Question

How long does it take the Sun to melt a block of ice at 0°C with a flat horizontal area 1.0 m² and thickness 1.9 cm? Assume that the Sun's rays make an angle of 29° with the vertical and that the emissivity of ice is 0.050.

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Answer 1

We will first find the energy required to melt the whole ice
Q = m L
Where L is the latent heat of fusion and m is the mass of the ice
m = density x volume = density x horizontal area x thickness
m = 934 x 1 x 1.9 x 10^-2
m = 17.746 kg
Q = 17.746 x 334 = 5927.16 J
We should find the amount of energy given by the sun
Angle from the horizontal is (90⁰  - 29⁰)= 61⁰
The maximum solar flux is 1.362 kW / m²
The intensity at this angle is
I = 1.362 x cos (61⁰)
I = 0.6603 kW/m²
Net heat absorbed by the ice per second is
= emissivity x intensity x area of the ice
= 0.050 x 0.6603 x 1.0
= 0.33015 kJ/s
Thus the time taken to melt the whole ice is
t = 5927.16 J / 330.15 J/s
t = 17.95 s
t = 0.00499 hr