## 2 Materials and Methods
We have:  
\[\Delta E_{1x}=\Delta E\lambda_{1,T_{x}}=C_{2}\lambda_{1}^{-5}e^{-\frac{C_{2}} {\lambda_{1}T_{x}}}\Delta\lambda_{1}, \tag{4}\]  
\[\Delta E_{2x}=\Delta E\lambda_{2,T_{x}}=C_{2}\lambda_{2}^{-5}e^{-\frac{C_{2}} {\lambda_{2}T_{x}}}\Delta\lambda_{2}. \tag{5}\]  
Dividing Equation (3) by Equation (4) and taking logarithms, we have the following expression for the emitter under study:  
\[\ln\!\left(\frac{\Delta E_{1x}}{\Delta E_{2x}}\right)=-5\ln\!\left(\frac{ \lambda_{1}}{\lambda_{2}}\right)+\ln\!\left(\frac{\Delta\lambda_{1}}{\Delta \lambda_{2}}\right)-\frac{C_{2}}{T_{x}}\!\left(\frac{1}{\lambda_{1}}-\frac{1} {\lambda_{2}}\right) \tag{6}\]  
and for the reference source:  
\[\ln\!\left(\frac{\Delta E_{10}}{\Delta E_{20}}\right)=-5\ln\!\left(\frac{ \lambda_{1}}{\lambda_{2}}\right)+\ln\!\left(\frac{\Delta\lambda_{1}}{\Delta \lambda_{2}}\right)-\frac{C_{2}}{T_{0}}\!\left(\frac{1}{\lambda_{1}}-\frac{1} {\lambda_{2}}\right)\!. \tag{7}\]  
From Equations (6) and (7) we have the equation for the source color temperature \(T_{x}\) calculation using the available temperature value of the reference emitter \(T_{0}\):  
\[\ln\!\left(\frac{\Delta E_{10}/\Delta E_{20}}{\Delta E_{1x}/\Delta E_{2x}} \right)=C_{2}\!\left(\frac{1}{\lambda_{1}}-\frac{1}{\lambda_{2}}\right)\cdot \left(\The results of aerosol ignition of certain concentration, that was produced inside the chamber, as well as the explosion pressure and the explosion pressure rise rate are automatically recorded by the data processing system. This further data analysis enables us to conclude which is the successful ignition mixture (Figure 2).  
Figure 1: Twenty-liter spherical explosion chamber. The unit layout. 1—Water output, 2—pressure sensor, 3—pressure gauge, 4—dust collector 0.6 dm3, 5—air intake, ignition source, 6—chemical igniters, 7—rebound sprayer, 8—fast-acting valve, 9—water intake, 10—air and resultant outlet.  
Figure 2: Pressure trend (P, MPa) for the period (t, ms) of dust-gas mixture combustion inside the explosion chamber: P\({}_{\rm d}\)—expansion pressure of the combustion chamber; P\({}_{\rm ex}\)—explosion pressure; td—exhaust valve delay; t\({}_{1}\)—combustion time; t\({}_{2}\)—induction time; t\({}_{\rm v}\)—ignition delay time; W\({}_{\rm P}\)—breakpoint in the rising part of the pressure curve; dP/dt—pressure rise rate at the explosion.  
A pressure gauge with a response time of 0.2 ms is applicable for pressure measurements up to 2 MPa. Timing of pressure and flame radiation spectrum data recording from the ignition moment was controlled by ExTest software. To exclude the influence of the decomposition products of chemical igniters on the test result, the mixture was ignited by flash over. The energy produced from electrical initiation was 1 kJ.  
Photometric measurement of light fluxes involved in the Equation (8) was carried out by means of photoelectric unit (Figure 3).  
The luminous flux was projected onto the inlet diaphragm of the unit using a rotatable flat mirror and lens. The luminous flux, after passing through the diaphragm, was recorded by photomultipliers using a beam splitting system, the signals of which were recorded from the oscilloscope screen. Two spectral intervals were separated by means of 15 nm bandpass interference filters.  
The recording device was calibrated using standard stripe incandescent lamp. Its luminous flux was projected onto the inlet diaphragm of the unit through a hole in a rotating disk (chopper) using a rotary flat mirror and lens.  
To measure the absolute radiation intensity, we used photomultipliers powered by high-voltage rectifier with electronic regulation.  
For the radiator processes recording, it is necessary to consider not just the receiver's absolute sensitivity, but also the wavelength interval where this sensitivity remains effective.  
One of the basic parameters of photodetectors is their time constant of the order of \(10^{-8}\)-\(10^{-10}\) s.  
The photomultipliers are characterized by significant photocurrent amplification factor and are well protected from the interferences caused by external electric fields. A relatively high input current of multistage photomultiplier enables to record output signals by cathode oscilloscopes without special broadband amplifiers involvement.  
Figure 3: Basic diagram of temperature measurement. 1—Explosion chamber watch window, 2—band-lamp, 3—diaphragm, 4—splitter, 5—light filter, 6—photo multiplier, 7—cathode amplifier, 8—oscillograph.  
The oscilloscope's beam deviations are proportional to the radiation energy of the selected spectral intervals  
\[D=\kappa\Delta E_{1} \tag{9}\]  
where \(D\) is oscilloscope beam deviation, and \(\Delta E\) is defined by Formula (3).