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One end of a rod length 20cm is inserted...

One end of a rod length `20cm` is inserted in a furnace at `800K`. 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 `750K` in the steady state. The temperature of the surrounding air is `300K`. 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=6.0xx10^(-1)Wm^(-2)K^(-4)` .

Text Solution

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The correct Answer is:
D
Heat flowing through the rod per second in steady state,

`(dQ)/(dt) = (Ka d theta)/x ` …….(i)
Heat radiated from the open end of the rod per second in steady state,
`(dQ)/(dt) = A sigma (T^4 - T_(0)^4)`……..(ii)
From Eqs. (i) and (ii),
`(Kd theta)/x = sigma (T^4 - T_(0)^4)`
`(K xx 50)/0.2 = 6.0 xx (10^-8) [(7.5)^4 - (3)^4] xx 10^8`
`K = 74 W//m-K`
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