- #1

walterwhite

- 3

- 0

## Homework Statement

The unit area intensity of radiation from the Sun at the photosphere is 6.33*10

^{7}W/m

^{2}.

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*10

^{7}W/m

^{2}. Thanks.