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What is the total intensity of the sun?

1 Answer

May 9, 2018

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

Explanation:

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

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

Given the sun is a sphere (though not a perfect one), we can use:
$L = 4 π r^{2} σ T^{4}$ $L=4pir^2sigmaT^4$

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

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

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