Blackbody Model

A blackbody is a perfect absorber and emitter of radiation. That is, in a perfect blackbody, all radiation incident on the object is re-emitted, and emittance is a function only of temperature. In nature, true blackbodies do not exist. However, many objects approximate blackbodies.

In the discussion that follows, a number of equations are given that describe the electromagnetic energy emitted by a blackbody. Before getting into the mathematics of perfect emitters, let's describe the blackbody curves in this figure. These curves show the amount of energy radiated at each wavelength for blackbodies of various temperatures. The red line is the blackbody curve for the earth, whose ambient temperature (the "average" temperature given off by the soil, water, vegetation, and built environment) is about 300 Kelvin. The area under this curve is the total energy emitted across all wavelengths by the earth. You can see on the figure that the area under the 1200 K curve is greater than the area under the 300 K curve. There is a direct relationship between the temperature of a blackbody and the amount of electromagnetic energy it emits. The hotter the object, the more energy it gives off. Even though a perfect blackbody is only a theoretical construct, most objects in nature behave like "imperfect" blackbodies, and you will find they obey this principle. For instance, consider this diagram which overlays the theoretical curve created by a perfect blackbody and the actual curve created by the Sun.The hotter an object is, the more electromagnetic energy it emits. This is the relationship the Stefan-Boltzmann Law (below) describes.

You should also notice on the "Blackbody Radiation" figure that the curves for hotter temperatures "peak" at lower wavelengths than do the curves for cooler temperature objects. Just as the total amount of energy emitted by an object depends on its temperature, the wavelength at which the largest portion of energy is emitted depends on temperature. Hotter objects emit more energy at lower wavelengths than do cooler objects. Think about this relationship. It takes more energy to make something hotter, and the quantum description of electromagnetic radiation (section 2.33) indicates that EM radiation with more energy has a shorter wavelength. Now, you are seeing an instance where hotter objects (more energy) emit more at shorter wavelengths than do cooler objects. Notice how, on the diagram, the peak of the 300 K line is at about 9 micrometers. Indeed, the earth continually emits radiation at 9.7 micrometers. It is extremely important to take this "background" radiation into account when collecting remote sensing data in the thermal infrared portion of the electromagnetic spectrum. Now look again at the figure in which the solar radiation curve and 6000 K blackbody curve are superimposed. Notice that the "peak" wavelengths are between 0.4 and 0.8 micrometers -- the wavelengths of visible light! The wavelength at which a blackbody has its peak emittance is given by Wien's Displacement Law (below).

Plank's Radiation Law for Blackbodies gives the spectral radiance of an object as a function of its temperature.

Wien's Displacement law

If we differentiate Plank's Radiation Law for blackbodies and set it equal to zero, we arrive at a formula which gives the wavelength of maximum radiance for a blackbody of a given temperature. This formula is referred to as Wien's Displacement Law.

Finally, if a blackbody is acting as a perfect emitter, the total emitted energy over the whole spectrum is given by the Stefan-Boltzmann law:

At this point you have a fairly good understanding of the properties of electromagnetic radiation as it travels through a vacuum. In the next module we will consider what effects the earth's atmosphere has on this energy as it moves from its source, through the atmosphere, and to our sensors.