Minus sign

Hence, the same teclmiques used to calculate are also used for Cg. Note that equation (A1.5.28) has a geometrical factor whose sign depends upon the geometry, and that, unlike tlie case of the two-body dispersion interaction, the triple-dipole dispersion energy has no minus sign in front of the positive coefficient Cg. For example, for an equilateral triangle configuration the triple-dipole dispersion is repulsive and varies... 

Here L is the Onsager coefficient and the minus sign (-) indicates that the concentration flow occurs from regions of high p to low p in order that the system irreversibly flows towards the equilibrium state of a... 

Ionic charge should be indicated by an Arabic superscript numeral preceding the plus or minus sign Mg2 +, PO -. 

Loss of a particular group should be indicated by the use of a minus sign located outside the parentheses or to the right of the + sign. Spaces should be left on either side of the minus sign to reduce any confusion as to its meaning. Thus one would write ... 

The rate of a process is expressed by the derivative of a concentration (square brackets) with respect to time, d[ ]/dt. If the concentration of a reaction product is used, this quantity is positive if a reactant is used, it is negative and a minus sign must be included. Also, each derivative d[ ]/dt should be divided by the coefficient of that component in the chemical equation which describes the reaction so that a single rate is described, whichever component in the reaction is used to monitor it. A rate law describes the rate of a reaction as the product of a constant k, called the rate constant, and various concentrations, each raised to specific powers. The power of an individual concentration term in a rate law is called the order with respect to that component, and the sum of the exponents of all concentration terms gives the overall order of the reaction. Thus in the rate law Rate = k[X] [Y], the reaction is first order in X, second order in Y, and third order overall. 

In this expression, called Pick s first law, the proportionality constant D is the diffusion coefficient of the solute. Since J = (l/A)(dQ/dt) and c = Q/V, where Q signifies the quantity of solute in unspecified units, it follows that D has the units length time", or m sec in the SI system. The minus sign in Eq. (9.69)... 

We divide by Avogadro s number to convert the partial molar Gibbs free energy to a molecular quantity, and the minus sign enters because the force and the gradient are in opposing directions. Recalling the definition of chemical potential [Eq. (8.13)], we write jUj + RT In aj = ii2 + RT In 7jC, where aj... 

A minus sign indicates a signal to high field. 

T] Approximate solution. Use minus sign if foreed and natural eonveetion oppose eaeh other. 

The pins sign corresponds to the downstream transition and the minus sign to the upstream one. This equation is solved along each path beginning at the respective end points—the initial condition of the Led for the downstream transition and the feed condition for the upstream transition. If either path fails to evolve continuously in the expected direction, the difference form, from Eq. (16-136),... 

Tj is the surface excess (Davies and Rideal, Jnteifacial Phenomena, 2d ed.. Academic, New York, 1963). For most purposes, it is sufficient to view Vj as the concentration of adsorbed component i at the surface in units of, say (g mol)/cm . R is the gas constant, T is the absolute temperature, Y is the surface tension, and a is the activity of component i. The minus sign shows that material which concentrates at the surface generally lowers the surface tension, and vice versa. This can sometimes be a guide in determining preliminarily what materials can be separated. 

Membrane Limitations Chemical attack, fouling, and compaction are prominent problems with RO and NF membranes. Compaction is the most straightforward. It is the result of creep, slow cold flow of the polymer resulting in a loss of water permeability. It is measured by the slope of log flux versus log time in seconds. It is independent of the flux units used and is reported as a slope, sometimes with the minus sign omitted. A slope of—0.001, typical for noncelhilosic membranes, means that for every threefold increase in log(time), 10 seconds, a membrane looses 10 percent of its flux. Since membranes are rated assuming that the dramatic early decline in permeability has already occurred, the further decline after the first few weeks is veiy slow. Compaction is specific to pressure, temperature, and envi-... 

The plus sign indicates a positive sequence harmonic and the minus. sign a negative sequence harmonic. Their effect is same as for the positive and the negative seqtience components discussed in Section I2.2(v) and ctiuses pulsation in the magnetic field and hence, in the torque of a rotiitimi machine. 

In these equations the minus sign always indicates a partial pressure which decreases in time, i.e. the partial pressure is that of a reactant. 

Fig. 5.4. The stability of complex systems is determined by changes in the free work Wf. Note the minus sign - systems try to move so that they produce the maximum work.

The minus sign results from the definition of Ap, which is equal to p2 - Pi, a negative quantity. The term q is known as the seepage velocity and is equivalent to the velocity of approach v , which is also used in the definition of the Reynolds number. 

The minus sign shows that the heat of reaction is exothermic. 

The minus sign in the equation denotes that the heat flow is positive in the direction of decreasing temperature. 

FIGURE 23.11 The principal re mechanisms in glycolysis and glncoi Activators are indicated by plus sign inhibitors by minus signs. 

Minus-leitung, /. (Elec.) negative lead, -pol, m. negative pole, -zeichen, n. minus sign. 

The sign before each variable indicates how the variable influences quantity supplied. A minus sign indicates they are inversely related and a positive sign indicates they are directly related. Thus, in the example of coal, raising the price of coal is likely to increase quantity supplied, whereas raising the price of labor is likely to decrease the quantity supplied. 

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