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