Show that radiation at a distribution of temperatures decreases the estimate (34.34) of the uniform temperature radiative response λ₀ by proving the result in the case where the radiation comes from two different temperatures. Assume I = aσ (T − y)⁴ + bσ (T + y)⁴ =240 W/m², for fixed values of a + b = 1 and y, and repeat the computation leading to the estimate (34.34)

a) Show that the distributed estimate decreases for the specific values (a = b = 1/2, y = 1 K); 

b) Prove analytically that the distributed estimate decreases for any values of a, b, y and start with a = b = 1/2; 

Transcribed Image Text:

- Fo approx = A(o T*) = 40 T³AT 3.76 AT W/m? K-!