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 ?

Total surface area of the star = 4πR2

By Stefan – Boltzmann black body kept at temperature T radiates heat per unit surface area per second given by

E = σT4

σ = Stefan-Boltzmann constant.

Now

Q/4πR2 = σT4

=> T4 = Q/(σ4πR2)

=> T =  {Q/(4πσR2)}1/4

=> T =  (1/√2R){Q/(πσ)}1/4

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