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 6.0 A when connected to 120 V.

A) What is the resistance of the wire?

B) How long will it take the heater to melt 660 g of accumulated ice at -10C ? 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)

R = V/I = 120 / 6 = 20 ohm

B)

The specific heat of water is 1 calorie/gram °C = 4.186 joule/gram °C

so to raise the temperature of water to 0 degree heat consumes by ice is

Q1 = mC(delta T) = 660 * 4.186 * 10 = 27627.6 Joule

to melt this ice at 0 degree heat required

Q2 = Latent Heat Fusion * mass = 334 * 660 = 220440 Joule

Q1 + Q2 must be supplied by the resistive wire So

Q1 + Q2 = I^2 R * t

t = (Q1 + Q2) / (I^2* R)

= 248067.6 / (36 * 20) = 344.54 sec

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