One end of a rod of length \( 20 \mathrm{~cm} \) is inserted in a furnace at \( 800 \mathrm{~K} ...

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One end of a rod of length \( 20 \mathrm{~cm} \) is inserted in a furnace at \( 800 \mathrm{~K} \). The sides of the rod are covered with an insulating material and the other end emits radiation like a blackbody. The temperature of this end is \( 750 \mathrm{~K} \) in the steady state. The temperature of the surrounding air is \( 300 \mathrm{~K} \). Assuming radiation to be the only important mode of energy transfer between the surrounding and the open end of the rod, find the thermal conductivity of the rod. Stefan constant \( \sigma=6.0 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4} \)
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