Question

The sun emits energy in the form of electromagnetic waves produced by nuclear reactions deep in the sun's interior. Assume that the rate of energy emission is W for this problem. Find the intensity of electromagnetic radiation at the surface of the sun (radius r =R = ). Ignore any scattering of waves as they move radially outward from the center of the sun. W/m2 Find the radiation pressure on an absorbing object at the surface of the sun, ignoring wave scattering. Pa Repeat for r = R/2, in the sun's interior. intensity of radiation W/m2 radiation pressure Pa What is the ratio of the intensity of radiation at the sun's surface to that given in Section 32.4 for sunlight just before it enters the earth's atmosphere? (Give only the order of magnitude of this ratio.)

Answer 1

Answer:

I = W / 4π R_{s}²,   P = W / 2π c R_{s}², Io /I_{earth} = 10⁴  

Explanation:

The intensity is defined as the ratio between the emitted power and the area of ​​the spherical surface

               I = P / A

Since the emitted power is constant and has a value of W for this case, let's look for the area of ​​the sphere on the surface of the sun

             A = 4π $R_{s}$²

             I = W / 4π R_{s}²

.- The radiation pressure for total absorption is

             P = S / c

Where S is the Pointer vector that is equal to the intensity

Let's replace

             P = W / 2π c R_{s}²

.- We repeat for r = R_{s}/2

              I₂ = W / 4π (R_{s}/ 2)²

              I₂ = 4 W / 4π R_{s}²

              I₂ = 4 Io

              I₀ = W / 4piRs2

    We calculate the radiation pressure

             P₂ = I₂ / c

             P₂ = 4 I₀ / c

             P₂ = 4 (W / 4pi c Rs2)

.- the relationship between these magnitudes is

            I₂ / I₀ = 4

            P₂ / P₀ = 4

Let's calculate the intensity on the surface where the Earth is

            r = 1.50 10¹¹ m

           $I_{earth}$ = W / 4π r²

           Io / I_{earth}   = r² /$R_{s}$²

          Io /I_{earth}  = (1.5 10¹¹ / 6.96 10⁸) 2

          Io /I_{earth} = 4.6 10⁴

          Io /I_{earth} = 10⁴