PhysicsLAB Resource Lesson
Incandescent Solids and Radiation

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Incandescent solids, like stars, incandescent light bulbs, and heated electric coils on your stovetop or inside your oven, emit a continuous spectrum.

Image courtesy of Wikimedia
Scientists have discovered that the color of an incandescent solid is directly related to its temperature: red hot coals are around 800 ºC, a yellow incandescent light bulb's filament is around 3000 ºC, our sun has a surface temperature of around 5500 ºC, while blue hot stars have surface temperatures around 25000 ºC. All objects radiate energy - but the wavelengths of their emitted energy may not fall in the visible spectrum (400-700 nm). For example, a human body (98.6 ºF = 37.5 ºC) emits radiant energy at 9300 nm which is in the IR portion of the electromagnetic spectrum.
When we say that an object radiates energy, we mean that it releases electromagnetic radiation in a range of wavelengths. The peak frequency, or wavelength, in its emission determines its color.

Image courtesy of Wikimedia 

Notice that the peak wavelength gets longer and the intensity of the emitted wavelengths decreases as the object's temperature decreases. This relationship is known as Wien's Displacement Law.
In these formulas,
  • f stands for the peak frequency,
  • l for wavelength, and
  • T for the maximum temperature measured in absolute Kelvin.
To convert the formulas from one to the other, recall that for electromagnetic radiation,
Further inspection of Wien's Law shows that all blackbodies emit the same spectrum based on their temperatures, independent of the materials out of which they are composed. Notice that the radiation is continuous, that is, it is not limited to the visible spectrum but includes IR and UV wavelengths.
To calculate the rate at which energy is radiated by a hot surface we use the Stefan-Boltzmann Law.
In this formula,
  • Pnet represents the net power measured in watts = J/sec,
  • e is the emissivity (0<=e<=1),
  • s is Stefan's constant which equals 5.67 ×10−8 W/(m2 K4),
  • T is the temperature of the hot surface, and
  • Tsurroundings is the temperature of the surrounding environment.
A radiating object having an emissivity of 1 is called a blackbody radiator. It is a perfect absorber and since it reflects no light, it appears "black" at normal temperatures. But when heated, it is also a perfect emitter of radiation producing the intensity vs wavelength graphs shown above for Wien's Law.
 If the sun has a surface temperature of 5500 Kelvin and is a blackbody radiator, what is the intensity, in watt/m2, of the sun's radiation when it reaches the earth's orbit? You may assume that the vacuum of space has a background cosmic radiation of approximately 3 K.

An object having an emissivity of 0 is a perfect reflector. It does not absorb any electromagnetic frequencies.

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