Along homogeneous resistance wire of radius ro = 5 mm is being used to heat the air in a room by the passage of electric current. heat is generated in the wire uniformly at a rate of g=5' 10^7w/m^3 as a result of resistance heating. if the temperature of the outer surface of the wire remains at 180°c, determine the temperature at r = 2 mm after steady operation conditions are reached. take the thermal conductivity of the wire to be k=8 w/m x °c.