Directly proportional quantities

Of the various parameters introduced in the Eyring theory, only r—or j3, which is directly proportional to it-will be further considered. We shall see that the concept of relaxation time plays a central role in discussing all the deformation properties of bulk polymers and thus warrants further examination, even though we have introduced this quantity through a specific model. 

The relationship between current flow and chemical reactions was estabUshed by Faraday who demonstrated that the amount of chemical change was directly proportional to the quantity of charge passed (//) and to the equivalent weight of the reacting material. 

Grayness of a fabric swatch is not directly proportional to its content of black pigment (or artificial sod). A basic formula relating reflectance to the pigment content or concentration can be appHed to the evaluation of detergency test swatches (51,99—101). In simple form, an adaptation of the Kubelka-Munk equation, it states that the quantity (1 — i ) /2R (where R is the fraction of light reflected from the sample) is a linear function of the sod content of the sample. 

The second term in brackets in equation 36 is the separative work produced per unit time, called the separative capacity of the cascade. It is a function only of the rates and concentrations of the separation task being performed, and its value can be calculated quite easily from a value balance about the cascade. The separative capacity, sometimes called the separative power, is a defined mathematical quantity. Its usefulness arises from the fact that it is directly proportional to the total flow in the cascade and, therefore, directly proportional to the amount of equipment required for the cascade, the power requirement of the cascade, and the cost of the cascade. The separative capacity can be calculated using either molar flows and mol fractions or mass flows and weight fractions. The common unit for measuring separative work is the separative work unit (SWU) which is obtained when the flows are measured in kilograms of uranium and the concentrations in weight fractions. 

Direct costs are those that can be directly charged to a single product. The most obvious direc t cost is for raw materials, of which the quantity consumed is directly proportional to the amount of product manufactured. Direct process labor is also considered to be a direct cost. 

Air is usually the basic load component to an ejector, and the quantities of water vapor and/or condensable vapor are usually directly proportional to the air load. Unfortunately, no reliable method exists for determining precisely the optimum basic air capacity of ejectors. It is desirable to select a capacity which minimizes the total costs of removing the noncondensable gases which accumulate in a process vacuum system. An oversized ejector costs more and uses unnecessarily large quantities of steam and cooling water. If an ejector is undersized, constant monitoring of air leaks is required to avoid costly upsets. 

It should be noted that low-loss spectra are basically connected to optical properties of materials. This is because for small scattering angles the energy-differential cross-section dfj/dF, in other words the intensity of the EEL spectrum measured, is directly proportional to Im -l/ (E,q) [2.171]. Here e = ei + iez is the complex dielectric function, E the energy loss, and q the momentum vector. Owing to the comparison to optics (jqj = 0) the above quoted proportionality is fulfilled if the spectrum has been recorded with a reasonably small collection aperture. When Im -l/ is gathered its real part can be determined, by the Kramers-Kronig transformation, and subsequently such optical quantities as refraction index, absorption coefficient, and reflectivity. 

The Reynolds number, which is directly proportional to the air velocity and the size of the obstacle, is a critical quantity. According to photographs presented elsewhere, a regular Karman vortex street in the wake ot a cylinder is observed only in the range of Reynolds numbers from about 60 to 5000. At lower Reynolds numbers, the wake is laminar, and at higher Reynolds numbers, there is a complete turbulent mixing. 

Pressure drop under streamline flow conditions is directly proportional to the quantity of oil flowing. The effect of reduced flow rate after take-off points, as compared with full flow rate throughout the full length of the pipeline when there is no take-off, should be taken into account to ensure that variation in pressure is within the specified pump output. Special consideration is necessary with gravity and ring main systems serving several take-off points. 

If a fixed quantity of gas is held at a constant pressure and heated or cooled, its volume will change. According to Charles law, the volume of a gas at constant pressure is directly proportional to the absolute temperature. This is shown by the following equation ... 

Faraday s Law the quantity of charge (Q) passed in an electrochemical reaction is directly proportional to the number of moles (n) of substance reacted. Thus Q = zFn, where z is the number of electrons involved in one molecule of the reaction and F is the Faraday constant. 

Osmotic pressure, like vapor pressure lowering, is a colligative property. For any nonelectrolyte, ir is directly proportional to molarity, M. The equation relating these two quantities is very similar to the ideal gas law ... 

The amounts of substances liberated (or dissolved) at the electrodes of a cell are directly proportional to the quantity of electricity which passes through the solution. 

Coulometric analysis is an application of Faraday s First Law of Electrolysis which may be expressed in the form that the extent of chemical reaction at an electrode is directly proportional to the quantity of electricity passing through the electrode. For each mole of chemical change at an electrode (96487 x n) coulombs are required i.e. the Faraday constant multiplied by the number of electrons involved in the electrode reaction. The weight of substance produced or consumed in an electrolysis involving Q coulombs is therefore given by the expression... 

The quantity of solute B crossing a plane of area A in unit time defines the flux. It is symbolized by J, and is a vector with units of molecules per second. Fick s first law of diffusion states that the flux is directly proportional to the distance gradient of the concentration. The flux is negative because the flow occurs in a direction so as to offset the gradient ... 

The quantity rg is directly proportional to ilf ( see Chap. X) hence for any linear polymer homologous series their ratio, is a con-... 

Where Q, is the minimum detectable amount, R the detector noise level and s the detector sensitivity [135,146,151,152]. For a concentration sensitive detector the minimum detectable concentration is the product of Q, and the volumetric gas flow rate through the detector. The minimum detectable amount or concentration is proportional to the retention time, and therefore, directly proportional to the column radius for large values of n. it follows, then, that very small quantities can be detected on narrow-bore columns. 

Ohm s law states that a direct current carried between two points of a conductor varies in direct proportion to the voltage difference between the two points and is inversely proportional to the resistance offered to the conduction of the current by the conductor between the two points taken as a reference. Using the symbols I, V, and R to represent the quantities in the order given, Ohm s law can be written as ... 

Faraday s third law of electrolysis states that when the same quantity of electricity is passed through different electrolytes, the amounts of the different substances deposited, evolved at, or dissolved from the electrodes are directly proportional to their chemical equivalent weights. 

The SI unit of activity is the becquerel (Bq) 1 Bq = that quantity of radioactive material in which there is 1 transformation/second. Since activity is proportional to the number of atoms of the radioactive material, the quantity of any radioactive material is usually expressed in curies, regardless of its purity or concentration. The transformation of radioactive nuclei is a random process, and the number of transformations is directly proportional to the number of radioactive atoms present. For any pure radioactive substance, the rate of decay is usually described by its radiological half-life, TR, i.e., the time it... 

The amounts of specific substances deposited or liberated by the same quantity of electricity are directly proportional to their chemical equivalents. 

For osmotic drug delivery systems, Eq. (2) is of critical importance. This equation demonstrates that the quantity of water that can pass a semipermeable film is directly proportional to the pressure differential across the film as measured by the difference between the hydrostatic and osmotic pressures. Osmotic delivery systems are generally composed of a solid core formulation coated with a semipermeable film. Included in the core formulation is a quantity of material capable of generating an osmotic pressure differential across the film. When placed in an aqueous environment, water is transported across the film. This transported water in turn builds up a hydrostatic pressure within the device which leads to expulsion of the core material through a suitably placed exit port. 

Mass is a measure of the quantity of material in a sample. We can measure that mass by its inertia —the resistance to change in its motion—or by its weight—the attraction of the sample to the earth. Since weight and mass are directly proportional as long as we stay on the surface of the earth, chemists often use the terms interchangeably. (Physicists do not do that.)... 

Not all of the nuclei of a given sample of a radioactive isotope disintegrate at the same time the nuclei disintegrate over a period of time. The number of radioactive disintegrations per unit time that occur in a given sample of a naturally radioactive isotope is directly proportional to the quantity of that isotope present. The more nuclei present, the more will disintegrate per second (or per year, etc.). 

The initial rate was directly proportional to the quantity of catalyst, and was increased by vigorous stirring. The DP of the polymer formed was independent of the quantity of catalyst. 

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