The earth receives at its surface radiation from the sun at the rate of $$1400$$ $$W/m2$$. The distance of the centre of the sun from the surface of the earth is $$1.5$$ x $$1011$$ m and the radius of the sun is $$7.0$$ x $$108$$ m. Treating the sun as a black body it follows from the above data that its surface temperature is

Question

Infinity Learn · Accepted Answer

Let TK be the temperature of sun.Energy E radiated per unit area per second $$=$$σ$$T4(Stefan$$'s $$law)$$.Total surface area of sun $$=4$$$$π$$$$Rs2$$∴Total energy radiated per unit solid angle $$=$$σ$$T4Rs2Now$$ intensity of radiation at earth $$=$$σ$$T4Rs2/Res2where$$ $$Res=$$ distance between earth and sun.Substituting the given values, we get $$1400=5$$⋅$$67$$×$$10$$−$$8T47$$⋅$$0$$×$$1081$$⋅$$5$$×$$10112Solving$$, we get T $$=$$ $$5803$$ K.

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