It Glows!... Wait. Why is it glowing!?

Everyone probably knows the phrase 'white hot', many people know that steel glows different colors as you heat it up, and a fair few know that some metals don't really glow much even when you melt them, like lead or aluminum. Also, that molten rock (i.e. magma. You know you said that in Dr. Evil's voice) can appear pretty much the same color as hot steel.

Wazupwitdat?

Let's find out.
First, let's talk about light, super briefly. Light is what we call the visible portion of the electromagnetic spectrum. If you look at the different groupings of wavelengths, you can find things like x-rays, ultraviolet light, visible light, infrared light, microwaves, etc.

Electromagnetic Spectrum, from Wikipedia.

One of the key findings of quantum mechanics is the dual wave-particle nature of light, and the quantized bits of stuff that make up electromagnetic radiation are called photons (no, we can't make torpedoes out of em). In other words, the light we see are photons being emitted or reflected by a body (actually *all* emitted electromagnetic radiation consists of photons). So let's talk photons.

From quantum mechanics, the energy of a photon is proportional to its frequency,
\[E = \hbar \omega\]
Where \(\hbar\) is Planck's constant and \(\omega\) is the frequency of the emitted photon. The wavelength of the photon is related to the frequency as follows:
\[\lambda = \frac{2\pi c}{\omega}\]
Photons are classified as bosons, and can exist in two states, called spins (+/- 1). Additionally, as the temperature of a body is increased, the number of photons emitted also increases.

These assertions lead to the famed Planck Black-Body Spectrum, which expresses the energy density (read: intensity) of the light emitted by an object as a function of frequency and temperature:
\[\rho(\omega) = \frac{\hbar \omega^3}{\pi^2c^3(e^{\frac{\hbar \omega}{k_B T}} - 1)}\]


So what does this distribution look like at some different temperatures?

It looks like this. More or less.

There are some things to note in this diagram. First: at all temperatures, there's a whole lot of photons in the infrared range. This really shouldn't surprise us, as that is the heat you'd feel being emitted by the piece. Secondly, you can see a change in the relative proportion of the part of the curve in the visible range (400 - 790 THz): this corresponds to the change in the colors that we see as we heat something up. Note how there is very little present in the visible region at 200 C, but progressively more shifts into the visible region as the temperature increases.

Now, let's imagine we're looking at something like a lump of charcoal, or a piece of steel. We can see the following colors (this is the fairly standard system used by blacksmiths and the like, though the names may change a bit):

Temperature (deg. C)	Subjective Color
480	Faint red glow
580	Dark red glow
730	Bright red, slightly orange
930	Bright orange
1100	Pale yellow-orange
1300	Yellow-white
>1400	White (yellowish from a distance)

For reference, the melting point of lead is around 330 C, for aluminum it's about 660 C and iron it's about 1540 C. Lead melts well before there's enough photons being emitted in the visible range for an obvious glow at most conditions. Aluminum melts at a much higher temperature, but is not generally known for glowing as readily as steel or iron. However, it can glow readily in its liquid state when maintained at sufficiently high temperatures (seen in some types of aluminum smelting and foundry operations). Steel hangs around as a solid for a good long time while emitting visible photons, so is probably the best known example among metals.

OK, cool. But time for a bit of reality: of course, not everything behaves exactly like a black-body and there are usually other sources and sinks for photons. Real materials emit light at a fraction of that predicted by black-body radiation (this fraction is called the material's emissivity). This is the big reason why aluminum doesn't glow as readily as iron or steel does: the emissivity of aluminum is typically about 1/10 the value for iron and steels. But a lot of materials do come close enough to a black-body for the above to apply reasonably well.

Science!