The total intensity I(T) radiated from a blackbody (at all wavelengths λ) is equal to the integral over all wavelengths, 0 < λ < ∞, of the Planck distribution (4.28). (a) By changing variables to x = hc/λkBT, show that ¡(T) has the form I(T) = σT4 where a is a constant independent of temperature. This result is called Ste fan’s fourth-power law, after the Austrian physicist Josef Stefan.
I(λ,T) = (2πhc^2)/(λ^5)*(1/(e^(hc/λkBT))-1)
The Attempt at a Solution
I understand that I need to substitute x into the equation and the easy part that I get:
out of the second part. However the first part seems to be just inflating the equation by substitution to which it will merely increase continually.
I did end up substituting:
into the numerator to get:
just not sure where to go from here.