ETME360 Spring 2014
E -  #4
Pyrometry Temperature Error - Solution
R. Larson

When a material with spectral emissivity less than ε=1 is viewed with a standard optical pyrometer, the indicated target temperature (or "Blackbody" temperature) will differ from the true target temperature depending on the wavelength at which the measurements are made and the emissivity of the target.  The Temperature error, defined as Error = (Ttarget - TBlackbody), can be calculated by using the formula derived in class that relates temperatures, emissivities, and wavelengths:
1/Ttarget - 1/TBlackbody = (
λ ln ε)/C2, where C2 =1.439*104mm*K

a.            For measurements at λ=0.80 μm, λ=0.65 and λ=0.40 μm, and a blackbody temperature of 1000 C, plot the temperature error as a function of emissivity (using any computer graphing program.)  

 I calculated error for a number of different emissivities, and graphed: See the EXCEL plot and setup, below. Mathcad or other programs would have worked fine but I thought EXCEL was a natural for this type of comparison:


b.            Write a few sentences comparing your plots, and provide a general prediction of performance at shorter and longer wavelengths.


It is clear from the plotted relationship that shorter wavelengths yield smaller errors for a given emissivity.