Electrostatic unit

While the Systeme International d Unites (SI) system of units is not particularly relevant to physical chemistry and requires additional and sometimes awkward constants, its broad use deserves attention. The majority of the derivations are made in the cgs/esu (centimeter-gram-second/electrostatic unit) system of units however, both the SI and cgs systems are explained and tables for their interconversion are given in Chapters V and VI. 

In reduced electrostatic units, the factor is eliminated and the Poisson equatic becomes ... 

Because the charge on an electron is 4 80 X 10 electrostatic units (esu) and the dis tances within a molecule typically fall m the 10 cm range molecular dipole moments... 

Coulomb s law. This relationship poses no particular difficulties as a qualitative statement the problem arises when we attempt to calculate something with it, since the proportionality constant depends on the choice of units. In the cgs system of units, the electrostatic unit of charge is defined to produce a force of 1 dyne when two such charges are separated by a distance of 1 cm. In the cgs system the proportionality factor in Coulomb s law is unity and is dimensionless. For charges under vacuum we write... 

The carbon black (soot) produced in the partial combustion and electrical discharge processes is of rather small particle si2e and contains substantial amounts of higher (mostly aromatic) hydrocarbons which may render it hydrophobic, sticky, and difficult to remove by filtration. Electrostatic units, combined with water scmbbers, moving coke beds, and bag filters, are used for the removal of soot. The recovery is illustrated by the BASF separation and purification system (23). The bulk of the carbon in the reactor effluent is removed by a water scmbber (quencher). Residual carbon clean-up is by electrostatic filtering in the case of methane feedstock, and by coke particles if the feed is naphtha. Carbon in the quench water is concentrated by flotation, then burned. 

The symbols 5+ and 5- indicate polarity of the two ends or poles of the electrically neutral molecule. Such a polar molecule constitutes a permanent dipole, i.e., two equal and opposite charges (e) separated by a distance (d) in space. A quantitative measure of the polarity of a molecule is the dipole moment (p in Debye units), which is defined as the product of the charge (e in electrostatic units) and the distance (d in cm). 

Now one electrostatic unit of potential is equal to 300 volts. We find then that the intensity of the field will amount to 300 million volts/cm and when polar molecules arc introduced into this field, we must expect the deviation depicted in Fig. 5. 

As we have seen, Ohm s law requires that the distance t> between the planes shall be proportional to the intensity X of the field thus we may write v — uX, where u is the value which v will have when X is unity (unity in whatever units we decide to use, electrostatic units or volts... 

If we were to forget that the flow of current is due to a random motion which was already present before the field was applied—if we were to disregard the random motion entirely and assume that each and every electron, in the uniform field X, moves with the same steady velocity, the distance traveled by each electron in unit time would be the distance v used in the construction of Fig. 16 this is the value which would lead to a current density j under these assumptions, since all electrons initially within a distance v of the plane AB on one side would cross AB in unit time, and no others would cross. Further, in a field of unit intensity, the uniform velocity ascribed to every electron would be the u of (34) this quantity is known as the mobility of the charged particle. (If the mobility is given in centimeters per second, the value will depend on whether electrostatic units or volts per centimeter are used for expressing the field strength.)... 

The roentgen is the international unit of quantity for both x-rays and y-rays. It is the quantity of this radiation which will produce, as a, result of ionization, one electrostatic unit of charge, of either sign, in one cubic centimeter of dry air (as measured at 0° C and standard atmospheric pressure). 

Whether electrostatic technology is superior to magnetic device technology is debatable. What is of interest is that, in a 1998 marketing and technical support documentation pack from a major electrostatic unit manufacturer, most of the information supplied related primarily to cooling water applications rather than boilers. The boiler data, such as there was, concerned only smaller, simple systems (e.g., HW boilers and steam ovens). 

In this system, centimeter is the unit of length, erg is the unit of energy, and statcoulomb (also called the electrostatic unit or esu) is the unit of charge. In this book we accommodate both systems of units and write Coulomb s law in the form... 

Unlike the rest of the chapter, here we adopt Gaussian electrostatic units which are typically used in the literature devoted to molecular capacitors and double layer theory. 

Before closing this section, it is worth mentioning that the hyperpolarizability tensors are complex quantities usually given in the old cgs system of units of esu (electrostatic units). The transformation into the International System is readily obtained with the relationship ... 

Roentgen (R)—A unit of exposure (in air) to ionizing radiation. It is the amount of x or gamma rays required to produce ions carrying 1 electrostatic unit of electrical charge in 1 cubic centimeter of dry air under standard conditions. Named after William Roentgen, a German scientist who discovered x rays in 1895. 

The dimensions of units in electricity and magnetism are the origin of much confusion. In the days when mechanical and thermal quantities were expressed in cgs, two different systems were introduced for the electrical and magnetic quantities. They are the esu (electrostatic units) and the emu (electromagnetic... 

The Poisson equation in electrostatic units for planar symmetry may be written... 

Despite the complication due to the interdependence of orbital and spin angular momenta, the Dirac equation for a central field can be separated in spherical polar coordinates [63]. The energy eigenvalues for the hydrogen atom (V(r) = e2/r, in electrostatic units), are equivalent to the relativistic terms of the old quantum theory [64]... 

Calculations of the electronic structure of molecules, crystals and surfaces are often performed in atomic units. They are defined by setting the most important constants equal to unity h — eo — me — 1, where me is the electronic mass. The Coulomb law is written in electrostatic units V(r) = q/r, so that the time-independent Schrodinger equation for the hydrogen atom takes on the simple form ... 

The product of the charge 8e and the distance d between the charges, ijl = 8ed, is called the dipole moment. The unit for the dipole moment is the debye (D), which is defined as pi for charge of the magnitude of the electronic charge e [4.803 X 10 esu (electrostatic unit)] and the separation J of 1A between the charges. 

Helmholtz Wied. Ann. vii, 337,1897) showed from electrostatic considerations that if M be the electric moment per sq. cm. of the. .interface expressed in electrostatic units then the difference of electric potential across the interface was related to the electric moment by the expression... 

M the moment per sq. cm. in electrostatic units may be expressed more fully in terms of p, the volume density of charge at a distance OB from an imaginary plane drawn somewhere in the non-homo-geneous region between the phases, thus... 

A short digression on units is perhaps appropriate here. We shall use either Gaussian rrrrits in this book or, much more frequently, Hartree s atomic units. Gaussian units, as far as we are concerned, are identical with the old cgs system of units with the added proviso that charges are measured in unnamed electrostatic units, esu. The value of e is thus 4.803206808 X 10 esu. Keeping this number at hand is all that will be required to use Gaussian rmits in this book. 

Electrical Units. They may be subdivided into EMU (emu)-electromagnetic and ESU (esu electrostatic units. EMU ate based on the strength of magnetic poles (m and m ) ... 

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