Of Particular Significance

# Chapter 12, Endnote 2

If electromagnetic waves of all frequencies can cause heating, why is is often said that infrared light has to do with heat?

For instance, from this site: “Infrared is radiated heat: the feeling of warmth from the sun on your face; the heat from a coal fire, or a toaster. It is even the same form of heat emitted by your own body. It is the most basic form of heating known to [humans].” But this isn’t really true.

All light waves carry energy. They deposit that energy in any material that can absorb them; that energy tends over time to be taken up in random motion of the materials’ molecules, namely heat.

But not all frequencies of light are readily absorbed by the body. Light at visible and infrared frequencies is readily and efficiently absorbed, and so its energy is deposited, which is why we feel warm in sunlight. This is in contrast to radio waves or X-rays, which are less efficiently absorbed, though they would heat you also if they were sufficiently intense.

Conversely, the frequency of light waves most readily emitted by a hot object is given by combining the quantum formula E = f[h] with another classic formula that relates energy to temperature: E = T [kB], where [kB] is yet another conversion factor known as Boltzmann’s constant, and the temperature has to be expressed in Kelvin (not in Fahrenheit or in Centigrade/Celsius) so that zero temperature, or “absolute zero”, is equivalent to zero energy. Taken together, they tell you that the average frequency f of light emitted by an object is proportional to its temperature T.

• faverage= T [ kB / h ],

At room temperature, where T is about 300 Kelvin, the average frequency emitted by an object is several trillion cycles per second, below that of visible light and squarely in the infrared. In the wider universe, T is about 2.7 Kelvin, corresponding to microwave frequencies; and this is why the CMB, the cosmic microwave background, lies in the microwave range.

Hot objects glow because at temperatures close to or above a thousand degrees (in any of the temperature scales), light begins to be emitted in the visible frequency range. More precisely, even though the average frequency of light emitted by a hot oven heating element or glowing coal is still infrared light, and thus invisible, some of its higher frequencies of light have reached the lower end of the visible range. This is why these elements glow visibly, and always starts off as red in appearance because red light has the lowest frequency of all visible light. The higher the temperature, the broader the range of visible light being emitted, and so the glow goes from red to orange to yellow to bluish-white. (It rarely appears green or blue or violet because in most materials, even when light of those frequencies is emitted, light of red, orange and yellow frequencies are still being emitted too, and our eyes and brains view such a combination of all those frequencies as white.)

Meanwhile, the Sun’s outer temperature is several thousand degrees. It too emits a great deal of infrared light, but it emits plenty of visible light at all frequencies, which is why its light appears white to our eyes.

For a long and more detailed explanation, see this webpage.

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