Published by:
CGP EDU Academic Team
Published on: September 13, 2026
The surface of a pond of area 50 m 2 is covered with ice at 0 ºC. If the earth receives 1400 watt of solar radiation per square meter and the ice reflects 90% of the radiation, how much ice will melt per hour?
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Calculate the total solar radiation incident on the pond area.
The total area of the pond is 50 m² and the solar radiation received is 1400 W/m².
Total solar power = Area × Solar radiation = 50 m² × 1400 W/m² = 70000 W.
Step 2: Calculate the amount of radiation absorbed by the ice.
Since the ice reflects 90% of the radiation, it absorbs 10% of the incident radiation.
Power absorbed = Total solar power × (1 - reflection rate) = 70000 W × (1 - 0.9) = 70000 W × 0.1 = 7000 W.
Step 3: Determine the amount of ice melting using the latent heat of fusion of ice.
The latent heat of fusion of ice is approximately 334,000 J/kg.
The energy needed to melt ice can be calculated using the formula: Energy = Power × Time.
Considering time as 1 hour (3600 seconds):
Energy = 7000 W × 3600 s = 25200000 J.
Step 4: Calculate the mass of ice that will melt.
Mass of ice melted = \frac{Energy}{Latent heat} = \frac{25200000 J}{334000 J/kg} ≈ 75.4 kg.
Therefore, approximately 75.4 kg of ice will melt per hour.
The total area of the pond is 50 m² and the solar radiation received is 1400 W/m².
Total solar power = Area × Solar radiation = 50 m² × 1400 W/m² = 70000 W.
Step 2: Calculate the amount of radiation absorbed by the ice.
Since the ice reflects 90% of the radiation, it absorbs 10% of the incident radiation.
Power absorbed = Total solar power × (1 - reflection rate) = 70000 W × (1 - 0.9) = 70000 W × 0.1 = 7000 W.
Step 3: Determine the amount of ice melting using the latent heat of fusion of ice.
The latent heat of fusion of ice is approximately 334,000 J/kg.
The energy needed to melt ice can be calculated using the formula: Energy = Power × Time.
Considering time as 1 hour (3600 seconds):
Energy = 7000 W × 3600 s = 25200000 J.
Step 4: Calculate the mass of ice that will melt.
Mass of ice melted = \frac{Energy}{Latent heat} = \frac{25200000 J}{334000 J/kg} ≈ 75.4 kg.
Therefore, approximately 75.4 kg of ice will melt per hour.
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