Assume that the sun is a sphere of radius 6.96 * 10⁸ m and that its surface temperature is 5.8 * 10³ K. If the sun radiates at a rate of 3.90 * 10²⁶ W and is a perfect emitter, at what rate is energy emitted per square meter at the sun's surface?

6.4 * 10^7 W/m^2

Explanation:

The sun is assumed a sphere and therefore can be calculated by the surface area of a sphere.

surface area of sphere = 4πr^2 where r is the radius of the earth in m.

r = 6.96 * 10^8 m

substitute the value into the formula

surface area of the sun = 4 * 3.142 * (6.96 * 10^8) ^2

the sun radiates at a rate of 3.90 * 10^26 W

to calculate the rate of energy emitted per square meter of the sun, we need to divide the rates at which the sun radiates energy per second by the surface area of the sun

that is P/surface area = 3.90 * 10^26 / (4 * 3.142 * (6.96 * 10^8) ^2 = 6.4 * 10^7 W/m^2