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 portions of the rod are inside the chamber and the rest is thermally insulated from the surrounding. The cross section going into the evacuated chamber is blackened so that it completely absorbs any radiation falling on it. The temperature of the blackened end is `17^(@)C` when steady state is reached. 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.