The Sun radiates like a perfect blackbody with an emissivity of exactly 1. (a) C
ID: 1476986 • Letter: T
Question
The Sun radiates like a perfect blackbody with an emissivity of exactly 1.
(a) Calculate the surface temperature of the Sun, given it is a sphere with a 7.00 108 m radius that radiates 3.80 1026 W into 3 K space. Incorrect: Your answer is incorrect. How is the rate of heat radiated related to the emissivity of the object? What is the surface area of the Sun? (in K)
(b) How much power does the Sun radiate per square meter of its surface? (in W/m2)
(c) How much power in watts per square meter is this at the distance of the Earth, 1.50 1011 m away? (This number is called the solar constant.) W/m2
Explanation / Answer
(a)
Stefan-Boltzmann Law
R=T
R=P/A =P/4R²
T=P/4R²
T =forthroot{ P/4R²} =
=forthroot{3.8•10²/4•5.67•10••(7•10)²} =5744 K
(b)
P= P/4R²=3.8•10²/4• •(7•10)² =6.17•10 W/m²
(c)
P= P/4R²=3.8•10²/4• •(1.5•10¹¹)² =1344 W/m²
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