MHT CET20255 May 2025Evening ShiftPhysicsThermal Properties of MatterActual
The outer surface of star in the form of a sphere radiates heat as a black body at temperature ' T '. The total radiant energy per unit area, normal to the direction of incidence, received at a distance ' R ' from the centre of a star of radius ' r ' is ( R > r ) ( = Stefan's constant)
Options
- Ar^2 ~T ^4 R ^2
- Br^2 T^4 4 R^2
- Cr ^2 ~T ^4 R ^4
- D4 r^2 T^4 R^2
Correct answer
A. r^2 ~T ^4 R ^2
Step-by-step solution
The radiant energy per unit area received normal to incidence at distance R from a star of radius r radiating as a black body at temperature T is determined through the Stefan-Boltzmann law and spherical radiation geometry. The star's total radiative power is P = (4 r^2) T^4 . At distance R , this power distributes uniformly over the spherical surface area 4 R^2 , yielding the intensity I = P 4 R^2 . Substituting gives I = (4 r^2) T^4 4 R^2 = r^2 T^4 R^2 . Final Answer: A