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.

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for power
The power $ P $ is given by $ P = I\times A $, where $ I$ is the intensity ($1350\ \text{W/m}^2$) and $ A$ is the surface - area of a sphere. The formula for the surface - area of a sphere is $ A = 4\pi r^{2}$. The average distance from the Sun to the Earth $ r=1.5\times 10^{11}\ \text{m}$.
## Step2: Calculate the surface - area of the sphere
Substitute $ r = 1.5\times 10^{11}\ \text{m}$ into the formula $ A = 4\pi r^{2}$.
$$
\begin{align*}
A&=4\pi(1.5\times 10^{11})^{2}\
&=4\pi\times2.25\times 10^{22}\
&=9\pi\times 10^{22}\ \text{m}^{2}
\end{align*}
$$
## Step3: Calculate the power output of the Sun
Substitute $ I = 1350\ \text{W/m}^2$ and $ A=9\pi\times 10^{22}\ \text{m}^{2}$ into $ P = I\times A$.
$$
\begin{align*}
P&=1350\times9\pi\times 10^{22}\
&=12150\pi\times 10^{22}\
&\approx3.8\times 10^{26}\ \text{W}
\end{align*}
$$

# Answer:
$3.8\times 10^{26}\ \text{W}$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for power

Step2: Calculate the surface - area of the sphere

Step3: Calculate the power output of the Sun

Answer: