Star Temperatures

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Peak of intensity vs frequency plot

Wien's Displacement Law

When the temperature of a blackbody radiator increases, the overall radiated energy increases and the peak of the radiation curve moves to shorter wavelengths. When the maximum is evaluated from the Planck radiation formula, the product of the peak wavelength and the temperature is found to be a constant.

Calculation

This relationship is called Wien's displacement law and is useful for determining the temperatures of hot radiant objects such as stars, and indeed for a determination of the temperature of any radiant object whose temperature is far above that of its surroundings.

It should be noted that the peak of the radiation curve in the Wien relationship is the peak only because the intensity is plotted as a function of wavelength. If frequency or some other variable is used on the horizontal axis, the peak will be at a different wavelength.

Development of relationship

Intensity as a function of temperature and wavelength

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Wien's Displacement Law

For a blackbody radiator, the temperature can be found from the wavelength at which the radiation curve peaks.

Discussion

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Radiation Curves

The wavelength of the peak of the blackbody radiation curve decreases in a linear fashion as the temperature is increased (Wien's displacement law). This linear variation is not evident in this kind of plot since the intensity increases with the fourth power of the temperature (Stefan- Boltzmann law). The nature of the peak wavelength change is made more evident by plotting the fourth root of the intensity.

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Radiation Curves

The wavelength of the peak of the blackbody radiation curve decreases with increasing temperature according to Wien's displacement law. The fourth root of the intensity shows the variation of the wavelength more clearly than the plot of the full radiated intensity.

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