Question

According to the Stefan-Boltzmann law, how much energy is radiated into space per unit time by each square meter of the Sun’s surface? If the Sun’s radius is 696,000 km, what is the total power output of the Sun?

Answer 1

`3.8469943828* 10^(26)\ W`

Step-by-step explanation:

`\sigma` = Stefan-Boltzmann constant =
`5.67* 10^(-8)\ W/m^2K^4`

T = Surface temperature of the Sun = 5778 K

r = Radius of the Sun = 696000 km

From Stefan-Boltzmann law

`F=\sigma T^4\\\Rightarrow F=5.67* 10^(-8)* 5778^4\\\Rightarrow F=63196526.546\ W/m^2K`

Power is given by

`P=F4\pi r^2\\\Rightarrow P=63196526.546* 4\pi* (696000000)^2\\\Rightarrow P=3.8469943828* 10^(26)\ W`

The power output of the Sun is
`3.8469943828* 10^(26)\ W`