A solid sphere of copper, R meters in radius is heated in an induction furnace. The alternating magnetic field in the induction furnace produces currents within the piece, which generate heat uniformly in all parts of the sphere. Two thermocouples have been embedded in the sphere, r, and r₂ [m] meters from the center of the sphere. When a steady state is reached, the outer thermocouple reads T₁ [°C] and the inner thermocouple reads T₂ [°C]. a) What is the rate of heat transfer from the sphere to the surroundings? b) What is the temperature at the center of the sphere?