## Wiens displacement law the spectral distribution

As the surface temperature rises, the peak of the spectrum moves towards shorter wavelengths (higher frequencies). This is in line with the common experience that as a lump of coal or an iron bar or a tungsten filament gets heated, it begins to glow. Not only does it become brighter, but the predominant colour of the light changes from deep red to bright yellow to 'white-hot'.

Experiment shows that the relationship between the temperature and the wavelength at the peak of the curve follows a simple relation known as Wien's displacement law, which states that the higher the temperature the lower the wavelength at which radiation is maximum. We can see this in Figure 11.2. At 2500 K the maximum occurs at about 1160 nm, moving to 970 nm at 3000 K and 830 nm at 3500 K.

Wien's displacement law: XmT = Constant

Xm = wavelength at which Mx is maximum T = absolute temperature

The value of Wien's constant is found by experiment to be 2.9 x 10-3 mK.

Wien's law allows us to calculate the temperature of an object from the colour of the emitted light. For example, the spectral radiant exitance of the sun is maximum at a wavelength of about 500 nm. Hence we can calculate the temperature of the surface of the sun as follows:

The radiation maximum falls right into the middle of the visible spectrum. From the viewpoint of the evolution of mankind this is not at all surprising! (The temperature of the sun's surface should not be confused with the temperature of the core interior of the sun, which is ~1.5 x 107 K.)

From Wien's law we can deduce temperatures of distant objects without having to go there!

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