Temperature apparent

Thus, A is apparently temperature dependent, but not highly so, because the partition functions are not very sensitive functions of temperature. 

In summary, observations of increased rates of MW-assisted homogeneous reactions, compared with classically heated reactions at the same apparent temperature, may be explained by one or more of the following problems or effects ... 

An average of temperature records on the earth s surface over a year indicates that the earth s average surface temperature is about 14°C (57°F). But, the earth s 240 watts per square meter of thermal infrared radiation as measured by satellite is equivalent to the radiation emitted by a black body whose temperature is about -19°C (-3°F), not the 14°C (57°F) average measured at the earth s surface. The 33°C (60°F) difference between the apparent temperature of the earth as seen in space and the actual temperature of the earth s surface is attributed to the greenhouse effect. 

Kinetic complexity can produce apparently temperature-independent isotope effects. For example, a rise in temperature produces a smaller intrinsic isotope effect, in agreement with the conventional expectations of Chart 3, for an isotope-sensitive step that is partially rate limiting. If at the same time the rise in temperature makes other steps relatively more rapid so that the isotope-sensitive step then becomes more nearly rate-limiting, then the intrinsic isotope effect will be more fully expressed (Chart 4). If these effects roughly balance, then the isotope effect may appear to be independent of temperature while in fact fully in accord with semiclassical expectations. Seymour and Klinman have discussed in detail the problem of kinetic complexity in isotope-effect temperature dependences. 

This exponential temperature dependenee represents one of the most severe non-linearities in chemical engineering systems. Keep in mind that the apparent temperature dependence of a reaction may not be exponential if the reaction is mass-transfer limited, not chemical-rate limited. If both zones are eneountered in the operation of the reactor, the mathematical model must obviously include both reaction-rate and mass-transfer effeets. 

In 1,1,2,2-tetrachlorethane solution, the spectra of thianthrene and trans-thianthrene 5,10-dioxide are temperature independent for the cis-isomer, the lower-field resonance shifts further downfield with increasing temperature while the signals for 2-, 3-, 7-, and 8- protons remain constant over a 200° range. In chloroform, small, apparant temperature-dependent shifts for thianthrene, at all positions, were attributed to temperature-dependent shifts of the reference solvent signal. Using this, it was shown... 

Figure 8.3 The effect of temperature of an enzyme reaction and the effect of the time-period of the activity measurements on the apparent temperature optimum (after Wiseman, 1975). The index numbers indicate the increase of temperature. It is important to note that in all cases the decrease of the rate of product formation is the consequence of partial inactivations only, i.e. the concentration of substrate must be enough to saturate the enzyme even at time...

The displacements of the framework atoms in the H structure of analcime from the symmetrized positions are listed in Table III. They are considerably larger than the displacements of 0.02-0.07 A found in synthetic zeolite NaA (3) which are the smallest displacements recorded so far in a pseudosymmetric structure. The displacement vectors in analcime can be related to the apparent temperature parameters of the A structure. Figure 3 shows the experimentally determined vibration ellipsoids of optically isotropic analcime (7). The strongly anisotropic ellipsoids are in reasonably good accord with the displacement vectors obtained independently by DLS. 

Apparent Temperature Optimum. A rise in temperature has a dual effect upon an enzyme-catalyzed reaction it increases the rate of the reaction, but it also increases the rate of thermal inactivation of the enzyme itself. Like the pH optimum, the temperature optimum may in certain instances be altered by environmental conditions, e.g., pH, type and strength of buffer, etc. The term temperature optimum, therefore, is useless unless the incubation time and other conditions are specified. A more enlightening term is apparent temperature optimum, which indicates that the optimum has been obtained under a... 

Pore diffusion leads to a reduction by half of the apparent activation energy of enzyme reactions, as in the case of chemical reactions (Levenspiel, 1999). In the literature it has been reported that pore diffusion leads to enhanced apparent temperature and pH stability owing to broadening of the optimal activity regions as a function of temperature and pH activity (Karanth, 1978). Hindered pore diffusion... 

Figure 12. Apparent growth temperatures for various Altiplano carbonates based on clumped isotope thermometry, plotted as a function of estimated maximum burial depth. Symbols discriminate among soil carbonates from sections near Callapa, Corque and Salla and lacustrine carbonates from near Tambo Tambillo, as indicated by the legend. The heavy solid line indicates an estimated burial geotherm, assuming a surface temperature of 20 °C and a gradient of 30 °C per km. The dashed lines define a 10° offset from this trend, which we consider a reasonable estimate of its uncertainty. Carbonates deposited within the last 28.5 Ma and buried to 5000 meters or less exhibit no systematic relationship between apparent temperature and burial depth, and show no evidence for pervasive resetting of deeply buried samples. Error bars are la (when not visible, these are approximately the size of the plotted symbol).

The temperature dependence of the rates of e.t. processes is therefore the obvious criterion for a choice between the Marcus model and a model of e.t. as a type of radiationless transition. In this respect, it must, however, be noted that an apparent temperature effect may appear in the theories of radiationless transitions, if the... 

Mixtures of small molecules (acetone-benzene, ethanol-water) were considered first. In Figures 1 and 2, a comparison is made between the predicted and experimental low-pressure VLE data (21,22) for these systems. An excellent fit to the data is obtained in both cases, with the use of one apparently temperature independent parameter (k j) per binary. 

Fig. 11.7 Apparent temperature dependence of selected bond distances (a) in Angstrom units and angles (b) (in degrees) in the naphthalene rings in the 1-methylnaphthalene clathrate...

Figure 17.1 Heat index (apparent temperature) chart.

National Weather Service. (2002). Heat index (apparent temperature) chart. Retrieved March 13, 2007 from http //www. crh.noaa.gov/dvn/tools/heatindex.pdf... 

Sullivan has studied the H2-I2 and D2-I2 systems quite extensively inducing the formation of the iodides both thermally and photochemically. The initial thermal studies of the H2-I2 system in the temperature range 667-800 °K confirmed the calculations of Benson and Srinivasan. Their calculations indicated that the apparent temperature dependence of the activation energy for reaction involving H2 observed by Bodenstein could be accounted for if an atomic mechanism produced HI in parallel with the molecular mechanism. 

Hops from deep sites to nearby, higher-energy sites contribute to the activation energy for transport. At lower and lower temperature, that contribution increases because a carrier spends most of its time in deeper and deeper sites. The apparent temperature-dependent activation energy mentioned in conjunction with Eq. (5) is easily understood on this basis. (Of course, any reorganization energy for the electron transfer process may also contribute to the temperature dependence.)... 

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