Temperature estimation

Accuracy of Pyrometers Most of the temperature estimation methods for pyrometers assume that the objec t is either a grey body or has known emissivity values. The emissivity of the nonblack body depends on the internal state or the surface geometry of the objects. Also, the medium through which the therm radiation passes is not always transparent. These inherent uncertainties of the emissivity values make the accurate estimation of the temperature of the target objects difficult. Proper selection of the pyrometer and accurate emissivity values can provide a high level of accuracy. 

In the first one, the desorption rates and the corresponding desorbed amounts at a set of particular temperatures are extracted from the output data. These pairs of values are then substituted into the Arrhenius equation, and from their temperature dependence its parameters are estimated. This is the most general treatment, for which a more empirical knowledge of the time-temperature dependence is sufficient, and which in principle does not presume a constancy of the parameters in the Arrhenius equation. It requires, however, a graphical or numerical integration of experimental data and in some cases their differentiation as well, which inherently brings about some loss of information and accuracy, The reliability of the temperature estimate throughout the whole experiment with this... 

Direct observations of the decompositions of a wide range of inorganic compounds [231—246], which are unstable in the electron beam, particularly azides and silver halides, have provided information concerning the mechanisms of radiolysis these are often closely related to the processes which operate during thermal decomposition. Sample temperatures estimated [234] to occur at low beam intensity are up to 470 K while, at higher intensity, 670 K may be attained. 

Ignition temperature estimated by extrapolating the steeply ascending portion of the CO2 formation curve to zero CO2 concentration Temperature which shows the maximum CO2 concentration... 

If sulfur isotopic equilibrium between coexisting sulfates and sulfides was attained, using average values of sulfates and sulfides, -i-22%c and +5%c, respectively, we could estimate temperature using the equation by Ohmoto and Rye (1979). This temperature seems too high compared with temperature estimated from fluid inclusions and mineral assemblages (section 1.3.3). That means that sulfates and sulfides precipitated under the condition far from equilibrium. 

Sulfur fugacity (/s ) As will be mentioned in section 2.4.3, fs2 can be estimated based on the Ag content of electram coexisting with argentite (or acanthite), the FeS content of sphalerite coexisting with pyrite and temperature estimated from homogenization temperatures of fluid inclusions. 

Both geothermometers are in agreement being close 380°C (Fig. 1.177). However, at the lower and higher temperatures the difference between the temperatures estimated from equations (1-82) and (1-83) becomes larger. 

Figure 1.178 represents a comparison between the stannite-sphalerite temperatures and homogenization temperatures of fluid inclusions or sulfur isotope temperatures. It can be seen in Fig. 1.178 that Nakamura and Shima s geothermometer would be rather consistent with the temperature estimated based on the fluid inclusions or sulfur isotope studies. It is notable that almost all stannite-sphalerite temperatures are within 30°C of average homogenization temperatures and sulfur isotope temperatures. 

Temperatures estimated based on equations (1-82 and 1-83) range from ca. 250°C to 350°C for both skarn-type and vein-type deposits except the Yatani epithermal Au-Ag vein-type deposits. 

Shikazono, N. (1985d) A comparison of temperatures estimated from the electrum-sphalerite-pyrite-argentite assemblage and filling temperatures of fluid inclusions from epithermal Au-Ag vein-type deposits in Japan. Econ. Geol, 80, 1415-1424. 

The /CO2-temperature relationships for the above-mentioned mineral-fluid equilibria are shown in Fig. 3.6. Based on the thermochemical calculations, minerals summarized above and temperatures estimated, we could estimate typical /CO2-temperature ranges for hydrothermal solutions from midoceanic ridges and back-arc basins. 

The following steps, implemented by a computer program written in C, generate the smoothed, recommended values. Input to the program consists of the set of observed density values, temperatures, estimated uncertainties, critical constants and values of certain parameters used by the program. 

Fig. 14.13 (a) Bubble temperatures estimated using the MRR method as a function of thermal conductivity for the rare gases, (b) Hydrogen peroxide concentration following sonication of pure water as a function of gas solubility in different rare gases ( ) He ( ) Ne (a) Ar ( ) Kr ( ) Xe ( ) He/Xe mixture [42] (reprinted with permission from the American Chemical Society)... 

Around 85% of the total amount of hydrogen is present as a metallic phase. It is assumed that there is a silicate rock core with a temperature estimated to be... 

In this early work, pressure was measured by connecting the cap of a pressure-re-lease Savillex [24] Teflon vessel to a pressure gauge outside the MW oven and the final temperature estimated by pointing an infrared sensor at the mixture in the vessel immediately after the heating was completed. 

The following table gives the values of the fraction of Schottky defects, S/N, in a crystal of NaBr, with the sodium chloride structure, as a function of temperature. Estimate the formation enthalpy of the defects. 

Table 92 Temperature (estimated from graph) required to achieve 0.1 s-1 or 0.3 s-1 (CO/metal surface atom)454 a turnover frequency of ... 

FIGURE 7 Temperature estimate response to step change in feed concentration. 

Figure 4. Plot of Li isotopic composition vs. MgO content for samples of the Kilauea Iki lava lake, Hawaii (Tomascak et al. 1999b). Cored basalt samples show a range of crystallization temperatures (estimated for four of the samples). The absence of permil-level variation in 5 Li indicates that Li isotopes do not fractionate appreciably during crystallization in mantle systems. Open symbols (o) are replicate measurements.

Eqs. 7.22 and 7.24 represent the velocities due to screw rotation for the observer in Fig. 7.9, which corresponds to the laboratory observation. Eq. 7.25 is equivalent to Eq. 7.24 for a solution that does not incorporate the effect of channel width on the z-direction velocity. For a wide channel it is the z velocity expected at the center of the channel where x = FK/2 and is generally considered to hold across the whole channel. The laboratory and transformed velocities will predict very different shear rates in the channel, as will be shown in the section below relating to energy dissipation and temperature estimation. Finally, it is emphasized that as a consequence of this simplified screw rotation theory, the rotation-induced flow in the channel is reduced to two components x-direction flow, which pushes the fluid toward the outlet, and z-direction flow, which tends to carry the fluid back to the inlet. Equations 7.26 and 7.27 are the velocities for pressure-driven flow and are only a function of the screw geometry, viscosity, and pressure gradient. 

Temperatures estimated from the measured intensity distributions at each port location during an 02/Ar oxidizer run in the 24-inch long combustor are plotted in Fig. 8.4, along with the measured hemispherical emissive power in the wavelength range from 425 to 800 nm. (The hemispherical emissive power, E, is related to the radiant intensity, /, by = ttI. Radiant intensity is also referred to as radiance.) The stoichiometry, 0/F)/ 0/F)st, for this run was about f.fO. The measured combustion temperature was about 2900 K, as compared to an adiabatic flame temperature of about 3650 K. The intensity measurements indicate that ignition occurs about 12 in. downstream from the injector. The intensity is near its peak at the most downstream port location, which indicates that combustion is still underway at that location. 

Potentially, the advantage of this thermometer will be that it allows the determination of temperatures of carbonate formation without kuowiug the isotope compo-sitiou of the fluid. Came et al. (2007), for example, presented temperature estimates for early Siluriau aud late Carboniferous seawater, which are consistent with varying CO2 concentrations. 

Calculated sulfate-sulfide temperatures, for conditions of complete isotope equilibrium, are typically between 450 and 600°C and agree well with temperatures estimated from other methods. Thus, the sulfur isotope data and temperatures support the magmatic origin of the snlfnr in porphyry deposits. 

If it is known that the cooling timescale is much longer, then either the wet diffusivity does not apply (Peck et ah, 2003 Page et ah, 2006), or the initial temperature estimate is inaccurate. 

Ri is sensitive to temperature and even a relatively small error in temperature estimate can introduce a sizable discrepancy into the apparent p02 based on some PFCs. The relative error introduced into a p02 determination by a 1 °C error in temperature estimate ranges from 8 Torr/°C for PFTB [207] to 3 Torr/°C for PFOB (perflubron) [223] or 15-Crown-5-ether [218] when p02 is actually 5 Torr. HFB exhibits remarkable lack of temperature dependence and the comparative error would be 0.1 Torr/°C [224], Recognizing differential sensitivity of pairs of resonances within a single molecule to p02 and temperature, Mason et al. [207,225] patented a method to simultaneously determine both parameters by solving simultaneous equations. However, generally it is preferable for a p02 sensor to exhibit minimal response to temperature, since this is not always known precisely in vivo and temperature gradients may occur across tumors. 

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