A cylindrical rod of length 50cm and cross sectional area `1cm^(2)` is fitted between a large ice chamber at `0^(@)C` and an evacuated chamber maintained at `27^(@)C` as shown in figure. Only small protions of the rod are insid ethe chamber and the rest is thermally insulated from the surrounding. The cross section going inti the evacuted chamber is blackened so that it completely absorbe any radiation falling on it. The temperatuere of the blackened end is `17^(@)C` when steady state is reachhed. Stefan constant `sigma=6xx10^(-s)Wm^(-2)K^(-4)` . Find the thermal conductivity of the material of the rod.

Explanation

Blackened portion will absorb heat energy by radiation and deliver `0^@C` chamber by conduction process.
`((17))/(0.5)kA=(17-0)/(R )=sigmaeA{(300)^4-(290)^4}`
`e=1` for blackened object.