Question 536: Thermodynamics & KTG

Question

Assuming the Sun to be a spherical body of radius $$R$$ at a temperature of $$TK$$, evaluate the total radiant powered incident of Earth at a distance $$r$$ from the Sun
Where r0 is the radius of the Earth and $$\sigma $$ is Stefan's constant.

Accepted Answer

Total power radiated by Sun $$ = \sigma {T^4} 	imes 4\pi {R^2}$$
The intensity of power at earth's surface $$ = {{\sigma {T^4} 	imes 4\pi {R^2}} \over {4\pi {r^2}}}$$
Total power received by Earth $$ = {{\sigma {T^4}{R^2}} \over {{r^2}}}\left( {\pi r_0^2} ight)$$

Answer

$$4\pi r_0^2{R^2}\sigma {{{T^4}} \over {{r^2}}}$$

Answer

$$\pi r_0^2{R^2}\sigma {{{T^4}} \over {{r^2}}}$$

Answer

$$r_0^2{R^2}\sigma {{{T^4}} \over {4\pi {r^2}}}$$

Answer

$${R^2}\sigma {{{T^4}} \over {{r^2}}}$$

Thermodynamics & KTG

Assuming the Sun to be a spherical body of radius $R at a temperature of TK, evaluate the total radiant powered incident of Earth at a distance r from the Sun Where r0 is the radius of the Earth and \sigma $ is Stefan's constant.

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