stefan_boltzmann-law

Equation #8: Stefan-Boltzmann Law

From gamma rays to infrared to radio, we have the whole range of frequencies of electromagnetic radiation. An ideal body (although for practical purposes we can take the Sun to be one) absorbs (and emits) radiation at all of these frequencies.

When trying to study black body radiation, scientists realized that the power (energy per unit time) radiated per unit area was proportional to its temperature to the fourth power. At first it was an empirical formula, with a constant σ (Stefan-Boltzmann constant) set so as to match the data obtained. However, Boltzmann derived it theoretically later on.

For an interesting example of the law in action, see
https://www.youtube.com/watch?v=sUp_WZKZID4

This law is used extensively in astronomy today. We can take the radiation of distant stars to be nearly black body radiation and thus measure their temperature. For details go see
https://www.youtube.com/watch?v=l1lIo2ehLNo

You can find a good theoretical explanation here
https://www.youtube.com/watch?v=8hJx2Kjtz0U

derivation from Planck radiation law
http://farside.ph.utexas.edu/teaching/sm1/lectures/node85.html

 

For more equations, see Famous Equations in Physics

Stefan-Boltzmann Law
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