Question

part a
estimate the average power output of the sun, given that about 1350 w/m² reaches the upper atmosphere of the earth.
express your answer with the appropriate units.
s = value units
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Explanation:

Step1: <Use the formula for power>

The formula for power is \( P = I\times A \), where \( I = 1350\,\text{W/m}^2 \) (intensity) and \( A\) is the surface - area of a sphere with radius \( r\) (the average distance from the Sun to the Earth, \( r=1.5\times 10^{11}\,\text{m}\)). The surface - area of a sphere is \( A = 4\pi r^{2} \).

Step2: <Calculate the surface - area>

Substitute \( r = 1.5\times 10^{11}\,\text{m}\) into the formula for the surface - area of a sphere:
\( A=4\pi(1.5\times 10^{11})^{2}\)
\( A = 4\pi\times2.25\times 10^{22}\)
\( A=9\pi\times 10^{22}\,\text{m}^2\approx 2.83\times 10^{23}\,\text{m}^2\)

Step3: <Calculate the power output>

Substitute \( I = 1350\,\text{W/m}^2\) and \( A\approx2.83\times 10^{23}\,\text{m}^2\) into \( P = I\times A\):
\( P=1350\times2.83\times 10^{23}\)
\( P\approx3.82\times 10^{26}\,\text{W}\)

Answer:

\(3.82\times 10^{26}\,\text{W}\)