The Wien displacement law informs us on the wavelength of the emission of thermal radiation. The emitted flux (power per unit area) is given by the Stefan-Boltzmann law. This law appears quite surprising at first glance since the total emitted power is proportional to the fourth power of the temperature! That strong temperature dependence means that as objects get hotter they "glow" with much greater intensity. This observation is also not readily explained by classical physics. The Stefan-Boltzmann law also contains a constant known as the Stefan-Boltzmann constant, which must also be explained by any theory of thermal radiation
Determining the temperature of the earth's surface
We can use the Stefan-Boltzmann law and a few facts about our solar system to calculate the temperature at the surface of the earth and the other planets. We will show this calculation for the earth, but the same procedure can be used for the any planet. We assume that the sun is a "black body" with a temperature of 5600 K. To obtain the total emitted power we also need to know the surface area of the sun. We can use an estimate for the radius to calculate the surface area. Remember that the Stefan-Boltzmann law gives W = sigmaT4, which is the power emitted per unit area. Thus, the total power P = W x A where A is the area. Once we have the total power we use the distance of the earth from the sun and the radius of the earth to determine what fraction of that total radiation energy is captured by the earth. Finally, we assume that the earth is at equilibrium, which must mean that the emitted energy is equal to the incident energy. These steps are shown in the following slides..
The Stefan-Boltzmann is used to calculate the radiation contribution in thermal physics. Other sources of thermal exchange can be found in conduction and convection. Thus, radiation, conduction and convection are the three important contributions to the calculations of heat transfer in engines, solar power generation and many other applications.
