Equilibrium temperature Teq

If AH is constant, integrating the above equation from an equilibrium temperature Teq to the optimal temperature ropt yields... 

The yield of different pyrolysis products depends on the cellulose quality such as the average value for DP. the proportion of low molecular weight polymer, crystallinity, as well as the water content and the acidity of the sample. The experimental conditions influencing the chemistry of the pyrolysate include the equilibrium temperature Teq, temperature rise time (TRT), total heating time (THT) (see Section 4.1), and pyrolysis experimental setup [25,26]. A variation in pyrolysis products depending on cellulose type is exemplified in Table 7.2.1. This table gives the yield of gases, tar, char, and water for two commercially available celluloses [13]. 

Figure 6.1.15. The yield of fragment molecules with a specific number of atoms as a function of equilibrium temperature (Teq) during pyrolysis of polypropylene.

The temperature where the enthalpy rises sharply is a characteristic property of semicrystalline polymers. This temperature is defined as the equilibrium temperature, Teq, since it characterizes the structure closest to the equilibrium state in a semicrystalline polymer. 

The enthalpy of crystallization, AH, equilibrium temperature, Teq, and activation energy of crystallization, Uact, values are summarized in Table 1. 

Figure 3.5 H2/air combustion in a catalytic channel with full-height 2b=. 2 mm (the catalytic wall is located at y—0 and the center at y=0.6mm), = 5.0, Tin = 400 K, 01iN = lm/s, p=10bar. Distribution of local equilibrium temperature Teq(y) = T(y) + TH2(y)Q/cp and nondimensional temperature excess (or equivalently energy excess) T q = ( Tgq — — Adapted from Zheng and Mantzaras (2014) (with...

It is widely accepted [52-56] that generic gasifier models are set up using history matching, meaning that experimentally measured residual carbon and individual deviations from equilibrium for selected reactions are specified in the model. Equation (5.31) introduces a so-called approach temperature Tapp, which is defined as the difference between the measured physical gas temperature Tp of the process and the associated, calculated apparent equilibrium temperature Teq, according to the gas composition see Figure 5.6, which describes the individual deviation from equilibrium. 

Ac susceptibility measurements performed on the sample with the smallest clusters in a bias field are shown in Fig. 14. x has a maximum that shifts to higher temperature as the bias field increases, while that of x decreases. This apparently contradicts the classical behavior since the bias field reduces the activation energy. This bizarre feature is clarified by the measurements on the larger particles at sufficiently high field (300 Oe), since in that case the maximum, shifted to higher temperature, is not frequency dependent (Fig. 15). Under these conditions, the x response is dominated by the equilibrium susceptibility, and the temperature at the maximum is the temperature of the equilibrium susceptibility Teq 2/uII/kn,... 

In isothermal measurements, the time required to establish equilibrium conditions (teq) can be determined in a simple experiment illustrated in Figure 3.24. The solvent is thermostated at the desired temperature and stirred at moderate rate. After introducing an excess amount of solid into the solvent, samples of clear solution are removed at different times and analyzed for concentration subsequently. When the solution concentration reaches a constant value, saturation is achieved and the minimal equilibration time (for that temperature) can be derived from the concentration-time plot, as given in Figure 3.24. 

As a second example, let us consider stability to thermal fluctuations. Let the temperature of a local region of interest be Teq + a, where Teq is the equilibrium temperature and a is a small deviation. As we have seen in Chapter 3, the entropy production due to heat flow is... 

Experimental studies on how temperature affects equilibria reveal a consistent pattern. The equilibrium constant of any exothermic reaction decreases with increasing temperature, whereas the equilibrium constant of any endothermic reaction increases with increasing temperature. We can use two equations for A G °, Equations and, to provide a thermod3mamic explanation for this behavior AG = -RT x Teq AG° — AH°-TAS°... 

Assume the existence of a phase a which tends upon cooling to change (wholly or partly) into a phase (1. At one temperature TCL] there is equilibrium between the two phases this implies that the free energy G of the material in both phases will be equal. At T< Teq the value of G will be... 

Teq is the temperature on the equilibrium curve having the same conversion or the same reaction quotient as the actual outlet gas. 

P is also related to the temperature approach to equilibrium. This can be seen when approximating the equilibriiun constant by ln(Keq)=A-B/Teq and similarly ln(Qr) A-B/T (B is positive). The resulting equations can be written as ... 

Build the simple reactor system shown in Eigure W8.1. The reactor should be modelled as a separator with a volume of 2 m. The reaction, given below, is equilibrium limited. The relationship between Teq (in terms of activities) and the reaction temperature (in kelvin) is also given below. The system is very non-ideal, so an activity model should be used, i.e. the UNIQUAC model, and the reaction equilibrium should be measured in terms of activities rather than molar concentrations. 

Figure 2.12 shows the effect of varying the chemical equilibrium constant. As ( Teq)366 increases, the required vapor boilup and reflux to maintain conversion and product purities decrease because driving the reaction to the product side becomes easier. The compositions of the impurities in the two products shift as the fractionation decreases (lower vapor and liquid rates in the column) to having more of the nonadjacent reactant components in the product. Figure 2.13 gives the temperature profiles for three values of K q. 

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