Blackbody radiation is a common phenomenon that probably is familiar to you. When you see stars of different colors, when you observe an electric heating coil on a stove turn red, or when you observe a lightbulb, you are observing blackbody radiation. A blackbody is a device that converts heat into radiant energy. Heating an object to different temperatures causes that object to radiate energy of different wavelengths and therefore, different colors.
The energy density, dU in the wavelength range dl is given by the expression:
The expression in brackets is the Planck distribution and is symbolized by r(l,T). This distribution gives us the radiation density at a given temperature and wavelength
Plank distribution depends on temperature. Fig. 1 shows Plank distributions at three different temperatures.
Fig. 1. Plank distribution at temperatures: 2500K - green line, 3000K - blue line, and 3500K - red line.
You can see that Plank distribution does not depends on temperature by a linear low, and therefore determination the temperature from measured r(l,T) is not a simple task. However you can pay attention that that the exponent in the Plank equation is much larger than 1 for our range of wavelength and temperatures. For example, for l=800 nm and T=5000K
Thus the Plank equation could be simplified:
and
Thus the slope of graph of
versus 1/l will give us hc/kT.
In order to get r(l,T) from the experimental data you have to take into account that measured signal depends not only
on r(l,T) but also on the effectiveness of diffraction grating G(l) and CCD detector S(l) . The measured signal reads as:
Blank(l)- Dark(l)= G(l)S(l)r(l,T)
From this equation you can calculate r(l,T) measuring Blank(l), Dark(l), and using literature data for G(l) and S(l)