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

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 °C]). The chest is filled with 30 kg of ice at 0°C. The inner wall surface temperature of the ice chest is assumed to be constant at 0°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°C. How long would it take to completely melt the ice? Assume negligible heat transfer through the bottom surface.

Explanation / Answer

step;1

Given that

Area A=LB=50*40=2000 cm^2=0.2 m^2

thickness t=0.03 m

thermal conductivity k=0.033 W/m.C

mass m=30 kg

temperature differenxce=25 c

latent heat of fusion L=333.2*10^3 J/kg

step;2

now we find the time to melt the ice

Q/t=AK[T2-T1]/L

mL/t=0.033*0.2*25/0.03

30*3.332*10^5/t=5.5

time t=18.2*10^5 sec

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