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Consider an ice chest with the following dimensions: length = 50 cm, width = 40

ID: 2074815 • Letter: C

Question

Consider an ice chest with the following dimensions:
length = 50 cm, width = 40 cm, and height = 30 cm, made of a 3-cm-thick insulating material (k 5 0.033 W/[m 8C]). The chest is filled with 30 kg of ice at 0C. The inner wall surface temperature of the ice chest is assumed to be constant at 0C. The latent heat of fusion of ice is 333.2 kJ/kg. The outside wall surface temperature of the chest is assumed to remain constant at 25C. How long would it take to completely melt the ice? Assume negligible heat transfer through the bottom surface

Explanation / Answer

Solution

Known:

l = 50 cm = 0.5m

w = 40 cm =0.4m

h = 30 cm = 0.3m

x = 3 cm = 0.03m

k = 0.033 W/moC

m = 30 kg

Tice= 0oC

Lf= 333.7 kJ/kg

Toutside= 25oC

Area of heat transfer = 2(0.5m*0.3m)+2(0.4m*0.3m)+(0.4m*0.5m)

= 0.3m2+0.24m2+0.2m2

= 0.74 m2

Heat required for melting 30 kg ice

Q = m. Lf

=(30 kg)* (333.7kJ/kg)

= 10011 kJ

Time required for 10011 kJ heat

(t) = 10011000/20.35

= 491941 seconds

= 136.5 houes