NEET2010PhysicsThermal Properties of MatterActual
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 , whose outer surface radiates as a black body at a temperature T ~K is given by (where is Stefan's constant)
Options
- Ar^2 ~T ^4 / R ^2
- Br^2 T^4 / 4 r^2
- Cr^4 T^4 / r^4
- D4 r^2 T^4 / R^2
Correct answer
A. r^2 ~T ^4 / R ^2
Step-by-step solution
If r is the radius of the star and T its temperature, then the energy emitted by the star per second through radiation in accordance with Stefan's law will be given by A T ^4=4 r ^2 T ^4 In reaching a distance R this energy will spread over a sphere of radius R ; so the intensity of radiation will be given by S= P 4 R^2 = 4 r^2 T^4 4 R ^2