Show that radiation at a distribution of temperatures decreases the estimate (34 34) of the uniform temperature radiative response 0 by proving the result in the case where the radiation comes from two different temperatures Assume I a (T y) 4 b (T y) 4 240 W m 2 , for fixed values of a b 1 and y, ...

a We compute with some precision that if T 4 240 then T 255069 K 0 ...

Show that radiation at a distribution of temperatures decreases the estimate (34.34) of the uniform temperature radiative

Question:

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;

Distribution
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