A uniform rod of thermal conductivity of `65J//m-s-^(@)C` is surrounded by an insulator on its sides. One of its ends is put in a furnace, while the other end is kept exposed. If the temperature gradient of the rod is `-75^@C//m`, find the emissive power of the exposed end.

Explanation

If `(DeltaQ)/(Deltat)` is the rate of heat conduction through the rod from the end at the furnace to the exposed one, then
`(DeltaQ)/(Deltat)=KA((-DeltaT)/(l))`
Where A is the cross-sectional area and `(DeltaT)/(l)` the temperature ture gradient.
`((DeltaQ)/(Deltat))(1)/(A)=K((-DeltaT)/(l))`
But `((DeltaQ)/(Deltat))(1)/(A)` is the emissive power (E) of the free end.
`E=K((-DeltaT)/(l))=65 J//m-s-^(@)Cxx75^@C//m=4875W//m^(2)`\