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 1.0 cm ? assume that the sun's rays make an angle of 37 ∘ with the vertical and that the emissivity of ice is 0.050?

The first step in solving this problem is to calculate for the volume of ice: 
V = A w

V = 1 m^2 (0.010 m)

V = 0.010 m^3

 
At 0°C, the density of solid block of ice is: d = 917 kg / m^3 

Therefore the mass of the solid ice is:

m = 917 kg / m^3  * 0.010 m^3

m = 9.17 kg

The heat of fusion of ice is equivalent to 333.55 kJ/kg, therefore: 
Phase change enthalpy = 333.55 kJ/kg (9.17 kg)

Phase change enthalpy = 3,058.65 kJ = 3,058,650 J

 
Using 1kW/m^2 insolation energy: 
1kW/m^2 * (.05) * sin(90°-37°) = 39.93 Watts = 39.93 Joule/s m² 

Therefore the time required to melt the ice is:

t = (3,058,650 J) / [39.93 Joule/s m² * (1 m^2)]
t = 76,600.3 s = 21 hours 16 min 40 seconds

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