Thermalization length, effective

Rodebush has also implied that the accuracy with which very low temperatures can be measured is restricted by the uncertainty principle and by the nature of the substance under investigation. However, the accuracy of a temperature measurement is not limited in a serious way by the uncertainty principle for energy, inasmuch as the relation between the uncertainty in temperature and the length of time involved in the measurement depends on the size of the thermometer, and the uncertainty in temperature can be made arbitrarily small by sufficiently increasing the size of the thermometer we assume as the temperature of the substance the temperature of the surrounding thermostat with which it is in either stable or metastable equilibrium, provided that thermal equilibrium effective for the time of the investigation is reached. 

Effective thermalization length, the b value for origin-centered gaussian distribution (see text) only when G[( < 0.2 is a truncated power law distribution used by Freeman and his associates. For the free-ion yield in kcal/mole. 

A recent examination of the bulk phase behavior of mixtures (0.5 - 70 mol%) of 8a with CCH-4 by thermal microscopy, DSC, and deuterium NMR spectroscopy with a deuterated analog of 8a has provided a detailed picture of the solubilization of this ketone in the liquid crystalline phases of CCH-4 (42), and provides further clues to the origins of the solute length effect discussed above. This study indicates that the solubilization of 8a in the crystal-B phase is rather more complex... 

Length Effect. The heat transfer coefficient can vary significantly in the entrance region of the laminar flow. For hydrodynamically developed and thermally developing flow, the local and mean heat transfer coefficients h, and h, for a circular tube or parallel plates are related as [19]... 

The thermowell arrangements shown in Figure 7-108 present other methods that can be used in making the 1-inch connections in process piping. To evaluate each of the thermowell details shown, these are summarized and appraised in Table 7-16a. This table presents an analysis showing the active, effective thermal lengths inside the pipe and how they compare in speed of response, and to what instruments they are best applied. It also shows that it is not practical to use certain well arrangements for temperature instruments. 

From these calculations, it is obvious to condude that the first reaction is synchronous with similar bond lengths formed whereas the second one is asynchronous with quite different bond lengths formed. Furthermore, the dipole moments remained the same for GS and TS in the first reaction whereas they are noticeably increased in the TS for the second. All these conclusions strongly support the evidence and interpretation of important spedfic not purely thermal MW effects when asynchronous mechanisms are involved. 

The phase or optical path length variation — (d x /) is a function of radial position in the ZnSe and CVD diamond windows and is shown in Fig. 20. The variation for CVD diamond over the effective beam width is over a factor of 250 smaller. Three factors combine to yield this large difference the smaller temperature rise in CVD diamond due to the higher thermal conductivity (AT a factor of more than 7 smaller in CVD diamond), the smaller value of dn/df for diamond (a factor of 5.8), and the thickness of the window, which for CVD diamond is only l/6th of that in ZnSe. For an example similar to that shown in Fig. 18 the thermal lensing effect in the ZnSe window was found to be equivalent to a lens of 3-5 m focal length, whereas for the CVD diamond window the effect was negligible [27,34]. 

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