Temperature correction, example

It has also been inferred that differences found between crystallinities measured by density and those from heat of fusion by DSC area determination, as given for polyethylenes in the example of Figure 4 [72], may be related to baseline uncertainties, or not accounting for the temperature correction of AHc. Given that similar differences in crystallinity from density and heat of fusion were reported for isotactic poly(propylene) [43] and polyfaryl ether ether ketone ketone), PEEKK [73], other features of phase structure that deviate from the two-phase model may be involved in the crystallinity discrepancy. 

We will finish the example with a couple of points which will prove useful later in the chapter. If we insert the harmonic oscillator potential into the temperature correction formula (11.2), we get... 

The temperature-time superposition principle is illustrated in Figure 8 by a hypothetical polymer with a TK value of 0°C for the case of stress relaxation. First, experimental stress relaxation curves are obtained at a series of temperatures over as great a time period as is convenient, say from 1 min to 10 min (1 week) in (he example in Figure 8. In making the master curve from the experimental data, the stress relaxation modulus ,(0 must first be multiplied by a small temperature correction factor/(r). Above Tg this correction factor is where Ttrt is the chosen reference... 

It is clear from the Nemst equation that the temperature of the solution affects the response slope (2.303A7//0 of the calibration curve. The electrode voltage changes linearly in relationship to changes in temperature at a given pH therefore, the pH of any solution is a function of its temperature. For example, the electrode response slope increases from 59.2mV/pH at 25°C to 61.5 mV/pH at a body temperature of 37°C. For modem pH sensing systems, a temperature probe is normally combined with the pH electrode. The pH meter with an automatic temperature compensation (ATC) function automatically corrects the pH value based on the temperature of the solution detected with the temperature probe. 

The constant 3 is an order of magnitude estimate which depends on the approximate analysis for the model of Figure (4.10). In addition, the burning rate m " and the properties a and cp should be evaluated at some appropriate mean temperature. For example, in Equation (4.34), the more correct expression for is... 

No large variation in sampling rates is observed among the different studies, despite differences in exposure conditions, such as wind speeds, temperature, and SPMD mounting layout. It should be noted, however, that the effect of temperature is partially accounted for by our use of temperature-corrected log A oa values. An example of the application of Eq. 3.68 for calculating atmospheric concentrations is given in Box 3.3. 

EXAMPLE 9.5 Calculating the Adsorption Energy from the Brunauer-Emmett-Teller Isotherm. The BET analysis uses p/p0 rather than p as a variable just as we used this pressure ratio to compare Langmuir adsorption at different temperatures in Example 9.3. What corrections, if any, are needed in the apparent adsorption energy of about 14 kJ mole-1 as calculated in Example 9.3 ... 

Correlations for friction factors and heat transfer coefficients are rated in HEDH. Some overall coefficients based on external bare tube surfaces are in Tables 8.11 and 8.12. For single passes in cross flow, temperature correction factors are represented by Figure 8.5(c) for example charts for multipass flow on the tube side are given in HEDH and by Kays and London (1984), for example. Preliminary estimates of air cooler surface requirements ram be made with the aid of Figures 8.9 and 8.10, which are applied in Example 8.9. 

Conductivity is measured in the field with a portable probe. It is typically part of the temperature and pH meter, enabling us to measure all three parameters simultaneously. The meter software will perform the temperature correction to 25°C. The probe calibration is verified with a standard prepared as a solution of potassium chloride of a known conductivity. For better accuracy, field meters may have up to four different ranges of conductivity measurements, for example, 0-20pmho/cm ... 

Thermocouple electromotive force is affected by pressure. Usually the indicated temperature is slightly less than the true temperature. For example at 5.0 GPa and 1300°C, the Pt/PtlORh thermocouple indicates a temperature being about 50° C too low. The corrections are approximately linear with both pressure and temperature. 

If the cations of interest, Ba2+ and Ti4+ in the case of barium titanate, can be obtained in solution in the correct ratio then precursors to the final required product can be formed. Subsequent heating of the precursors leads to the formation of BaTi03 (BT) involving the minimum of ion diffusion distances. Because of this the oxides can be formed at relatively low temperatures, for example 500 °C rather than the usual > 1000 °C necessary to effect the solid state reaction between mixed oxides. 

In some cases, researchers have recorded the reference spectra at the same temperature and in the same gas atmosphere as were applied for the respective measurements of the sample. Particularly in the NIR range, a temperature correction can become necessary. For example, Sels et al. (2001) used a spectrum of the catalyst matrix (layered double hydroxide) suspended in methanol and aqueous H2O2. Brik et al. (2001) recorded their BaSC>4 reference spectra at various temperatures. Lu et al. (2005) recorded the spectra of their catalyst support, CaC03, as references under the conditions of the catalytic reaction, that is, in a mixture of ethene or propene in O2 and He at 473 K. Rao et al. (2004) heated their reference material to reaction temperature to generate the baseline. 

Because of doubt about the weighing error and the temperature correction, it was necessary to repeat the determination see the results given in Example 1 on p. 56. The new value of [aJo was +152.61 0.23 deg dm (g cm. Evidently the optical purity of the specimen was quite high the difference from the literature value of +152.70 is not significant at the 95 percent confidence level. 

They may also be suitable for following gelation in near-line or laboratory experiments at a constant temperature. For example, a vibrational viscometer was used to determine the coagulation time of reimeted milk at fixed temperatures (Sharma et al., 1989, 1992). However, in non-isothermal physical gelation, the elastic modulus depends on the temperature dependence of the resonant response so that precise correction for the influence of temperature must be known. 

These equations are approximately correct because they successfully establish the relationship between the coefficients of transport with pressure and temperature. For example, the molecular diffusivity is proportional to the 3/2... 

We have noted that the equilibrium constant Kj for reaction depends only on the system temperature T and the standard state. Often, we need to determine how the equilibrium constant changes with temperature. For example, during a reactor design we routinely want to know whether product yield can be improved by an increase or decrease in operating temperature. Furthermore, many tables (discussed at the end of 10.4.2) give values for equilibrium constants only at selected temperatures then we must correct those values to the temperature of our situation. 

Turning to the other meanings of the word heat listed in most dictionaries, one finds that a degree of hotness is impUed. This indicates that heat is stUl confused with its intensive parameter temperature. The example the heat of this room is unbearable is expressed correctly by saying the temperature of this room is unbearable. The improper use of heat in this case becomes clear on recognizing that,... 

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