planck's law

We said a couple times while talking about flames that all matter gives off electromagnetic radiation (EMR or light) according to its temperature. Flames contain hot particles and so they glow. The law that describes how EMR is given off as a function of temperature is called Planck’s Law, and any matter that follows Planck’s Law perfectly is called a black body.

The Planck’s Law equation above gives you qλ, which is the energy flux at a given wavelength. (Remember EMR has a wavelength.) On the right side you plug in the temperature T and the wavelength λ. All the rest of the symbols are famous constants.

Max Planck devised his law in 1900, and this was the first observation that led to quantum mechanics.

Think back to our question from ghandirocks about whether or not there could ever be a black flame. We brought up Planck’s Law to try and figure this out, which describes the light (or EMR) given off by something hot. Flame colors can have different explanations, but the most common is that flames are hot and have particles in them.

The Clear Science Staff fired up our computers and plotted the emissive power from Planck’s Law (qλ) depending on the temperature of the hot thing. It’s a weird-shaped function you see above, which tends to have a maximum (and it’s a log scale) in the visible light region between what we call ‘violet’ and 'red.’ You might already know this: that hotter things tend to burn blue and colder things burn red.

For a flame not to emit any visible light, it just needs to be really cold, like 500 K. This is 227 °C or 440 °F, which might be a slightly high oven temperature when you’re cooking. Most flames burn around 2000-3000 °C, so that would be a very cold flame. Remember though, this is just to make the flame colorless. For it to be BLACK it would have to absorb light instead of emitting it. So if there were lots of particles, like a very sooty flame, and it were also cold like this, then yes you could think of it as a black flame.

We saw how Planck’s law allows you to calculate how much of each wavelength of light (or electromagnetic radiation) something emits due to its temperature. By the way, this is how people first figured out how hot the sun is. (It’s about 5505 °C, 5778 K, or 9941 °F.)

Look how the peak of the curve, the most light from the sun, falls between what we would call blue (or violet) and red. It’s such a great coincidence that we can see (with our eyes) light in that range, and that’s what the sun happens to emit the most of! Or, if you look at it a different way, we evolved well-adapted to our environment, with eyes that detect the most useful kind of light: the light from the sun.