Blackbody Radiation

Blackbody - a hypothetical body consisting of a sufficient number of molecules absorbing and emitting electromagnetic radiation in all parts of the electromagnetic spectrum so that:
  1. all incident radiation is completely absorbed; and
  2. in all wavelengths bands and in all directions (isotropically), maximum possible emission is realized.

Although a blackbody does not really exist, we will consider the planets and stars (including the earth and the sun) as blackbodies. Even though by definition, they are not perfect blackbodies, for the sake of understanding and simplicity we can apply the characteristics of blackbodies to them.

According to the above definition, a blackbody will emit radiation in all parts of the EM spectrum, but by intuition, we know that one will not radiate in all wavelengths equally. So the first thing we would like to know about blackbody radiation is in what wavelengths is radiation emited primarily. Secondly, we know that all blackbodies do not radiate energy at the same rate, certainly shown by the sun's power compared to that of the earth. Therefore, it would be beneficial to know something about the rate of blackbody emission. Fortunately for us, we can answer both questions knowing only one characteristic of an object -- temperature.

Wien's Displacement Law

alpha = lamda max X Temperature

Wien's displacement law says that the wavelength of the maximum emitted radiation is inversely proportional to the absolute (°K) temperature. If we plug in the temperatures of the earth and the sun, we will see that lambda max is 10µm and .49µm, respectively. Whereas the earth emits mostly infrared radiation, the sun emits mostly visible light. In fact, 43% is visible, 37% is near infrared and only 7% is ultraviolet. Wien's law allows us to determine temperatures of other stars depending on its color. Something that glows blue hot is much warmer that one that glows red hot!

Stefan-Boltzmann's Law

E = Sigma X Temperature to the fourth

Stefan-Boltzmann's law states that the rate that a body emits radiation (per unit area) is directly proportional to the body's absolute temperature to the fourth power. With this fact we can determine that the sun radiates 160,000 times more energy than the earth. In fact we receive only 1/2 billion of the sun's total energy. This is enough however to light New York City street lights for 2 days by collecting light for twelve hours on one football field!

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