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# The sun having surface temperature  ${T}_{S}$ radiates like a blackbody. The radius of sun is ${R}_{S}$  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

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a
T=TsRS2R
b
T=TS
c
T=Ts2RSR
d
T=TsRSR
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detailed solution

Correct option is A

[Step 1]:  Energy absorbed per unit time by earth’s surface, if its radius is r, is[Step 2]:  Qabs=σ4πRS2TS44πR2×πr2∵solar constant ,S=P4πb2⇒S=4πa2σT4s4πb2 [Step 3]: Energy radiated per unit time by earth’s surface,  Qrad=σ(4πr2)T4[Concept]:  Qabs=Qrad[Step 4]:   ⇒T4=Ts44Rs2R2[Step 5]:   T=TsRs 2R

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