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 2.0 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.

It takes 40 hours to melt the block of ice.

Explanation:

According to the principles of radiation and heat transfer respectively:

ΔQ = I(dt)eAcosθ  (I = Solar energy density; dt = time taken; e = emissivity; A = Area of block; θ = angle between the sun ray and the horizontal)

ΔQ = mLf  (ΔQ = Heat change; m = mass of ice; Lf = Specific latent heat of fusion of ice)

but m = ρV = ρ.A.dx, therefore, the heat transfer equation can be re-written as:

ΔQ = ρ.A.dx.Lf

Lets equate the radiation equation and the modified heat transfer equation, we have:

ρ.A.dx.Lf = I(dt)eAcosθ

ρ.dx.Lf = I(dt)ecosθ    (Striking out the area)

Let's make dt the subject of formula,

dt = ρ.dx.Lf /I.e.cosθ

ρ = Density of ice,

Lf =

e = 0.050

θ = 32 deg. C

Now, let's substitute the terms:

Therefore, the time taken for the ice to completely melt is 40 hours (Two significant figures)

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