Calculating the Sun's Power Output

[Jtappan]

Homework Statement

The Sun emits electromagnetic waves (including light) equally in all directions. The intensity of the waves at the Earth's upper atmosphere is 1.4 kW/m2. At what rate does the Sun emit electromagnetic waves? (In other words, what is the power output?)
____ W

Homework Equations

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The Attempt at a Solution

I have no idea how to do this one...

I know it involves I = P/A

 

[Shooting Star]

If r is the dist of Earth from sun, then total energy W emitted by sun in one second will fall on the surface of a sphere of radius r in one second (after 8.3 mins or so).

W/(4*pi*r^2) = 1.4*10^3 (given). You have to plug in the value of r in meters. That's all.

 

[ogb p]

, where I is the intensity, P is the power, and A is the area. We are given the intensity and can assume the area is the surface area of a sphere with a radius equal to the distance from the Sun to the Earth. So, using the formula, we can rearrange it to solve for power: P = I*A. Plugging in the values, we get P = (1.4 kW/m2)*(4π*(149.6*10^9 m)^2) = 3.846*10^26 W. This is the power output of the Sun, which is equivalent to about 3.846*10^23 kW. This is an incredibly large amount of energy, but it makes sense given that the Sun is the primary source of energy for all life on Earth and is responsible for driving many natural processes on our planet.