The sun radiates like a perfect blackbody with an emissivity of exactly 1.

Question

(a) Calculate the surface temperature(K) of the sun, given it is a sphere with a 7.00 multiplied by 108 m radius that radiates 3.80 multiplied by 1026 W into 3 K space.

(b) How much power(W/m^2)does the sun radiate per square meter of its surface?

(c) How much power(W/m^2)in watts per square meter is this at the distance of the earth, 1.50 multiplied by 1011 m away? (This number is called the solar constant.)

Answer 1

(a)
Stefan-Boltzmann Law
R=σT⁴
R=P/A =P/4πR²
σT⁴=P/4πR²
T =forthroot{ P/4σπR²} =
=forthroot{3.8•10²⁶/4•5.67•10⁻⁸•π•(7•10⁸)²} =5744 K
(b)
P₀= P/4πR²=3.8•10²⁶/4•π •(7•10⁸)² =6.17•10⁷ W/m²
(c)
P₁= P/4πR₀²=3.8•10²⁶/4•π •(1.5•10¹¹)² =1344 W/m²