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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? (Q stands for Stefan’s constant)

1. Q/4πR²σ
2. (Q/4πR²σ)⁻¹/²
3. (4πR²Q/σ)¹/⁴
4. (Q/4πR²σ)¹/⁴

Correct answer: (Q/4πR²σ)¹/⁴

Solution

The rate of energy radiated by a black body is given by Stefan-Boltzmann law: P = σA(T⁴), where A = 4πR² is the surface area of the star. Rearranging for T, we get T = (P / (4πR²σ))¹/⁴. Substituting Q for P, the correct answer is (Q / 4πR²σ)¹/⁴.

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