The amount of radiant power produced by the sun is approximately 3.9x1026 W. Assuming the sun to be a perfect black body sphere with a radius of 6.96 x108m, find its surface temperature (in kelvins)
The radiant power produced by the sun is given by the Stefan-Boltzmann law:
Power = σ * A * T^4
Where σ is the Stefan-Boltzmann constant (approximately 5.67 x 10^-8 W/m^2K^4), A is the surface area of the sphere (given by 4πr^2) and T is the surface temperature of the sun.
We can rearrange this equation to solve for T:
T^4 = Power / (σ * A)
T^4 = (3.9 x 10^26 W) / (5.67 x 10^-8 W/m^2K^4 * 4π(6.96 x 10^8 m)^2)
T^4 ≈ 1.04 x 10^17 K^4
Taking the fourth root of both sides, we can find the surface temperature:
T ≈ ∛(1.04 x 10^17 K^4)
T ≈ 6.77 x 10^5 K
So, the surface temperature of the sun is approximately 6.77 x 10^5 Kelvin.