**
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 = (T_{target}
-_{ }T_{Blackbody}), can be calculated by
using the formula derived in class that relates
temperatures, emissivities, and wavelengths:

1/T_{target} - 1/T_{Blackbody} = (λ
ln ε)/C_{2,
}where C_{2 }=1.439*10^{4}mm*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:**

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