Calculations versus temperature

Figure 1.25(b) shows the calculated versus temperature for the COj-CO system. 

In Germany and France the Baumii scale is calculated using 144.3 as the constant. The Baumii scale only includes the sulfuric acid concentration range of 0—93.19% H2SO. Higher concentrations are not included in the Baumh scale because density is not a unique function of concentration between 93% and 100% acid. The density of sulfuric acid versus temperature and concentration is shown in Figure 4 (50). 

There are significant differences in various data sets pubtished for oleum vapor pressure. A review of existing vapor pressure data plus additional data from 10 to 8600 kPa (1.45 to 1247 psi) over the entire concentration range of oleum is available (93), including equations for vapor pressure versus temperature. Vapor pressure curves for oleum calculated from these equations are shown in Figure 19. Additional vapor pressure data from 0.06 to 14 kPa (0.5—110 torr) is given in the titerature (92). 

Figure 4.28. Measured and calculated shock temperatures versus pressure for for-sterite for low-pressure (olivine), mixed phase, and high-pressure phase regime (possibly MgO periclase) -I- MgSi03 (perovskite)). Shock temperatures in the mixed phase regime (Ahrens et al., 1969).

Exploration of the region 0 < T < requires numerical calculations using eqs. (2.5)-(2.7). Since the change in /cq is small compared to that in the leading exponential term [cf. (2.14) and (2.18)], the Arrhenius plot k(P) is often drawn simply by setting ko = coo/ln (fig. 5). Typical behavior of the prefactor k and activation energy E versus temperature is presented in fig. 6. The narrow intermediate region between the Arrhenius behavior and the low-temperature limit has width... 

This is accomplished by constant feed concentrations through adjustment of the feed rate to keep C constant at various temperatures. After plotting the rate versus temperature, the curve can be differentiated, giving the derivative of 3r/3T. The change of the thermodynamic values of (-AH)/pc are minor and can be neglected and used as a constant multiplier of the measured slope. The 0 = V/F must be calculated for each measurement and also multiplied by the measured slope at the constant value of the concentration C. The technique is similar to the measurement of the activation energy discussed in Chapter 5.2. 

Some conditions require breaking up the exchanger into multiple parts for the calculations rather than simply using corrected terminal temperatures. For such cases one should always draw the q versus temperature plot to be sure no undesirable pinch points or even intermediate crossovers occur. 

Figure 5. LRO-parameter S versus temperature as determined by X-ray diffraction and as calculated from resistivity measurement for CujoPtso (fit-parameter in eqn(3) A=0 7) ( ) X-rays, ( ) resistivity The curve is calculated with the Foumet model taking for the interaction energies W =720k and W2=1220k ...

The Hausbrand vapor-pressure diagram [127, 128] in Figure 8-40 is a useful approach for the steam distillation calculation. This particular diagram was prepared for six organic compounds and the corresponding water vapor pressure as (it - ps) for three system pressures of 760, 300, and 70 mm Hg versus temperature,... 

Calculate the gas cooling and condensing heat loads for each increment separately and plot a curve representing the total heat load versus temperature. 

Network properties and microscopic structures of various epoxy resins cross-linked by phenolic novolacs were investigated by Suzuki et al.97 Positron annihilation spectroscopy (PAS) was utilized to characterize intermolecular spacing of networks and the results were compared to bulk polymer properties. The lifetimes (t3) and intensities (/3) of the active species (positronium ions) correspond to volume and number of holes which constitute the free volume in the network. Networks cured with flexible epoxies had more holes throughout the temperature range, and the space increased with temperature increases. Glass transition temperatures and thermal expansion coefficients (a) were calculated from plots of t3 versus temperature. The Tgs and thermal expansion coefficients obtained from PAS were lower titan those obtained from thermomechanical analysis. These differences were attributed to micro-Brownian motions determined by PAS versus macroscopic polymer properties determined by thermomechanical analysis. 

If we look at Figure 3.5, we see that some liquids present a curve of viscosity versus temperature above that of water while others lie below. By systematically varying the a and values in Eq. (3.3) and using these to calculate the /q values versus the temperature, we obtain the information about their influence on the viscosity versus temperature relationship. Those plots that lie below the water curve in Figure 3.5 may represent the rules needed to model liquids such as benzene, methanol, or ethyl acetate. The a and coefficients that produce /q values leading to plots above water in Figure 3.5 are candidates for the modeling of liquids such as ethanol, propanol, or butanol. 

The long command tells the program to show the reaction s equilibrium constant versus temperature and calculate its equilibrium equation pH = causes the program to render the equation in terms of pH instead of log aH+. To find the equilibrium lines written in terms of pe and Eh, we type... 

Fig. 23.6. Calculated saturation indices (log Q/K) of aluminum-bearing minerals plotted versus temperature for a hot spring water from Gjogur, Hveravik, Iceland. Lines for most of the minerals are not labeled, due to space limitations. Sampling temperature is 72 °C and predicted equilibrium temperature (arrow) is about 80 °C. Clinoptilolite (zeolite) minerals are the most supersaturated minerals below this temperature and saponite (smectite clay) minerals are the most supersaturated above it.

A comparison of this new volatility ratio with measured literature data is given in Figure 3 where deviation ratios of pNH3(meas)/PN 3(calc) are plotted versus temperature where comparison is made with the SWEQ calculation model of reference 2. This plot shows that these new data are in fair agreement with the calculated values with ratios of about 1.05 at both 80 and 120°C. Fortunately for the authors these data also agree quite well with previously measured data reported by Miles and Wilson... 

The intensity versus wavelength distribution according to the Planck equation for the black-body emission is used to calculate the temperature (see Fig. 12). This calculation is based on two severe approximations. The first concerns with the assumption that the system is an ideal black body, which corresponds to assuming that the emissivity e equal to 1. On the contrary, real systems are gray bodies that possess emissivity values less than 1. In addition, the e dependence on the wavelength and on the pressure is generally neglected. 

Figure 3.3. Equilibrium linear susceptibility (x/Xiso) versus temperature for an infinite spherical sample on a simple cubic lattice. The dotted lines are the results for independent spins, while the solid lines show the results for parallel and random anisotropy calculated with thermodynamic perturbation theory, as well as for Ising spins calculated with an ordinary high-temperature expansions. We notice in this case that the linear susceptibility for systems with random anisotropy is the same as for isotropic spins calculated with an ordinary high-temperature expansion. The dipolar interaction strength is hj = a/2a = 0.004.

Fig. 19 AGrxn versus temperature for the unimolecular pathways of 2-picolinylperoxy radical. 2 3 denoted by open diamond 2 4a denoted by solid square 2 4b denoted by open triangle 2 5 denoted by dash 2 6 denoted by symbol x 2 7 denoted by solid diamond. All energies calculated at the B3LYP/6-311+G(d,p)//B3LYP/6-31G(d) level of theory.

We will leave for a homework problem the calculation of the equilibrium conversion of methanol versus temperature and pressure. Figure 3-18 is a plot of the equilibrium conversion versus temperature. 

We need to calculate the rate versus temperature and the equUibrium conversion versus temperature. From the requirement that the rate must be consistent with equihhrium, we have... 

Figure 4 Equilibrium composition versus temperature initial composition 1 mol n-Ci6(s)> 4 mol 02(g), and 7 mol H20(g) 1 atm (Calculations using HSC Chemistry...

Process collected data using the instrument data analysis system and plot the calculated values of storage (elastic) modulus ( ), loss (viscous) modulus ( "), complex modulus ( ), and tanS versus temperature. 

Fig. 1.25 Computed versus temperature curves as a function of the mixing ratio of gases (a) for the CO2-H2 system, calculated using eqn (1.141) (b) for the COj-CO system.

Calculate Cp/R, S/R, and (H — H29R)/RT between 300 and 6000 K in 100 K increments. Plot these calculated thermochemical quantities versus temperature and compare with the experimental data given in the file thermotables. csv. 

Plot the surface coverage 6 versus temperature assuming first-order kinetics (n = 1) for the following initial coverages 6a =0.2,0.4,0.6,0.8,1.0. For these calculations, assume /3 = 10 K/s, T0 = 300 K, final temperature T = 475 K, A = 1013 s-1, Ea = 24 kcal/mol. Are the calculated TPD curves symmetric with respect to temperature Does the temperature at the peak desorption rate (i.e., Tp) depend on initial surface coverage Compare Tp from these simulations with the value predicted by the formula derived in part 1, above. 

Pfeifer et al. (263) conclude from their measurements of T, and T2 versus temperature in samples with controlled water contents that the lifetime of sorption complexes of water is 3.5 x 10-9 sec at 50°C with nonlocalized cations and at - 10°C with localized ones. Water was found to be bound more strongly in faujasites with higher Si/Al ratios, which agrees with model calculations by Dempsey (282) of the electrostatic fields around cations. At higher coverages the mobility of H20 is independent of the Si/Al ratio and is two orders of magnitude lower than in bulk water. 

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