Answer :
(a) Mass of the iceberg ≈ 1.6514 × 10¹⁵ kg
(b) Heat transfer needed to melt the iceberg ≈ 6.369 × 10²⁰ J
(c) Time needed to melt the iceberg using solar energy ≈ 88.29 days
a) Mass Calculation:
The volume (V) of the iceberg:
V = L × W × T = (160,000 m) × (45,000 m) × (250 m) = 1.8 × 10¹² m³
The mass (m) of the iceberg:
m = ρ × V = 917 kg/m³ × 1.8 × 10¹² m³ = 1.6514 × 10¹⁵ kg
b) Heat Transfer to Melt the Ice:
Q1 = mcΔT, where ΔT = 0°C - (-250°C) = 250°C
Q1 = (1.6514 × 10¹⁵ kg) × (2090 J/(kg°C)) × (250°C) = 8.671 × 10¹⁹ J
Q2 = mL_f = (1.6514 × 10¹⁵ kg) × (3.34 × 10⁵ J/kg) = 5.502 × 10²⁰ J
Total heat required to melt the ice:
Q_total = Q1 + Q2 = 8.671 × 10¹⁹ J + 5.502 × 10²⁰ J = 6.369 × 10²⁰ J
c) Time to Melt with Solar Energy:
Area exposed to sunlight:
A = L × W = (160,000 m) × (45,000 m) = 7.2 × 10⁹ m²
Energy received from the Sun per day:
Energy/day = Solar energy absorption rate × Area = 100 W/m² × 7.2 × 10⁹ m² = 7.2 × 10¹¹ J/day
Time required to melt the ice:
t_melt = Q_total / Energy/day = (6.369 × 10²⁰ J) / (7.2 × 10¹¹ J/day) = 88.29 days
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