Question

Power of sunlight on Earth The Sun emits about 3.9 * 1026 J of electromagnetic radiation each second. (a) Estimate the power that each square meter of the Sun’s surface radiates. (b) Estimate the power that 1 m2 of Earth’s surface receives. (c) What assumptions did you make in part (b)? The distance from Earth to the Sun is about 1.5 * 1011 m and the diameter of the Sun is about 1.4 * 109 m

Answer 1

Answer:

a)6.34 x  $10^{7}$W/m²

b)1.37 x $10^{3$ W/m²

c) see explanation.

Explanation:

a)The relation of intensity'I' of the radiation and area 'A' is given by:

I= P/A

where P= power of sunlight i.e 3.9 x $10^{26}$ J

and the area of the sun is given by,

A= 4π$R_{sun}$ => 4π$(\frac{1.4*10^{9} }{2} )^{2}$

A=6.15 x $10^{18}$m²

$I_{sun}$ =  3.9 x $10^{26}$ / 6.15 x $10^{18}$ => 6.34 x  $10^{7}$W/m²

b) First determine the are of the sphere in order to determine intensity at the surface of the virtual space

A= 4π$R$

Now R= 1.5 x $10^{11$m

A=  4π x 1.5 x $10^{11$ =>2.83 x $10^{23$ m²

The power that each square meter of Earths surface receives

$I_{earth$ =   3.9 x $10^{26}$/2.83 x $10^{23$ =>1.37 x $10^{3$ W/m²

c) in part (b), by assuming the shape of the wavefront of the light emitted by the Sun is a spherical shape so each point has the same distance from the source i.e sun on the wavefront.