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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 $Q$?

($\sigma$ stands for Stefan's constant)

  • A$\frac{Q}{{4\pi \sigma {R^2}}}$
  • B${\left( {\frac{Q}{{4\pi \sigma {R^2}}}} \right)^{\frac{1}{2}}}$
  • C${\left( {\frac{Q}{{4\pi \sigma {R^2}}}} \right)^{\frac{1}{4}}}$
  • D${\left( {\frac{{4\pi \sigma {R^2}}}{Q}} \right)^{\frac{1}{4}}}$
AIPMT 2012, Medium
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