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A metal rod of cross-sectional area 1.0 cm² is heated at one end. At a certain instant the temperature gradient is 5.0 deg C/cm at cross-section A and 2.5 deg C/cm at cross-section B. The heat capacity of the portion AB is 0.40 J per deg C and the rod's thermal conductivity is 200 W/m-deg C. Neglecting heat loss to surroundings, find the rate at which the temperature of part AB rises.

1. 10 deg C/s
2. 12.5 deg C/s
3. 15 deg C/s
4. 17 deg C/s

Correct answer: 12.5 deg C/s

Solution

Heat in at A minus heat out at B gives net power into AB; dividing by the heat capacity 0.40 J/deg C gives 12.5 deg C/s.

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