Blackbody Radiation
A blackbody is an ideal emitter of light. That means that it emits radiation across all wavelengths in a predictable way that doesn't omit any particular wavelengths. This property is not generally true of just any object. So an ideal blackbody is rather different that a colored t-shirt, but we'll elaborate on that in a moment. A piece of ash is a much better approximation, as you'll understand soon.
It is a curious property of nature that objects that are ideal emitters of light are also ideal absorbers, so they are able to absorb light incident on them regardless of wavelength. Keep in mind that this is not generally true of objects like t-shirts. For instance, as we've discussed before, a red t-shirt is red precisely because it doesn't absorb red light. Instead that red light is diffusely reflected back in our direction and we see the shirt as red. Furthermore, when we look at objects with our eyes we don't receive any information about wavelengths outside the narrow visible spectrum. Why this matters is that certain materials like water tend to appear transparent (almost) in the visible spectrum and yet are completely opaque just outside the visible spectrum. In that sense water doesn't absorb visible light almost at all, but it very strongly absorbs infrared and UV and beyond. Recall that in our section on color that we saw the absorption spectrum of water. Here is that link: https://www.geogebra.org/m/MRaRGHHG
When we speak of blackbodies we consider all wavelengths, visible or not.
Under usual circumstances blackbodies don't emit the same wavelengths that they absorb. Think of a black piece of coal bathed in sunlight. In the visible spectrum it absorbs very well, which is why it looks black (it doesn't reflect any light back). It gets hotter and hotter and will start radiating more light back to the environment on account of being hot. The light coming off will, however, be mostly infra-rad (IR) and not visible light like the sunlight it absorbed. When the rate that light energy gets absorbed by the piece of coal (power) matches the rate of light energy being radiated out, we have thermal equilibrium (if we assume for now that there is very little heat transfer due to other mechanisms). For instance, in vacuum, radiation is the whole story of heat transfer.
A black piece of coal does a good job of absorbing many wavelengths, but a blackbody is assumed to be 100% effective at absorbing all wavelengths. An even better black body than a piece of coal or a black t-shirt is something like a cardboard box with a little hole cut in it. If the hole is small, looking into the hole, you see black even if light is entering. In this sense, it is the hole, and not the box, that is the ideal blackbody. This hole is much like the pupil of our eyes.
The idea is that light of all colors enters the hole, and then bounces around the inside of the box and little by little gets fully absorbed before having a chance to ever exit the small hole. If we don't use cardboard, but maybe clay, then we can see what happens as the clay gets hotter without worrying about starting a fire. Regardless of temperature, what we find is that there is broad-spectrum light being emitted from the hole that depends only on the temperature of the clay and not on the wavelengths of light that originally entered the hole. The shape of the curve is what didn't line up with electromagnetic theory at the beginning of the 20th century. Theory could not account for it. The shape of the curve can be seen below.
Characteristics of Blackbody Radiation
While the theory that leads to the shape of the curve is beyond the scope of our course, we will still be a little quantitative. You will notice if you play with the slider, that with higher temperatures, the intensity peaks at lower wavelengths, which have higher frequencies. The relationship is simple, and is called Wien's displacement law. You can think about peak moving, or being displaced as a function of temperature:Here, , and temperature T is in kelvin. From this simple relationship, we can determine the temperature of everything from the rubber on a race car's tire to the surface of the sun - never needing contact as with a standard thermometer.
Another characteristic of this curve is that the area under it represents the total energy given off by an object per unit time per unit surface area. This is shown in the interactive graphic in watts per square meter. While you can see from playing with the slider that the value rises with temperature, what probably isn't obvious is that it rises in proportion to the 4th power of temperature in kelvin. This is referred to as the Stefan-Boltzmann Law, and written in terms of the power given off by an object is: In this equation, is the emissivity of the object, and characterizes how good a black body the object really is, where is an ideal black body. The surface area of the object is A. Lastly, , which is known as the Stefan-Boltzmann constant, which is derived from other constants of nature.
The problem with all of this is that electromagnetic theory didn't agree with this. In fact, there was no peak intensity from EM theory. It went to infinity at zero wavelength! So did the total irradiated energy from any object at any temperature! Clearly something was wrong. Historically, the disagreement between the measured curve and the calculated one based on EM theory was called the ultraviolet catastrophe since it was around the UV wavelengths that things started to go very, very wrong.
Stars as Blackbodies
Stars are nearly perfect blackbodies in the sense of this chapter. If a star's light intensity is plotted versus wavelength, it looks just like the curve above with a bunch of tiny dips along the curve that are indicative of chemistry within the star. It also depends on whether you measure the star's spectrum from space or from earth. Our atmosphere will absorb characteristic wavelengths as well. Below you can see the ideal blackbody spectrum, the sun's spectrum seen from space, and the sun's spectrum measured from sea level on earth. Notice the missing wavelengths in the sea level plot due to atmospheric absorption by water vapor, nitrogen, oxygen, etc.
