Symbols used in equations

In the list of equations of state and of some other equations used in detonation calculations, which follows, the symbols listed by Cook (Ref 12, pp 376-78) will be used, with a few exceptions. Small v will be used for specific volume (cc per gram of expl) and small e for specific energy, although some investigators use caps. For pressure which does not include intrinsic pressure, tu, small p will be used, while P will be used for total pressure p + tu (See eq 6) and not for p/p2 listed by Cook. Some of the symbols used in equations of state are not listed by Cook... 

The double arrow indicates that reactions occur in both the forward and reverse directions and that the final result is a mixture of all three substances. The temperature at which the reaction occurs is 350°C. The pressure at which the reaction occurs, 25 000 kPa, is also shown above the arrow. A catalyst is used to speed the reaction, so the catalyst is mentioned, too. Other symbols used in equations are shown in Table 2. 

Refer to Appendix A to see more symbols used in equations. 

In equations, symbols are used to show the physical states of the reactants and products. Reactants and products can exist as sohds, liquids, and gases. When they are dissolved in water, they are said to he aqueous. It is important to show the physical states of a reaction s reactants and products in an equation because the physical states provide clues about how the reaction occurs. Some basic symbols used in equations are shown in Table 10-1. 

Symbols are listed in alphabetical order by the section of the chapter in which they appear. Only symbols which have not been previously listed or which are used in a different sense from previous listings are included for each section. Symbols used in equations for simplification of the form are generally defined immediately thereafter and are not listed in the Notation section found at the end of each chapter. 

Table 4-1. Symbols Used in Equations and Thermodynamic Functions...

Generally, each formula in an equation is followed by an abbreviation, in parentheses, that gives the physical state of the substance solid (5), liquid (/), or gas (g). If a substance is dissolved in water, it is in an aqueous (aq) solution. Table 8.2 summarizes some of the symbols used in equations. 

Symbols used in Table VII are defined for each equation in the second column of the table. 

The <7i values are identical to op The symbol was changed in order to be consistent with the other symbols used in the equation. 

Equation 1 describes the change of mass, pesticides, within the tank at any given time. The symbols used in this derivation are defined as follows ... 

In view of the large seasonal differences in atmospheric dispersion in New York City and the improved models obtained, dispersion-normalized data based on 7 A.M. measurements were used in this first stage of development for all of the source apportion models reported here. In order to keep the notation as simple, as possible, this has not been indicated explicitly in the symbols used in the equations. Dispersion normalization, however, is implicit in all of the models reported. 

A proportionality symbol has been used in Equation 22 because the original equation (see Ref. ) seems to have a problem with units. In this equation, CTq(E ) is the in-... 

Equation (4.5) is known as the Rankine-Hugoniot equation. Hie symbols used in the above three equations, which are applied to. 

B Most symbols are defined near where they are used in equations. Unless defined otherwise locally, certain notations have the meanings in this list. 

Although convenient to use in equations, the symbol H+ (aq) does not really represent the structure of the ion present in aqueous solution. As a bare hydrogen nucleus (proton) with no electron nearby, H + is much too reactive to exist by itself. Rather, the H+ attaches to a water molecule, giving the more stable hydronium ion, H30 +. We ll sometimes write H+(aq) for convenience, particularly when balancing equations, but will more often write H30+(fl(/) to represent an aqueous acid solution. Hydrogen chloride, for instance, gives C (aq) and H30+(d /) when it dissolves in water. 

State symbols Symbols used in chemical equations to denote whether a reactant or product is a solid (s), a liquid (I), a gas (g), or an ion in aqueous solution (aq). 

Because of convention, the symbols for the chemical potential, used in Equation 6.44 and Equation 6.45, and the dipole moment are the same. Further evaluation of Equation 6.48 proceeds through introduction of the LCAO-MO expansion (Equation 6.18) and, dependent on the level of theory, consideration of relevant approximations such as the NDDO formalism (Equation 6.31) in the case of semiempirical MNDO-type methods. Because the calculation of the dipole moment is usually considered a somewhat demanding test of the quality of the wavefunctions employed in the quantum chemical model, this property is included in the comparative statistical analysis of various methods to calculate molecular descriptors as presented in Section V. 

All symbols used in the following derivation of the equations required to plot the NMR line shapes are listed below. 

KnA does not depend on the pressure and the gas composition inside the catalyst pellet Furthermore the following symbols are used in Equation 7.97 ... 

The symbols used in the equations, correspond to the following quantities ... 

Symbols used in the computer program are in parentheses. Minimum fluidizing rate by Leva s Equation, Eq. 9-20... 

---