Calculate the temperature the entire sky would have to be in order to transfer h

Question

Calculate the temperature the entire sky would have to be in order to transfer heat by radiation at 1000 W/m2 - about the rate at which the sun transfers heat when it is directly overhead on a clear day. This is the effective temperature of the sky, a kind of average that takes account of the fact that the sun occupies only a small part of the sky but is much hotter than the rest. Assume that the body receiving the heat has a temperature of 25.0°C, and that the value of emmissivity of the earth is 0.65.

Explanation / Answer

1 =1000 W/m2

T1 = 25.0°C = 298K

2 = 0.65

E = T4 from stefan - boltmanlaw

1 /2 = T24 /T14

1 /2 = T24 /2984

1000/0.65 = T24 /2984

T24 = 1538.46/7886150416

T24 = 1.95 X 10-7

T2 = (1.95 X 10-7 )-4

T2 = 6.91 x 1026 k

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