A wooden ice box has a total area of 1.50 m2 amd walls with an average thickness of 2.0 cm. The box contains ice at 0.0 oC. The inside of the box is kept cold by melting ice. How much ice melts in one day if the ice box is kept in the shade of tree at 29 oC. (Assume the thermal conductivity of wood is 0.16 kJ/s m oC

m = 9.1 x 10⁶ kg

Explanation:

First, we need to find the rate of heat transfer through the box to the ice. For this purpose, we use Fourier's Law of Heat Conduction:

Q = KA ΔT/L

where,

Q = Rate Of Heat Transfer = ?

K = Thermal Conductivity = 0.16 KW/m.°C = 160 W/m.°C

A = Area = 1.5 m²

ΔT = Difference in Temperature = 29°C - 0°C = 29°C

L = Thickness of wall = 2 cm = 0.002 m

Therefore,

Q = (160 W/m °C)(1.5 m²)(29°C)/(0.002 m)

Q = 3.48 x 10⁶ W

Now, we find the amount of heat transferred in one day to the ice:

q = Qt

where,

q = amount of heat = ?

t = time = (1 day)(24 h/1 day)(3600 s/1 h) = 86400 s

Therefore,

q = (3.48 x 10⁶ W)(8.64 x 10⁴ s)

q = 3 x 10¹¹ J

Now, for mass of ice melted in a day:

q = m H

m = q/H

where,

m = mass of ice melted in a day = ?

H = latent heat of fusion of ice = 3.3 x 10⁵ J/kg

Therefore,

m = (3 x 10¹¹ J)/(3.3 x 10⁵ J/kg)

m = 9.1 x 10⁶ kg

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