The amount of radiant power produced by the sun is approximately 3.9x10^26W. Assuming the sun to be a perfect black body sphere with a radius of 6.96x10^8m find its surface temperature
To find the surface temperature of the sun, we can use the Stefan-Boltzmann law, which states that the power radiated by a black body is proportional to its surface area and the fourth power of its temperature.
The equation is:
Power = 4πR²σT⁴
where
Power = 3.9x10^26 W (power produced by the sun)
R = 6.96x10^8 m (radius of the sun)
σ = Stefan-Boltzmann constant = 5.67x10^-8 W/m²K⁴
T = surface temperature of the sun (what we need to find)
Rearranging the equation to solve for T:
T⁴ = Power / (4πR²σ)
T⁴ = (3.9x10^26 W) / (4π(6.96x10^8 m)²(5.67x10^-8 W/m²K⁴))
T⁴ = 1.539499x10^3 K⁴
Taking the fourth root of both sides, we find:
T = (1.539499x10^3 K⁴)^(1/4)
T ≈ 5778 K
Therefore, the surface temperature of the sun is approximately 5778 K.