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 32 ∘ with the vertical and that the emissivity of ice is 0.050.

Express your answer to two significant figures and include the appropriate units.

Answer 1

the amount of heat energy required to melt the this ice
= mass of ice x latent heat of ice
= density of ice x volume of ice x latent heat of ice
= density of ice x flat area of ice x thickness of ice x latent heat of ice
= 917 x 1 x (1.9 x 10^-2) x 334 =5819.28 J=5.58kJ
now the sun rays makes an angle of 32∘ with the vertical so the angle made with horizontal =62∘
i'm taking the solar maximum flux = 1.362kW/m^2 (when perpendicular to surface)
but total intensity when sun rays makes an angle 50∘ with horizon
I = 1.362 x cos(62∘) = 0.0.693kW/m^2
net heat absorb by ice /sec = emissivity of ice x intensity of sun x area of ice
=0.05 x 0.693 x 1 = 0.034 kW or kJ/sec
hence time required to melt the ice completely = (3.37/0.034 = 99.11sec or (1.65min)


now you have to remember this value. The solar constant includes all types of solar radiation, not just the visible light. It is measured by satellite to be roughly 1.361 kilowatts per square meter (kW/m²) at solar minimum and approximately 0.1% greater (roughly 1.362 kW/m²) at solar maximum