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Question

The surface of the earth receives solar radiation at the rate of 1400Wm2. The distance of the centre of the sun from the surface of the earth is 1.5×1011m and the radius of the sun is 7.0×108m. Treating the sun as a black body, it follows from the above data that the surface temperature of the sun is about

A
58000K
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B
5800K
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C
6000K
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D
6200K
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Solution

The correct option is C 5800K
The energy radiated from a blackbody from Stefan's law is E=σAT4
For sun E=4πR2σT4
where σ=5.67108 is Stefan's constant, T is the surface temp of the blackbody in Kelvin and A is the surface area of the blackbody.
The solid angle subtended by a unit surface area on earth's surface at sun's center is dΩ=14πr2 where r is the distance from sun's center to earth.
Given,
EdΩ=1400
R=7108
r=1.51011
4πR2σT414πr2=R2r2σT4=1400
T4492.251065.67108=1400
T4=.11341016
T=5.83103=5830

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