- #1
walterwhite
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Homework Statement
The unit area intensity of radiation from the Sun at the photosphere is 6.33*107 W/m2.
a) Check this value using the calculus of the Stefan-Boltzman Law, assuming the Sun is a blackbody emitter ([itex]\epsilon[/itex] = 1) with a surface temperature of 5777K.
Homework Equations
Stefan-Boltzmann Law:
[tex]E_b = \int_0^∞ \! E_{\lambda,b} \, \mathrm{d} \lambda = σT^4[/tex]
Planck's Law:
[tex]E_{\lambda, b} = {\frac{2\pi hc^2}{\lambda^5[e^{(hc/\lambda kT)}-1]}} [/tex]
where:
[itex]c = 2.998*10^{14} \ \mu m \ s^{-1}[/itex]
[itex]h = 6.626 * 10^{-34} \ J \ s[/itex]
[itex]k = 1.381 * 10^{-23} \ J/K [/itex]
[itex]c = 2.998*10^{14} \ \mu m \ s^{-1}[/itex]
[itex]h = 6.626 * 10^{-34} \ J \ s[/itex]
[itex]k = 1.381 * 10^{-23} \ J/K [/itex]
The Attempt at a Solution
I'm not sure how to solve the integral of the Stefan-Boltzmann Law. I know I can substitute [itex]E_{\lambda, b}[/itex] from Planck's law into the Stefan-Boltzmann law, but I have no idea how to integrate it then. Integration by substitution fails here and I have to prove using calculus, that the sun's [itex]E_b[/itex] is equal to 6.33*107 W/m2. Thanks.