Question

The rear window of a van is coated with a layer of ice at 0°C. The...

The rear window of a van is coated with a layer of ice at 0°C. The density of ice is 917 kg/m3, and the latent heat of fusion of water is 3.35 x 105 J/kg. The driver of the van turns on the rear-window defroster, which operates at 12 V and 18 A. The defroster directly heats an area of 0.69 m2 of the rear window. What is the maximum thickness of ice above this area that the defroster can melt in 4.4 minutes?

Given:

ice temp = 0oC

ice density = 917 kg/m3

Latent heat of fusion of water = 3.35 x 105 J/Kg

defroster V=12 V and I= 18 A

Area = 0.69 m2

time=264 s

Solution

power delivered P = VI = 12 x 18 =    216 Watts

heat delivered H = power x time = 216 W x 264 seconds =   57024 Joules

mass of ice melted = heat / latent heat offusion = 57024 J / 335000 J/kg =  0.170220896 kg

volume of ice melted = mass / density = 0.170220896 / 917 = 0.000185628 m3

thickness of ice melted = volume / area = 0.000185628 / 0.69 =   0.000269026 meter

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