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A cylindrical rod of length 50 cm and cross-sectional area 1 cm² is connected between a large ice chamber at 0 deg C and an evacuated chamber at 27 deg C; only the ends are inside the chambers and the rest is thermally insulated. The end facing the evacuated chamber is blackened and absorbs all radiation falling on it. In steady state this blackened end is at 17 deg C. Taking Stefan's constant sigma = 6 x 10⁻⁸ W/m²/K⁴, find the thermal conductivity of the rod.

1. 1.8 W/m/K
2. 0.9 W/m/K
3. 2.7 W/m/K
4. 3.6 W/m/K

Correct answer: 1.8 W/m/K

Solution

Balancing radiation in (at 300 K vs 290 K) against conduction over 17 K gives k about 1.8 W/m/K.

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