Older freezers developed a coating of ice inside that had to be melted periodica

Question

Older freezers developed a coating of ice inside that had to be melted periodically; an electric heater could speed this defrosting process. Suppose you're melting ice from your freezer using a heating wire that carries a current of 3.0A when connected to 120 V.

part A - What is the resistance of the wire?

part B - How long will it take the heater to melt 810g of accumulated ice at -10 %u2218C? Assume that all of the heat goes into warming and melting the ice, and that the melt water runs out and doesn't warm further.

Explanation / Answer

a) Ohm's law. V=I*R turns to R= V/I=120/3=40 ohms

b) Work = Power*Time =(I*V)*Time

To melt the ice, you need to heat it to melting temp then melt it. You need to apply enough work to melt it.

work to heat= mass * heat capacity * temperature difference
work to melt= mass *fusion heat capacity

Sum the two works, divide by I*V. That's the time it'll take.
t=(Wm+Wh)/(I*V)

Wm=810*2.11*(0-(-10)=17091 J

Wh=810*334=270540 J   

So t=(17091 + 270540)/(3*120)=798.975 sec

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