Consider two cavities of arbitrary shape and material, each at the same temperature T, connected by a narrow tube in which can be placed color filters (assumed ideal) which will allow only radiation of a specified frequency y to pass through. 

(a) Suppose at a certain frequency v', p T(v') dv for cavity 1 was greater than p r (v') dv for cavity 2. A color filter which passes only the frequency y' is placed in the connecting tube. Discuss what will happen in terms of energy flow. 

(b) What will happen to their respective temperatures? 

(c) Show that this would violate the second law of thermodynamics; hence prove that all blackbodies at the same temperature must emit thermal radiation with the same spectrum independent of the details of their composition.