Two concentric spheres of diameter D) = 0.8 m and D₁ = 1.2 m are separated by an air space and have surface temperatures of T₁ = 400 K and T₂ = 300 K.

(a) If the surfaces are black, what is the net rate of radiation exchange between the spheres?

(b) What is the net rate of radiation exchange between the surfaces if they are diffuse and gray with ε₁ = 0.5 and ε₂ = 0.05?

(c) What is the net rate of radiation exchange if D₂ is increased to 20 m, with ε₂ = 0.05, ε₁ = 0.5, and D₁ = 0.8 m? What error would be introduced by assuming blackbody behavior for the outer surface (ε₂ = 1), with all other conditions remaining the same?

(d) For D₂ = 1.2 m and emissivities of E) = 0.1, 0.5, and 1.0, compute and plot the net rate of radiation exchange as a function of ε₂ for 0.05 < ε₂ < 1.0.