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Question: A thermal reservoir at 100 C is connected to an ice -water mixture at 0 C via a copper pipe (thermal conductivity k=385 watt/m. K, density 8.96 g/cm³, diameter 0.5 cm, length 80 cm).

1) How long does it take to melt 20 grams of ice?

2) If the temperature drops linearly from 100 C to 0 C along the copper pipe, find the temperature as a function of pipe length.

3) If this copper pipe is disconnected from thermal reservoirs and placed in a thermal insulated box, proof its final temperature would be 50 C. Ccopper=0.093 cal/g C.

Please show all work and equations.

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