The sun having surface temperature TS radiates like a blackbody. The radius of sun is RS and Earth is at a distance R from the centre of sun. Earth absorbs radiation falling on its surface from sun only and is at constant temperature T. If radiation falling on Earth’s surface is almost parallel and Earth also radiates like a blackbody, then

Question

The sun having surface temperature  TS radiates like a blackbody. The radius of sun is RS  and Earth is at a distance R from the centre of sun. Earth absorbs radiation falling on its surface from sun only and is at constant temperature T. If radiation falling on Earth’s surface is almost parallel and Earth also radiates like a blackbody, then

Infinity Learn · Accepted Answer

[Step $$1$$]:  Energy absorbed per unit time by earth’s surface, if its radius is r, is[Step $$2$$]:  $$Qabs=$$σ$$4$$$$π$$$$RS2TS44$$$$π$$$$R2$$×π$$r2$$∵solar constant ,$$S=P4$$$$π$$$$b2$$⇒$$S=4$$$$π$$$$a2$$σ$$T4s4$$$$π$$$$b2$$ [Step $$3$$]: Energy radiated per unit time by earth’s surface,  $$Qrad=$$σ$$(4$$$$π$$$$r2)T4$$[Concept]:  $$Qabs=Qrad$$[Step $$4$$]:   ⇒$$T4=Ts44Rs2R2$$[Step $$5$$]:   $$T=TsRs$$ $$2R$$

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