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

Answer:

$3.8469943828\times 10^{26}\ W$

Explanation:

$\sigma$ = Stefan-Boltzmann constant = $5.67\times 10^{-8}\ W/m^2K^4$

T = Surface temperature of the Sun = 5778 K

r = Radius of the Sun = 696000 km

From Stefan-Boltzmann law

$F=\sigma T^4\\\Rightarrow F=5.67\times 10^{-8}\times 5778^4\\\Rightarrow F=63196526.546\ W/m^2K$

Power is given by

$P=F4\pi r^2\\\Rightarrow P=63196526.546\times 4\pi\times (696000000)^2\\\Rightarrow P=3.8469943828\times 10^{26}\ W$

The power output of the Sun is $3.8469943828\times 10^{26}\ W$