Q.
Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature t°C, the power received by a unit surface, (normal to the incident rays) at a distance R from the centre of the sun is (where σ is the Stefan's constant)
A) r²σ(t + 273)⁴/(4πR²)
B) 16π²r²σt⁴/R²
C) r²σ(t + 273)⁴/R²
D) 4πr²σt⁴/R²
Explanation
[Solution from source] The sun radiates P = 4πr²σ(t + 273)⁴. At distance R this spreads over 4πR², giving r²σ(t + 273)⁴/R² per unit area. Options using t⁴ forget to convert to kelvin, and dividing by an extra 4π is wrong. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.