Two identical steel plates A and B are placed side by side in a high-vacuum chamber. Both plates behave as perfect blackbodies and can be maintained at different steady temperatures.
a. (i) Plate A is kept at 600K. The rate of energy emission per unit area from plate B is observed to be exactly three times that from plate A. Calculate the temperature of plate B.
b. (ii) Derive a general expression for the temperature of plate B in terms of the temperature of plate A and the observed ratio RARB of their emissive powers.
c. (iii) If the emissive power of plate B were to be reduced to one-fourth of that of plate A, what would be the new temperature of B? (Give your answer correct to the nearest kelvin.)