Black Body Radiation Homework: Energy/Sec on 1m2 Earth from Sun

In summary, the radiation emitted from the Sun moves radially outward from the Sun and falls on an area of 1 m2 on Earth every second, with the power being spread out over a surface area of 2.82743e23 m^2.
  • #1
__JR__
14
0

Homework Statement


Assume that the radiation emitted from the Sun moves radially outward from the Sun and that no radiation is absorbed between the Sun and Earth. How much energy in the form of radiation will fall per second on an area of 1 m2 on Earth, if that area is perpendicular to the straight-line path of the radiation? The distance from the Sun to Earth is 1.5e11 m. Assume the total power output of the sun is 4.47 x 1026 W.


Homework Equations


Stefan Boltzmann forumla - E(T) = [tex]\sigma[/tex]T4


The Attempt at a Solution



Where I'm struggling is with the role the distance between the two bodies plays. Since the radiation is emitted radially outward, the distance between the two is relatively large, and the area on Earth is relatively small, does this mean I need to observe an infinitesimally small "window" on the surface of the sun whose radiated waves will strike this area on earth? Or, since the 1m2 on the curved surface of the Earth is relatively small I can assume that it, and a corresponding surface on the sun, is flat?

The power output of the sun can be determined by a surface temp of 6000K and a radius of 6.95x108 m (we solved this in an earlier problem).
 
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  • #2
At the distance of the Earth from the sun, the light is impinging on a spherical surface centered at the sun with the radius equal to the Earth's orbit. This surface area of this sphere is the area that the power is "spread" over.

Can you use this information to find the power per unit area at the Earth's distance from the sun? If so, the answer should then follow trivially.
 
  • #3
Imagine the radiation leaving the sun as the surface of an expanding sphere, calculate the surface area of this sphere when it reaches the Earth's surface (i.e a sphere with a radius equal to the distance between the sun and the earth). By considering what proportion of the total surface area 1m^2 is, you can work out how much of the total power strikes that area.
 
  • #4
Thanks for the replies, I think I've got the right answer.

So the total power output of the sun is 4.47e26 W, and the SA of the new sphere is 4*pi*(1.5e11)^2 m^2 = 2.82743e23 m^2.

Dividing gives 1580.94 w*m^(-2). Sound right?
 
  • #5
looks good to me!
 
  • #6
Prosthetic Head said:
looks good to me!

Looks good to me as well.

(BTW, that was perfect timing with our previous posts, Prosthetic Head!)
 
  • #7
Thanks again!
 

Related to Black Body Radiation Homework: Energy/Sec on 1m2 Earth from Sun

What is black body radiation?

Black body radiation is the electromagnetic radiation emitted by an object that absorbs all radiation incident upon it. It is also known as thermal radiation or Planck radiation.

What is the significance of the "Energy/Sec on 1m2 Earth from Sun" in the context of black body radiation?

The "Energy/Sec on 1m2 Earth from Sun" is a measure of the amount of energy that reaches the Earth's surface per second from the Sun. It is an important factor in the study of black body radiation because the Earth receives a significant amount of its energy from the Sun, which is a black body radiator.

How does black body radiation relate to the Earth's temperature?

The Earth's temperature is affected by black body radiation in two ways. First, the Sun's radiation warms the Earth's surface, leading to its average temperature. Second, the Earth itself emits radiation as a black body, which helps maintain its temperature.

What factors affect the amount of black body radiation emitted by an object?

The amount of black body radiation emitted by an object depends on its temperature and surface area. Higher temperatures and larger surface areas result in a greater amount of radiation being emitted. Additionally, the type of material and its emissivity also play a role in the amount of radiation emitted.

How does the study of black body radiation contribute to our understanding of the universe?

The study of black body radiation is crucial in understanding the behavior of objects in the universe, such as stars and planets. It helps explain the distribution of energy in the universe and is a fundamental concept in fields such as astrophysics and cosmology.

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