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Show c • .. . .. ' - ,; .' However, using the Wien's approximation, valid when exp(C2 /'AT) ~ 1, we can invert (10) to get an explicit expression for T(t) (13) For 'AT < 3000J.LK Wiens's approximation of the Planck expression is good to 1%. Since the two wavelengths used in this study are 0.8 and 1.0J.Lm, this implies that for particle temperatures less than 3000K, the approximation is very good. In reality as will be seen later, particle temperatures remain below 2500K for almost all cases. A detailed sensitivity analysis will not be given here but it can be shown, that, provided the particle emissivity is indeed independent of temperature and wavelength, the overall error in the temperature measurement is around 1%. Without the graybody assumption, the error is of the following form (14) The error is higher at higher temperatures. The constant of proportionality in equation (14) is of the order 1. Equation (14) also shows that the calibration temperature should be in the same range as the expected particle temperatures for the error to be small. 4. Results Intensity-time traces were measured for at least twenty particles for each set of experimental conditions (different wall temperatures, particle sizes and ambients). Figures 1-4 show the intensity-time traces and the calculated temperature-time traces for a few particles of a single set of experiments. The temperature-time traces show widely different qualitative behaviour from particle to particle. While some burn at almost constant temperature (Figure 1), many particles show temperature maxima (Figure 2) or even monotonic behavior, both increasing (Figure 3) and 8 |
