadth × width

Therefore, volume = 160000 m × 40000 m × 250 m = 1600000000000 m³

Therefore the mass = Density × Volume = 1600000000000 m³ × 917 kg/m³ = 1467200000000000 kg

(b). The heat, H required to melt the ice is given by

(The latent heat of fusion of ice) × (mass of ice)

H = 3.36×⁵10 J Kg-1 × 1467200000000000 kg = 4.93 × 10²⁰ J

The heat required to melt the ice shelf is 4.93 × 10²⁰ J

(c) The heat absorbed by the ice from the sun per day = 100 W/m² for 12 hour per day

The area surface area of the ice facing the sun = ice length × ice width = (160 km × 40 km) →

= 160 km × 1000 m/km × 40 km × 1000 m/km = 6.4 × 10⁹ m²

Therefore the heat absorbed = 100 W/m² × 6.4 × 10⁹ m² for 12 hour per day

= 6.4 × 10¹¹ W for 12 hour per day

= 6.4 × 10¹¹ J/s × 12 hr × 60 min/hr × 60 s/min = 2.7648×10¹⁶ J per day =  2.7648×10¹⁶ J/day

Therefore the number of days to melt the ice completely would be

(4.93 × 10²⁰ J)/(2.7648×10¹⁶ J/day) = 1.78 × 10⁴ days or

17831.31 days ×1/365 year/day = ‪48.8 years ≈ 49 years