Respuesta :
Assuming the sun's energy is radiated uniformly in all directions, the total power is (π [tex]r . ^{2}[/tex] * σ[tex]R^{2} T^{4}[/tex])/[tex]r^{2}[/tex]
According to Stefan's law, if the sun were a perfect blackbody, its energy output per second would be:
P=σA[tex]T^{4\left \ }[/tex]
(Where P is energy radiated per second and A is the area of the sun.)
⇒P=σ×4π[tex]R^{2} T^{4}[/tex].............(1)
Assuming r>>r., the strength of this power at the earth's surface is
I= P/4π[tex]r^{2}[/tex]
⇒I= σ×4π[tex]R^{2} T^{4}[/tex]/4π[tex]r^{2}[/tex]
(Inserting the value obtained from equation (1))
⇒I= σ[tex]R^{2} T^{2}[/tex]/[tex]r^{2}[/tex]
Due to its great distance from the sun, the earth only receives a small portion of the energy that is radiated. The earth can be visualized as a little disc with a radius equal to that of the planet.
The disc's surface area is [tex]r .^{2}[/tex] hence the earth's total radiant energy as received is:
PE=π[tex]r. ^{2}[/tex]×I
P E = (π [tex]r . ^{2}[/tex] * σ[tex]R^{2} T^{4}[/tex])/[tex]r^{2}[/tex]
Assuming the sun's energy is radiated uniformly in all directions, the total power is (π [tex]r . ^{2}[/tex] * σ[tex]R^{2} T^{4}[/tex])/[tex]r^{2}[/tex]
Learn more about the sun's energy here:-
https://brainly.com/question/1140127
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