Question

What are blackbody curves and what are the approximate shapes of such curves? What is the Stefan-Boltzmann law and how does it relate to a blackbody and a blackbody curve? What is Wien's displacement law and how does it relate to a blackbody and a blackbody curve?

Answer 1

The black body radiation curve shows that the black body does radiate energy at every wavelength. The curve gets infinitely close to the x-axis but never touches it. The curve touches at infinite wavelength. It also shows that the black body emits at a peak wavelength, at which most of the radiant energy is emitted. At 5000K the peak wavelength is about 5x10^-7m (500nm) which is in the visible light region, in the yellow-green section. At each temperature the black body emits a standard amount of energy. This is represented by the area under the curve.

Black body radiation curves showing peak wavelengths at various temperatures

As the temperature increases, the peak wavelength emitted by the black body decreases.

It therefore begins to move from the infra-red towards the visible part of the spectrum. Again, none of the graphs touch the x-axis so they emit at every wavelength. This means that some visible radiation is emitted even at these lower temperatures and at any temperature above absolute zero, a black body will emit some visible light.

The graph also shows:
As temperature increases, the total energy emitted increases, because the total area under the curve increases.
It also shows that the relationship is not linear as the area does not increase in even steps. The rate of increase of area and therefore energy increases as temperature increases.

Therefore the Power radiated is proportional to T⁴ for an identical body which explains why the area under the black body curves (the total energy) increases so much for a relatively small increase in temperature.

This rearranges to lp = 2.898 x 10^-3 / T

This rearranged equation shows why the peak wavelength decreases as temperature increases. This decrease in wavelength explains why objects glow first red, then orange-red, then yellow, then even blue. These colours are successive decreases in wavelength.