Approximations 5% rule

As an approximate rule, break-up of droplets occurs for a Weber number in excess of one, a rule of thumb that is actually valid for the range of viscosity ratios of the dispersed phase to the continuous phase of less than approximately five. Higher viscosities of the disperse phase lead to serious difficulties with emulsification because the shear energy is then dispersed in rotation of the droplets. 

Flowever, from the results and graphs attached and from other sources cited,the following approximate rules may be stated. 

P and tv of the cross-dimer were estimated using approximate rules found by analogy with the hydrocarbons. 

Trouton s rule phys chem An approximation rule for the derivation of molar heats of vaporization of normal liquids at their boiling points. traCit anz. riil ) true condensing point See critical condensation temperature. trii kan dens ir). point) true electrolyte puys chem A substance in the solid state that consists entirely of ions. trir i lek-tr9,lTt)... 

Equation (2.2) is sometimes referred to as the ideal gas law. However, for our present purposes, we must recognize that this law [like those summarized in (2.3a-d)] is merely a crude approximation that never describes any real gas exactly, except in the idealized limit of zero pressure (to be discussed in Section 2.3). Hence, we must sharply distinguish between crude empirical laws (which are at most approximate rules of thumb) and true thermodynamic laws as summarized in Table 2.1. A difficulty for the beginning student of thermodynamics is to distinguish those equations that are based on the ideal gas approximation (and thus are practically never true) from those of rigorous thermodynamic quality. We shall often flag equations of the former type with IG (ideal gas), for example... 

By the approximate rule, the answer should be 1.1 (two significant figures). However, a difference of 1 in the last place of 9.3 (9.3 0.1) results in an error of about 1 percent, while a difference of 1 in the last place of 1.1 (1.1 0.1) yields an error of roughly 10 percent. Thus the answer 1.1 is of much lower percentage accuracy than 9.3. Hence in this case the answer should be 1.06, since a difference of 1 in the last place of the least exact factor used in the calculation (9.3) yields a percentage of error about the same (about 1 percent) as a difference of 1 in thelastplaceof 1.06 (1.06 0.01). Similarly, 0.92 x 1.13 = 1.04. 

Thus an approximate rule emerges for comparing ID and 2D peak capacities the single-dimensional peak capacities multiply together to yield the 2D peak capacity. This rule illustrates the enormous separation power of 2D (more generally, multidimensional) forms of separation. 

A number of interesting rules are summarised in Table 4.11. It has to be mentioned, however, that these rules are approximate rules and that they are not to be used to find new equations by substitution of the one in the other ... 

At any temperature above 0°C, there will be spontaneous generation of elec-tron/hole pairs that is unrelated to incident light intensity. In addition, defects in the silicon may be sources of electrons and contribute dark electrons. Both of these processes are exponentially dependent on temperature, and CCDs must be actively cooled to reduce dark current to acceptable levels. The dark current is usually expressed as e pixel s (electrons per pixel per second) and depends both on the specific device and the temperature. A few examples are listed in Table 8.6. As an approximate rule of thumb, ihe dark current doubles for each 5°C increase in temperature. 

Approximate rules For short vanes, or open impellers Eh == 30per cent, for Volute Pumps Eh 50 to 60 per cent, for Turbine Pumps Eh 57 to 69 per cent. 

When actual data are not available, a useful approximate rule for ordinary temperatures and pressures, is to take y as 1.67 for monatomic gases, 1.40 for diatomic gases, 1.30 for simple polyatomic gases, such as water, carbon dioxide, ammonia and methane. It may be noted that the heat capacity ratio for hydrogen gas increases at low temperatures toward the vfdue for a monatomic gas. This matter will be explained in Chapter VI. 

Bartlett, J. Am. Chem. Soc., 52, 1374 (1932)3. Compare the results with those given by the approximate rule applicable at low pressures. 

With Equations (5), (25), and (30) one can also deduce approximate rules for the dependences of the CIDNP intensities on the strength of the magnetic interactions and on the field Bq. For the simple model system of a radical pair with one proton in the first radical, the population difference of the nuclear spin states a) and S) is seen to be... 

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