MHT CET Medical202625 April 2026Evening ShiftPhysicsThermal Properties of MatterActual
Assuming the Sun to be a perfectly spherical black body of radius R and is at a temperature T K , then the total radiant power incident on the Earth at a distance r from the sun is ( consider R_o is the radius of the Earth and is Stefan's constant).
Options
- AR^2 R_o^2 T^4 r^2
- BR^2 T^4 R_o^2 r^2
- CR_o^2 T^4 R^2 r^2
- DR_o^2 T^4 R^2 r^2
Correct answer
A. R^2 R_o^2 T^4 r^2
Step-by-step solution
The total power radiated by the Sun is given by Stefan's law: P = A T^4 = (4 R^2) T^4 The intensity of this radiation at a distance r from the Sun is: I = P 4 r^2 = (4 R^2) T^4 4 r^2 = R^2 T^4 r^2 The Earth intercepts this radiation over its cross-sectional area, which is R_o^2 . The total radiant power incident on the Earth is: P_ incident = I R_o^2 = R^2 R_o^2 T^4 r^2 Answer: R^2 R_o^2 T^4 r^2