Consider an ice chest with the following dimensions: length = 50 cm, width = 40
ID: 1532605 • 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 = 0.033 W/[m degree C]). The chest is filled with 30 kg of ice at 0 degree C. The inner wall surface temperature of the ice chest is assumed to be constant at 0 degree C. 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 25 degree C. How long would it take to completely melt the ice? Assume negligible heat transfer through the bottom surface.Explanation / Answer
l = 50 cm = 0.5m
w = 40 cm =0.4m
h = 30 cm = 0.3m
x = 3 cm = 0.03m
k = 0.033 W/m 0C
m = 30 kg
Tice = 0 0C
Lf = 333.2 kJ/kg
Toutside = 25 o C
Area of heat transfer = 2(0.5m*0.3m)+ 2(0.4m*0.3m)+(0.4m*0.5m)
= 0.3 m2 +0.24m2 +0.2m2 = 0.74 m2
Heat required for melting 30 kg ice
Q = m. Lf
=(30 kg)* (333.2kJ/kg) = 9996 kJ
Time required for 10011 kJ heat (t) = 9996000/20.35 = 491203 seconds