Sensitivity of temperature

Fig. 4.10 Absolute sensitivities of temperature maximum with respect to TJ (curve 1), A (2), %0 (3), Q (4), and (5) as a function of < . Here curves 2 and 3 overlap...

In multicomponent separations, the sensitivity of temperature to the key components is important. Figure 18.2a and b shows composition and temperature profiles for a depropanizer separating propane (C3) and lighter components from butane (C4) and heavier components. The temperature is sensitive to the composition of the keys between tray 3 and tray 13. Below tray 3 and above tray 13 the temperature is more sensitive to the concentration of nonkeys than to the concentration of the keys. Trays 8 to 10 show some tendency toward retrograde distillation (recognized by the maximum in the C4 concentration curve) and are best avoided. Moczek et al. (287) provide a detailed demonstration of the anomaly in temperature response in the retrograde distillation region. This leaves trays 3 to 7 and trays 11 to 13 as those suitable for temperatime control. 

The effect of pressure on the control temperature can be minimized by adequate selection of the temperature control location. Generally, all column temperatures have a similar sensitivity to pressure, but the sensitivity of temperature to composition varies widely from tray to tray. Therefore, locating the control temperature in a region highly sensitive to composition reduces its relative sensitivity to pressure changes (see Fig. 18.4). 

The term p is a reaction constant and is mathematically evaluated for a particular reaction by plotting log kjkQ against a. The slope of the straight lines is p, and reflects the sensitivity of the reaction under study to effects of substituents. The value of p is obviously affected by temperature, solvent changes, etc. 

The absolute measurement of areas is not usually usefiil, because tlie sensitivity of the spectrometer depends on factors such as temperature, pulse length, amplifier settings and the exact tuning of the coil used to detect resonance. Peak intensities are also less usefiil, because linewidths vary, and because the resonance from a given chemical type of atom will often be split into a pattern called a multiplet. However, the relative overall areas of the peaks or multiplets still obey the simple rule given above, if appropriate conditions are met. Most samples have several chemically distinct types of (for example) hydrogen atoms within the molecules under study, so that a simple inspection of the number of peaks/multiplets and of their relative areas can help to identify the molecules, even in cases where no usefid infonnation is available from shifts or couplings. 

Figure Bl.16.2. X-band TREPR spectra obtained at 0.1 ps after 308 mn photolysis of a fliiorinated peroxide dimer in Freon 113 at room temperature. Part A is the A/E RPM spectrum obtained upon direct photolysis part B is the E/A RPM spectrum obtained upon triplet sensitization of this reaction using benzophenone.

Optical metiiods, in both bulb and beam expermrents, have been employed to detemiine tlie relative populations of individual internal quantum states of products of chemical reactions. Most connnonly, such methods employ a transition to an excited electronic, rather than vibrational, level of tlie molecule. Molecular electronic transitions occur in the visible and ultraviolet, and detection of emission in these spectral regions can be accomplished much more sensitively than in the infrared, where vibrational transitions occur. In addition to their use in the study of collisional reaction dynamics, laser spectroscopic methods have been widely applied for the measurement of temperature and species concentrations in many different kinds of reaction media, including combustion media [31] and atmospheric chemistry [32]. 

Standardizing the Method Equations 10.32 and 10.33 show that the intensity of fluorescent or phosphorescent emission is proportional to the concentration of the photoluminescent species, provided that the absorbance of radiation from the excitation source (A = ebC) is less than approximately 0.01. Quantitative methods are usually standardized using a set of external standards. Calibration curves are linear over as much as four to six orders of magnitude for fluorescence and two to four orders of magnitude for phosphorescence. Calibration curves become nonlinear for high concentrations of the photoluminescent species at which the intensity of emission is given by equation 10.31. Nonlinearity also may be observed at low concentrations due to the presence of fluorescent or phosphorescent contaminants. As discussed earlier, the quantum efficiency for emission is sensitive to temperature and sample matrix, both of which must be controlled if external standards are to be used. In addition, emission intensity depends on the molar absorptivity of the photoluminescent species, which is sensitive to the sample matrix. 

Sensitivity From equations 10.32 and 10.33 we can see that the sensitivity of a fluorescent or phosphorescent method is influenced by a number of parameters. The importance of quantum yield and the effect of temperature and solution composition on f and p already have been considered. Besides quantum yield, the sensitivity of an analysis can be improved by using an excitation source that has a greater... 

Sensitivity Sensitivity in flame atomic emission is strongly influenced by the temperature of the excitation source and the composition of the sample matrix. Normally, sensitivity is optimized by aspirating a standard solution and adjusting the flame s composition and the height from which emission is monitored until the emission intensity is maximized. Chemical interferences, when present, decrease the sensitivity of the analysis. With plasma emission, sensitivity is less influenced by the sample matrix. In some cases, for example, a plasma calibration curve prepared using standards in a matrix of distilled water can be used for samples with more complex matrices. 

Precision The precision of a potentiometric measurement is limited by variations in temperature and the sensitivity of the potentiometer. Under most conditions, and with simple, general-purpose potentiometers, the potential can be measured with a repeatability of +0.1 mV. From Table 11.7 this result corresponds to an uncertainty of +0.4% for monovalent analytes, and +0.8% for divalent analytes. The reproducibility of potentiometric measurements is about a factor of 10 poorer. 

Figure 7.9 shows a schematic representation of this effect, in which the ratio of the two isotopes changes with time. To obtain an accurate estimate of the ratio of ion abundances, it is better if the relative ion yields decrease linearly (Figure 7.9) which can be achieved by adjusting the filament temperature continuously to obtain the desired linear response. An almost constant response for the isotope ratio can be obtained by slow evaporation of the sample, viz., by keeping the filament temperature as low as is consistent with sufficient sensitivity of detection (Figure 7.9). 

For the same polymer this parameter has values of 4.47 X 10" and 5.01 X 10 " kg sec" at 298 and 398 K, respectively. Since density is far less sensitive to temperature, these results show that the primary temperature dependence of viscosity is described by the temperature dependence of f. 

Viscosity is considerably more sensitive to temperature than elasticity. By varying the temperature, the relaxation time of the polymer will be changed. Hence different mechanical response might be expected on a fixed laboratory time scale for samples examined at different temperatures. 

The proviso all other things being equal in discussing the last point clearly applies to temperature as well, since the kinetic constants are highly sensitive to temperature. To evaluate the effect of temperature variation on the molecular weight of an addition polymer, we follow the same sort of logic as was used in Example 6.3 ... 

Of all the characteristic points in the phase diagram, the composition of the middle phase is most sensitive to temperature. Point M moves in an arc between the composition of the bottom phase (point B) at and the composition of the top phase (point T) at reaching its maximum surfactant concentration near T = - -T )/2. (Points B and Tmove by much smaller amounts, also.) The complete nonionic-amphiphile—oh—water—temperature... 

Acrylamide copolymerizes with many vinyl comonomers readily. The copolymerization parameters ia the Alfrey-Price scheme are Q = 0.23 and e = 0.54 (74). The effect of temperature on reactivity ratios is small (75). Solvents can produce apparent reactivity ratio differences ia copolymerizations of acrylamide with polar monomers (76). Copolymers obtained from acrylamide and weak acids such as acryUc acid have compositions that are sensitive to polymerization pH. Reactivity ratios for acrylamide and many comonomers can be found ia reference 77. Reactivity ratios of acrylamide with commercially important cationic monomers are given ia Table 3. 

In all appHcations involving zirconia, the thermal instabiHty of the tetragonal phase presents limitations especially for prolonged use at temperatures greater than - 1000° C or uses involving thermal cycling. Additionally, the sensitivity of Y—TZP ceramics to aqueous environments at low temperatures has to be taken into account. High raw material costs have precluded some appHcations particularly in the automotive industry. 

R. C. Strittmater, E. M. Wineholt, and M. E. Holmes, The Sensitivity of Double Base Propellant Burning Rate to Initial Temperature, MR-2593, BRL, Aberdeen, Md., 1976. 

Two-speed motors are typically used on noncondensing services where the process is not sensitive to temperature but mostly seasonal or variable throughput of fluids in the air cooler requires some degree of air flow control. This is a simple, rather inexpensive means to control air flow when volume air flow is not critical. Typical motor ratings are 1800/900 rpm, although 1800/1200 rpm types are available. 

Vehicle Fa.ctors. Because knock is a chemical reaction, it is sensitive to temperature and reaction time. Temperature can in turn be affected either by external factors such as the wall temperature or by the amount of heat released in the combustion process itself, which is directiy related to the density of the fuel—air mixture. A vehicle factor which increases charge density, combustion chamber temperatures, or available reaction time promotes the tendency to knock. Engine operating and design factors which affect the tendency to produce knocking are... 

Computer Models, The actual residence time for waste destmction can be quite different from the superficial value calculated by dividing the chamber volume by the volumetric flow rate. The large activation energies for chemical reaction, and the sensitivity of reaction rates to oxidant concentration, mean that the presence of cold spots or oxidant deficient zones render such subvolumes ineffective. Poor flow patterns, ie, dead zones and bypassing, can also contribute to loss of effective volume. The tools of computational fluid dynamics (qv) are useful in assessing the extent to which the actual profiles of velocity, temperature, and oxidant concentration deviate from the ideal (40). 

The arc and spark spectra of the individual lanthanides are exceedingly complex. Thousands of emission lines are observed. For the trivalent rare-earth ions in soUds, the absorption spectra are much better understood. However, the crystal fields of the neighboring atoms remove the degeneracy of some states and several levels exist where only one did before. Many of these crystal field levels exist very close to a base level. As the soUd is heated, a number of the lower levels become occupied. Some physical properties of rare-earth metals are thus very sensitive to temperature (7). 

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