Incremental heating

Let us assume a spherical mineral with radius R which initially contains a gas with concentration C0(r), r being the radial distance from the center. Upon incremental heating, this gas is lost to the extraction line and at the ith heating step when time is tf, the fraction of initial gas remaining is/(tf). Loss takes place by radial diffusion with temperature-dependent, hence time-dependent, coefficient 3>(t). We assume that the total amount of gas held by the mineral at t=0 is equal to one, i.e., that... 

First we consider the heat balance inside the tubular reactor. Figure 7.2 gives rise to the incremental heat-balance equation... 

The carbon monoxide and chlorine gas feeds are mixed in the T-junction of the reactor and then guided through the catalyst bed of the reactor. The catalyst, carbon particles with a diameter of 53-73 pm, is preconditioned by heating the reactor at 150 °C for 2 h under a constant argon flow. A mixture of 2/3 CO and 1/3 chlorine (4.5 seem min-1) is fed into the reactor. The reactor was incrementally heated to 220 °C the pressure at the inlet was -132 kPa and nominally atmospheric at the outlet [39],... 

To address this question, Re L3-edge EXAFS data were collected after loading the sample into a reactor and drying by incremental heating in a flow of 20% 02 and 80% helium to 798 K followed by a dwell at 798 K, and... 

T. C., and Dungan M. A. (1998) Inherited argon in a Pleistocene andesite lava " Ar/ Ar incremental-heating and laser-fusion analyses of plagioclase. Geology 26, 427-430. 

Farley, 2000 Reiners and Farley, 1999, 2001), but this relationship breaks down in samples subjected to intensive ductile or brittle deformation (e.g., Amaud and Eide, 2000 Kramar et al, 2001 Mulch et al, 2002). In general, it seems prudent to assume that a is related to the physical grain size when applying Equations (17) and (19) unless samples show textural evidence for the extensive development of subgrain boundaries that may act as fast diffusion pathways, or— in the case of K-feldspar— show direct evidence of the existence of multiple diffusion domains during incremental heating experiments. 

This is the same result we obtained by the statistical approach. That approach helps us visualize entropy changes in terms of the number of microstates over which the energy is dispersed, but the calculations are limited to simple systems like ideal gases. This approach, which involves incremental heat changes, is less easy to visualize but can be applied to liquids, solids, and solutions, as well as gases. 

At constant temperature, for some of the conditions presented, the quantity of heat captured actually decreases with an increase in the number of glazing layers—for example, at 110° F. brine temperature in July, the maximum heat is captured with five layers of glazing (Table IX). This simply means that the incremental heat loss due to reflection and absorption by the added layer of glazing is greater than the heat saved as a result of one more layer of glazing to act as an additional heat insulator. 

Figure 19. He/ Ncs vs. " He/ Ne. Data sources are given in the caption to Figure 11. In Figures 19-22, individual analyses carried out by stepwise crushing are plotted, but for incremental heating analyses only the total gas contents are shown in order to avoid possible inter-elemental fractionation during heating. The box shows theoretical values for the mantle. The mantle production ratio for " He / Ne = 2.2x10 (Yatsevich and Honda 1997). The range of He/ Nes shown by the box is between 4, the value for modem solar wind, and 9, the mean value for the time-integrated He/ Ne ratio of the upper mantle (Fig. 17).

Poland KA (1983) " °Ar/ Ar incremental heating plateaus for biotites with excess argon. Chem Geol (Isotop Geosci Sect) 1 3-21... 

Lee JKW (1995) Multipath diffusion in geochronology. Contrib Mineral Petrol 120 60-82 Lee JKW, Onstott TC, Hanes JA (1990) An " °Ar/ Ar investigation of the contact effects of a dyke intmsion, Kapuskasing Stmctural Zone, Ontario A comparison of laser microprobe and furnace extraction techniques. Contrib Mineral Petrol 105 87-105 Lee JKW, Onstott TC, Cashman KV, Cumbest RJ, Johnson D (1991) Incremental heating of hornblende in vacuo Implications for " °Ar/ Ar grochronology and the interpretation of thermal histories. Geology 19 872-876... 

The steady-state energy balance shows that the incremental heat... 

Thermogravimetric analytical techniques A group of thermal analytical techniques in which the change in mass of a sample undergoing incremental heating is used to identify the mineralogical composition. 

Sanidines were analyzed by total fusion, whereas volcanic glass was dated by incremented heating. ... 

With increasing load, gas-exit dry-bulb temperature will tend to fall and net-bulb temperature will rise, because more moisture mill have been evaporated. Incieasing air flow will lower the wet-bulb temperature, restoring the exit driving force to its desired value. As air flow is increased, the hot-end temperature controller increments heat flow commensurately. 

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