The average intensity of sunlight impinging on Earth is measured to be about $1.4 \mathrm {~kW} / \mathrm { m } ^ { 2 }$ What is the power of sunlight emitted by the sun? $\text { (Earth-Sun distance } = 1.5 \times 10 ^ { 8 } \mathrm {~km} \text {, Earth radius } = 6.4 \times$ $\left. 10 ^ { 3 } \mathrm {~km} \right)$
A) $7.2 \times 10^{14} \mathrm {~W}$
B) $4.0 \times 10 ^ { 26 } \mathrm {~W}$
C) $7.6 \times 10 ^ { 8 } \mathrm {~W}$
D) $3.2 \times 10 ^ { 22 } \mathrm {~W}$

Question

Quizplus · Accepted Answer

The power of sunlight emitted by the sun can be calculated using the formula for the power passing through a sphere centered on the Sun with a radius equal to the Earth-Sun distance. The surface area of this sphere is $4\pi r^2$, where $r$ is the Earth-Sun distance. Given the average intensity of sunlight ($1.4 \, \text{kW/m}^2$) and the Earth-Sun distance ($1.5 \times 10^{11} \, \text{m}$), the total power is $P = 1.4 \times 4\pi (1.5 \times 10^{11})^2$, which calculates to approximately $4.0 \times 10^{26} \, \text{W}$.

The Average Intensity of Sunlight Impinging on Earth Is Measured 1.4 kW/m21.4 \mathrm {~kW} / \mathrm { m } ^ { 2 }1.4 kW/m2

The Average Intensity of Sunlight Impinging on Earth Is Measured $1.4 \mathrm {~kW} / \mathrm { m } ^ { 2 }$