Sign conventions

Flere the subscripts and/refer to the initial and final states of the system and the work is defined as the work perfomied on the system (the opposite sign convention—with as work done by the system on the surroundings—is also in connnon use). Note that a cyclic process (one in which the system is returned to its initial state) is not introduced as will be seen later, a cyclic adiabatic process is possible only if every step is reversible. Equation (A2.1.9), i.e. the mtroduction of t/ as a state fiinction, is an expression of the law of conservation of energy. 

The IlyperChein log file includes calculated dipole moments of 111 oiccu les. To set th e am min t o f in form anon collected in th e log file, eh an gc the value of the Qu an turn Prin t Level set tin g in the eh em. in 1 File. Xote that the sign convention used in the quantum mechanical calculation of dipoles is opposite to that used in 111 oiccu lar mech an ics dipole calculation s this reflects th e differing sign conventions ofphysics and chemistry. 

Sign Conventions Since the reaction of interest occurs at the working electrode, the classification of current is based on this reaction. A current due to the analyte s reduction is called a cathodic current and, by convention, is considered positive. Anodic currents are due to oxidation reactions and carry a negative value. 

A consistent sign convention has been applied to the pressure-volume work term A positive dV corresponds to an expanded system, and work is done by the system to push back the surrounding atmosphere. 

Chemical engineers usually make detailed evaluations of costs rather than evaluations for profits or sales. However, the latter can be analyzed in a similar manner to costs by using the equations shown in Table 9-38. For this puraose, the sign convention will be reversed because an increase in sales or profits would be considered favorable, whereas an increase in cost would be considered unfavorable. The equations can be apphed to both batch and continuous processes. 

The sign associated with the pressure is opposite to that associated with the normal viscous stress. The usual sign convention assumes that a tensile stress is the positive normal stress so that the pressure, which by definition has compressive normal stress, has a negative sign. 

The information presented in this work builds upon developments from several more established fields of science. This situation can cause confusion as to the use of established sign conventions for stress, pressure, strain and compression. In this book, those treatments involving higher-order, elastic, piezoelectric and dielectric behaviors use the established sign conventions of tension chosen to be positive. In other areas, compression is taken as positive, in accordance with high pressure practice. Although offensive to a well structured sense of theory, the various sign conventions used in different sections of the book are not expected to cause confusion in any particular situation. 

Note that the sign convention of V/ ensures that the reaction rate is a positive quantity. 

To obtain the predicted shift for the carbon atom in methane, we subtract its absolute value from that of the reference molecule, resulting in a predicted shift of -3.9 ppm, which is in reasonable agreement with the experimental value of -7.0. Note the sign convention for shifts a negative number indicates that there is more shielding in the specified molecule than in the reference molecule, and a positive number indicates that there is less shielding than in the reference molecule. 

Figure 19.26 Orbitals u.sed in descnbing the bonding in metal-ij - cyclobutadiene complexe.s. The sign convention and axes arc as in Fig. 19.23...

The symbol and sign conventions used for substituent effects in this chapter are those most frequently used by writers on correlation analysis in organic chemistry. / or R effects which withdraw electrons from the ring are regarded as positive. See Ref. 48, pp. 229-230 for a more detailed consideration of symbol and sign conventions. 

In this equation the negative sign is introduced in order to maintain a consistency of sign convention when shear stress is related to momentum transfer as in Chapter 11. Since (du,/dy)v=o must be positive (velocity increases towards the pipe centre), R0 is negative. It is therefore more convenient to work in terms of / , the shear stress exerted by the fluid on the surface (= —Rq) when calculating friction data. 

In some books, you will see electron affinity defined with an opposite-sign convention. Those values are actually the electron-gain enthalpies (Chapter 6). 

The sign convention we have adopted is that the rate of a reaction is always positive. The rate of formation of a component is positive when the component is formed by the reaction and is negative when the component is consumed. 

Tables in reference sources often give electron affinities as positive values when the negative ion is more stable than the neutral atom. This convention is contrary to the sign convention for other energetic processes, which uses negative values when energy...

When comparing calculations, or calculations and experiment, it is important to ensure consistent sign conventions are applied. This requires that the absolute configuration of the enantiomer and photon hehcity used in a calculation be clearly specified. See Appendix B... 

When the sign convention adopted for rate is taken into account, this equation holds for both anodic and cathodic currents. 

The generalized stoichiometric coefficients are defined as positive quantities for the products of the reaction and as negative quantities for the reactants. The coefficients of species that are neither produced nor consumed by the indicated reaction are taken to be zero. Equation 1.1.2 has been written in inverted form with the zero first to emphasize the use of this sign convention, even though this inversion is rarely used in practice. 

This second form is preferred, provided that one keeps the proper sign convention for the stoichiometric coefficients in mind. 

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