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Properties of Matter question

2007 · Q140
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Properties of Matter question

2007 · Q140

NEETPhysicsProperties of MatterMCQ+4 / −1
Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature toC, the power received by a unit surface, (normal to the incident rays) at a distance R from the centre of the sun is
where σ\sigmaσ is the Stefan's constant.
  1. A
    r2σ(t+273)44πR2{{{r^2}\sigma {{\left( {t + 273} \right)}^4}} \over {4\pi {R^2}}}4πR2r2σ(t+273)4​
  2. B
    16π2r2σt4R2{{16{\pi ^2}{r^2}\sigma {t^4}} \over {{R^2}}}R216π2r2σt4​
  3. C
    r2σ(t+273)4R2{{{r^2}\sigma {{\left( {t + 273} \right)}^4}} \over {{R^2}}}R2r2σ(t+273)4​
  4. D
    4πr2σt4R2{{4\pi {r^2}\sigma {t^4}} \over {{R^2}}}R24πr2σt4​
View written solutionFree

Correct answer: C

Power radiated by the sun at t°C

=σ(t+273)44πr2 = \sigma {\left( {t + 273} \right)^4}4\pi {r^2}=σ(t+273)44πr2

Power received by a unit surface

=σ(t+273)44πr24πR2=r2σ(t+273)4R2 = {{\sigma {{\left( {t + 273} \right)}^4}4\pi {r^2}} \over {4\pi {R^2}}} = {{{r^2}\sigma {{\left( {t + 273} \right)}^4}} \over {{R^2}}}=4πR2σ(t+273)44πr2​=R2r2σ(t+273)4​

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