Two perfectly black spherical bodies are mounted inside a large evacuated chamber so that no heat exchange other than their own radiation takes place. Sphere A has radius 0.10m and is kept at 1200K, while sphere B has radius 0.20m and is kept at 800K.
a. (i) Show that the radiant power emitted by a spherical body is proportional to r2T4, where r is its radius and T its absolute temperature.
b. (ii) Using the result of part (i), obtain the ratio of the instantaneous radiant powers of spheres A and B.
c. (iii) Calculate the total energy radiated jointly by both spheres in 5 minutes, assuming their temperatures remain constant for this interval.