CONCEPT: Latent Heat of Fusion, Specific Heat Capacity & Heat Transfer by Radiat

Question

CONCEPT: Latent Heat of Fusion, Specific Heat Capacity & Heat Transfer by Radiation A fraction, f, of the power, P, of solar radiation incident per unit area, A, on the surface of a frozen lake is absorbed by the ice.

a) Derive an expression for how much time, t, it will take to warm a layer of ice with thickness h, through a temperature change T and then melt it. The density of ice is , the latent heat of fusion for ice is L and the specific heat capacity for ice is c.

b) Calculate how much time, in hours, it will take for the sun to melt a layer of ice 6 cm thick if the solar radiative flux is 750 W/m2, of which the ice absorbs a fraction, f = 0.8. The density of ice is 920 kg/m3, the specific heat capacity for ice is 2100 J/kg K. The latent heat of fusion for ice is 33.4 x 104 J/kg and the ice is initially at a temperature of -3 oC. ________ hrs

Explanation / Answer

a) Mass = density x volume = A h

Energy needed , Q = mc + mL
= ( A h ) c T + ( A h ) L

Power = Energy /time
Time = energy /power

Effective power absorbed = fP

Time, t = A h ( c T + L ) / fP

b) Unit area = 1 m^2
Volume = 1 x 0.06 = 0.06 m^3
Mass = A h = 920 x 0.06 = 55.2 kg

Effective power = fP = 0.8 x 750 = 600W

Using : t = A h ( c T + L ) / fP
Time in seconds = 55.2 ( 2100 x 3 + 334000 ) / 600
Time = 31307 seconds

Time = 8.69 hours

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