Black Body Radiation: How Do We Know How Hot the Sun Is?
How is it that scientists know the temperature of the Sun? Obviously, it's not possible to simply measure the temperature. By answering some fundamental questions in thermal physics and a little math, scientists were able to understand exactly how to calculate it.
Why Objects Radiate
Before we can understand the science that made calculating temperatures possible, we need to understand a core concept of thermal physics, radiation.
Let's say you leave an object out in the sun, continuously supplying the object with energy. What happens to the energy in the object? Some of the energy must be reflected in order for us to see the object. The rest is absorbed by the object, increasing its temperature. If you leave the object out, it should continue to absorb more energy. By our logic, the object should continuously increase in temperature until it completely boils away. However, we know that in the real world this is not what happens. At some point, the object will reach a stable temperature: we say the object is in thermal equilibrium. For this to happen, it must mean that the object not only absorbs and reflects energy but also radiates it. All objects perform thermal radiation and absorption to reach thermal equilibrium. So, in a way, all objects glow — though most of that glow is invisible infrared radiation, not visible light.
Defining a Black Body
In the real world, the thermal radiation of an object is not dependent on temperature alone: most real objects reflect part of the radiation that hits them rather than absorbing all of it, and they also emit less radiation than a perfect emitter would at the same temperature. So, to understand the true relationship between temperature and radiation, scientists needed an ideal object that absorbs all the radiation that falls on it and radiates the maximum possible amount of energy for its temperature. This is called a perfect black body. For a long time, it was difficult to find an object that met this criterion. It wasn't until Wilhelm Wien and Otto Lummer built one in 1895 that scientists had a working example: a hollow metal cavity with a small hole, its inner walls blackened. Any light that enters that hole bounces around inside and is essentially all absorbed by the black walls before it has any real chance of escaping. So, it can be said that the hole itself behaves as a perfect black body.
Two Radiation Laws
After running multiple experiments in which the temperature of a perfect black body (the hole in the cavity) was varied, scientists began to graph their results. Graphs of the wavelength of the emitted radiation against its intensity showed how the wavelength of maximum intensity varied with temperature. As the temperature increased, that wavelength became shorter.
It was also observed that the total intensity of light emitted was directly proportional to the temperature raised to the fourth power — a relationship first found experimentally, by comparing many results, and later confirmed theoretically. These two relationships are called Wien's Displacement Law and the Stefan–Boltzmann Law, respectively:
Calculating the Sun's Temperature
So, how do we know how hot the Sun is? It comes down to treating the Sun as a black body and applying the two laws above. First, we observe the Sun's spectrum to find which wavelength of light is emitted most strongly, and use Wien's Displacement Law to approximate its temperature. Once we have that temperature, the Stefan–Boltzmann Law lets us calculate the total energy the Sun emits. In this way, a few careful observations and two simple laws of thermal physics are enough to measure the temperature of a star we can never touch.
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