It is shown that the measurement of only one component of the Wein’s spectrum of thermal radiation in range λT ≤ 3000 ( ° ;C μm) is sufficient to estimate the true temperature and spectral emissivity of the selected component with sufficient accuracy, although more than one hundred years this statement was considered as incorrect. The proposed method is based on the formation of the linear dependence of the logarithm of the emissivity of not real wavelengths and artificially generated “virtual” spectral components.
Since the discovery of Wien’s exponential law of thermal radiation the concepts of emissivity and black-body factor were firmly established in physics. And measuring of the true temperature and emissivity became a problem “idem per idem” (the same through the same): To measure the true temperature it is necessary to know the emissivity and vice versa. A close look at this problem (on which the author spent more than sixty years) showed that its solution exists. Moreover, it was found that the measurement of any of the spectral components of radiation following to an exponential Wien’s law is enough to determine the value of true temperature and spectral emissivity of this component. Below we shall describe the proposed method which implements this statement1.
The method is based on the principle of double spectral ratio, based on the linear dependence of the logarithm of the emissivity for three selected components of the spectrum of thermal radiation, proposed in [
In proposed method a linear dependence of the three components, two of which are “virtual”, is generated artificially relative the selected spectral component and the requirement of proximity of wavelengths is eliminated.
Thus, only one spectral component is extracted from the Wien’s spectrum that is logarithmic,
where:
The value of the second pyrometer signal is determining by multiplying
where
Further, let’s form a third pyrometer signal proportional to the “virtual” component with a wavelength
where
Thus
Having these three pyrometer signals
Graphically this is shown in
length.
For the linearization of this dependence and formation of a linear dependence (this is a straight line
This formula determines the value of the true temperature at known a’priory linearity of logarithm of emis- sivity from the wavelength and has the form:
where
Usually for method of double spectral ratio the relation
Thus, substituting the values of
And get the expression for the “resultant” emissivity in the form of
If to follow to the linear dependence of emissivity from wavelength the “resultant” emissivity must be equal to zero,
This can be seen from the formula (7) for V and illustrated in
Let’s change the value of
Thus, we determine the value of
Substituting the expression for
where
Thus, the expression (6) for V, specifying the desired value of the true temperature at a linear dependence of the logarithm of the emissivity will have the form:
or
Moreover,
Thus, the desired value of the true temperature will be equal to
where,
And the emissivity will be equal to
As an example of proposed method let’s present the result of calculation of the true temperature for steel; data are taken from [
Steel
Let’s now choose a second “virtual” wavelength from the spectrum of thermal radiation, for example,
Then
The third signal
where:
To provide the linearity of logarithm of emissivity let’s change the value
Now by substituting
where:
Therefore
or
Therefore, the required temperature will be equal to
And the resulting error will be
The value of the logarithm of the emissivity will be equal to
And the resulting error will be
From this example we can see that proposed method based on selection of “virtual” components provides rather good accuracy.
Note that if to select the second “virtual” component of the spectrum with a wavelength
The described method and calculations performed on its base show that it can estimate fairly accurately the value of the true temperature and emissivity using only one real spectral component and two complementary “virtual” components of the emissivity spectrum which follows to Wien’s law and additional virtual spectral components can be selected rather arbitrarily. From a mathematical point of view, the proposed method is not rigorous, because formally Equation (1) includes two unknown parameters and the proposed heuristic approach is rather geometric in nature, but it provides, and quite simply, accurate measurements of true temperature and emissivity in spectral region
I am grateful to the staff of the Academic Council of the Joint Institute for High Temperatures of the Russian Academy of Sciences for fruitful discussion of this work.