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Properties of Matter question

2012 · Q165
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Properties of Matter question

2012 · Q165

NEETPhysicsProperties of MatterMCQ+4 / −1
If the radius of a star is R and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q?
  1. A
    Q4πR2σ{Q \over {4\pi {R^2}\sigma }}4πR2σQ​
  2. B
    (Q4πR2σ)−1/2{\left( {{Q \over {4\pi {R^2}\sigma }}} \right)^{ - 1/2}}(4πR2σQ​)−1/2
  3. C
    (4πR2Qσ)1/4{\left( {{{4\pi {R^2}Q} \over \sigma }} \right)^{1/4}}(σ4πR2Q​)1/4
  4. D
    (Q4πR2σ)1/4{\left( {{Q \over {4\pi {R^2}\sigma }}} \right)^{1/4}}(4πR2σQ​)1/4
View written solutionFree

Correct answer: D

Stefan’s law for black body radiation

Q=σeAT4Q = \sigma eA{T^4}Q=σeAT4

∴T=[Qσ(4πR2)]1/4 \therefore T = {\left[ {{Q \over {\sigma \left( {4\pi {R^2}} \right)}}} \right]^{1/4}}∴T=[σ(4πR2)Q​]1/4

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