# What is the total intensity of the sun?

May 9, 2018

$3.95 \cdot {10}^{26} W$

#### Explanation:

The Stefan-Boltzmann law is $L = A \sigma {T}^{4}$, where:

• $A$ = surface area (${m}^{2}$)
• $\sigma$ = Stefan-Boltzmann (~5.67*10^-8Wm^-2K^-4)
• $T$ = surface temperature ($K$)

Given the sun is a sphere (though not a perfect one), we can use:
$L = 4 \pi {r}^{2} \sigma {T}^{4}$

$T$ is known to be $5800 K$ and $r$ is known to be $7.00 \cdot {10}^{8} m$

$L = 4 \pi {\left(7.00 \cdot {10}^{8}\right)}^{2} \left(5.67 \cdot {10}^{-} 8\right) {\left(5800\right)}^{4} = 3.95 \cdot {10}^{26} W$