One end of a rod of length `20cm` is inserted in a furnace at `800K` The sides of the rod are coverd with an insulating meterial and the other end emits radiation like a black boy 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 imporatant mode of energy transfer between the surrounding and the open end of the rod, find the thermal conductivity of the rod Stefan's constant `sigma = 6.0 xx 10^(8) W m^(-2) K^(-4)` .

Explanation

Quantity of heat flowing through the rod per sec ond in steady state
`(dQ)/(dt) = (K.A d theta)/(x)..(i)`
Quantity of heat radiated from the end of the rod per second in steady state
`(dQ)/(dt)=A sigma (T^(4)-T_(0)^(4))` .....(ii)
From Eqs (i) and (ii) `(K.d theta)/(x) =sigma (T^(4)-T_(0)^(4))`
`(Kxx 50)/(0.2) = 6.0 xx 10^(-8) [(7.5)^(4) -(3)^(4)]xx10^(8)`
`K =74 W//mk`
.