© B.J. Korites 2018
B.J. KoritesPython Graphicshttps://doi.org/10.1007/978-1-4842-3378-8_12

Planck’s Radiation Law and the Stefan-Boltzmann Equation

B. J. Korites1 
(1)
Duxbury, Massachusetts, USA
 
In Chapter 10, you were introduced to Max Planck’s famous equation of black body radiation:
$$ S\left(\uplambda \right)=\frac{2\pi {c}^2h}{\uplambda^5}\frac{\varepsilon }{e^{\frac{hc}{\lambda kT}}-1}\kern0.5em J/s/{m}^3=W/{m}^3 $$
(B-1)
The power emitted by a surface over a bandwidth λ1 → λ2 is
$$ {P}_{\uplambda_1\to {\uplambda}_2}=\underset{\uplambda_1}{\overset{\uplambda_2}{\int }}S\left(\uplambda \right)d\uplambda \kern1em J/s/{m}^2=W/{m}^2 $$
(B-2)
With Equation B-1, this becomes
$$ {P}_{\uplambda_1\to {\uplambda}_2}=2\pi {c}^2h{\int}_{\uplambda_1}^{\uplambda_2}\frac{\uplambda^{-5}\varepsilon }{e^{\frac{hc}{\uplambda kT}}-1}d\uplambda \kern1.2em J/s/{m}^2=W/{m}^2 $$
(B-3)
In Chapter 10, you numerically integrated Equation B-3. Here you ...

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