Solar radiation reaches the earths atmosphere at a rate of $1353 W m^{- 2}$ . If 36% of this
radiation is reflected back into space and 18% is absorbed by the earths atmosphere. The
radiant emittance is given by $σ T^{4}$
where $σ$ is the Stefan-Boltzmanns constant and T is the
absolute temperature. What maximum temperature would an isolated black body on the
earths surface be expected to attain?
$(σ = 5.67 x 10^{- 8} W m^{- 2} K^{- 4})$ .

120^{o} C

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{63.9}^{o} C

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{50.7}^{o} C

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{31.4}^{o} C

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Solution

The correct option is C ${50.7}^{o} C$
Of the solar radiation reaching the earths atmosphere
36% is reflected back into space
18% is absorbed by the earths atmosphere
This implies that only 46% reaches the earths surface
If absorbed by a black body, expect that the maximum temperature of this body is given by
where $I_{s c} = 1353 W m^{- 2}$

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