A large body of lava from a volcano has stopped flowing and is slowly cooling. The interior of the lava is at 1200°C, its surface is at 450°C, and the surroundings are at 27.0°C.

(a) Calculate the rate at which energy is transferred by radiation from 1.00 m² of surface lava into the surroundings, assuming the emissivity is 1.00. 

(b) Suppose heat conduction to the surface occurs at the same rate. What is the thickness of the lava between the 450°C surface and the 1200°C interior, assuming that the lava's conductivity is the same as that of brick?