# Wein's Displacement Law for Light Bulbs?

I know Wein's Law $\lambda_{max}=\frac{b}{T}$ works for ideal black bodies. I have some clear glass incandescent light bulbs which have Tungsten as a filament. Would Wein's Law of displacement be a close enough approximation for these light bulbs in order for me to figure out the temperature of the filament?

If there are any definitive resources, I would love to read them!

Edit: I have access to a spectrometer, so I can find out their peak wavelength.

This is obviously a well researched subject. The short answer is that using Wein's law as is will result in a significant error, i.e., for, a tungsten filament, the black body approximation does not work very well.

This is mostly due to the uncertainty of the tungsten filament emissivity, which directly affects the relationship between the surface temperature of a filament and its thermal radiation spectrum.

The emissivity of a black body is defined as unity. The radiation spectrum of a surface with the emissivity lower than unity will be generally red shifted relative to the spectrum of a black body at the same temperature, so, if we apply Wein's law to calculate the temperature of the surface based on the peak of the specral curve, the surface will appear to be cooler than it actually is.

According to this article by FAR Associates, the emissivity of tungsten filaments, among other factors, may depend on the temperature and the wavelength and, in addition, it changes with time. For example, here is a chart from the article showing wavelength dependency of tungsten emissivity measured in multiple experiments under various conditions:

As can be seen from the chart, the emissivity of tungsten is all over the place.

Incidentally, the article talks about a multiwavelength pyrometer, FARS SpectroPyrometer, which presumably can measure the temperature of tungsten filaments pretty accurately, by analyzing the spectrum at many different wavelengths and inferring the temperature by comparing the results.

• So if I, for instance, have a peak at $\lambda$ = 1000nm, then how do I read the chart you provided to interpret the temperature of the filament? It looks like emittance is on the y-axis, not temperature.
– RJP
Jul 24, 2018 at 1:59