The radius of our sun is 6.98 x 10 8 m and its total power output is 3.85 x 10 2
ID: 1295715 • Letter: T
Question
The radius of our sun is 6.98 x 108m and its total power output is 3.85 x 1026 W.
a) Assuming the Sun emits as a perfect blackbody, calculate its surface temperature using the Stefan-Boltzman Law.
b) At what wavelength does the sun radiate its peak intensity?
c) What fraction of the total intensity is radiated between 550nm and 552 nm? Here we need Planck's blackbody spectrum in terms of intensity at a given wavelength I(wavelength) = [(2*pi*h*c2)/(lambda5)] * [1/ (ehc/lambda*kT-1)]
remeber to multiply by d*lambda for the wavelength range.
Explanation / Answer
a)
According to stefan's law,
emmisivity = sigma*T^4
Power/Area = sigma*T^4
T = (power/(Area*sigma))^(1/4)
= (3.85*10^26/(4*pi*6.98^2*10^16*5.67*10^-8))^(1/4)
= 5771.5 K
b)
According to wein's law,
lamda_m*T = constant
lamda_m = constant/T
= 2.89*10^-2/5771.5
= 5.007*10^-6 m
= 5007 nm
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