Q. 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? (σ stands for Stefan's constant)
A) (Q/(4πR²σ))^(1/4)
B) Q/(4πR²σ)
C) (Q/(4πR²σ))^(−1/2)
D) (4πR²Q/σ)^(1/4)
Explanation
[Solution from source] For a black body, power radiated = σT⁴ × area = 4πR²σT⁴. In steady state this equals the energy production rate Q, so T = (Q/(4πR²σ))^(1/4). The expression without the fourth root gives T⁴, not T. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.