Before we talk about the greenhouse effect, I need to introduce three physical laws that describe how radiation interacts with matter. The first one says all objects emit radiation. This is Planck's Law. If we look at how the mathematical form of this looks when we graph it, we can see here on this axis the wavelength of the radiation, down from short wavelength radiation, like x-rays and cosmic rays. To long wave radiation, infrared radiation, microwaves, radio waves on this axis. On this axis we have the energy emitted as a function of this wavelength. Planck's law for an object emitting radiation. Has this kind of almost bell shaped curve to it. And you can see a peak at a certain wavelength, and this is described in the mathematical relationship for Planck's law, and so that is the first law that we need you to appreciate. So then second law follows from Planck's law. It says hotter objects emit more radiation than cooler objects. This is called the Stefan-Boltzman Law and what it describes here is the area under these curves. So if we were to integrate this function. In other words, sum up the area under this curve and compare it to the area under this curve. We will see that a warmer object will have more area, more total energy as a function of its temperature than the cooler object. Again, hotter objects emit more radiation than the cooler objects. The third law is called Wien's Displacement Law and it says hotter objects emit their peak radiation at shorter wavelengths. And we can show that in this graph here that we were looking at before. Here we've got the warmer object and the cooler object. The warmer object, the peak radiation that it is emitting occurs at a shorter wavelength than the object that is cooler that has a longer wavelength of peak emission. And this is consistent with shorter wavelength radiation having more energy than longer wavelength radiation. So how do these radiation laws apply to the Earth's climate system? Let me show you. The sun has a surface temperature of 6,000 kelvin. In contrast, the Earth has a surface temperature of about 300 kelvin. This is a factor of 20 times greater temperature on the sun than the Earth. Keep that in mind. If we plug these numbers into Wien's displacement law and now I'm showing you the constant of 3,000 micrometers Kelvin, that's the constant that belongs in the Wien's displacement law. And I divide by 6,000 Kelvin for the sun. We can see that the wavelength of maximum emission is half a micrometer. This lies within the visible light portion of the spectrum. In contrast, if I plug 300K into the Wien's displacement law, then I end up with a value of ten micrometers for the peak wavelength, the wavelength of peak emission for the Earth. This lies in the infrared. So, this explains why sometimes you hear people say that the sun emits primarily in the visible and the Earth emits primarily in the infrared part of the spectrum. If we go back to the earlier laws. We see that, yes, even though that the peak wavelength of emission from the sun is in the visible at a much shorter wavelength than for the Earth, the sun emits more radiation at all wavelengths. So, when we say that the sun emits primarily in the visible. That doesn't mean that it's not emitting infrared radiation as well, it means that the radiation, the peak wave length of the emission lies in the visible.
