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 In Kelvins
The power radiated by a black body is given by the Stefan-Boltzmann law:
P = σ * A * T^4,
where P is the power radiated, σ is the Stefan-Boltzmann constant (approximately 5.67x10^-8 W/(m^2*K^4)), A is the surface area of the black body, and T is the temperature in Kelvin.
Since the sun is a perfect black body sphere, its surface area is given by:
A = 4πr^2,
where r is the radius of the sun.
Given that P = 3.9x10^26 W, r = 6.96x10^8 m, and σ = 5.67x10^-8 W/(m^2*K^4), we can substitute these values into the Stefan-Boltzmann law:
3.9x10^26 = 5.67x10^-8 * 4π * (6.96x10^8)^2 * T^4.
Simplifying and solving for T^4, we get:
T^4 = (3.9x10^26) / (5.67x10^-8 * 4π * (6.96x10^8)^2).
T^4 ≈ 6955.243.
Taking the fourth root of both sides, we find:
T ≈ 18.35 K.
Therefore, the surface temperature of the sun is approximately 18.35 Kelvin.