Inversely proportional

Boyle s law At constant temperature the volume of a given mass of gas is inversely proportional to the pressure. Although exact at low pressures, the law is not accurately obeyed at high pressures because of the finite size of molecules and the existence of intermolecular forces. See van der Waals equation. 

Graham showed that the rate of diffusion of different gases through a porous diaphragm was inversely proportional to the square roots of their densities this is the basis of a method of separation of gases, and has been applied successfully to the separation of hydrogen and deuterium. 

Graham s law of diffusion This law states that the rates at which two gases diffuse are inversely proportional to their densities, i.e. 

Raoult s law When a solute is dissolved in a solvent, the vapour pressure of the latter is lowered proportionally to the mole fraction of solute present. Since the lowering of vapour pressure causes an elevation of the boiling point and a depression of the freezing point, Raoult s law also applies and leads to the conclusion that the elevation of boiling point or depression of freezing point is proportional to the weight of the solute and inversely proportional to its molecular weight. Raoult s law is strictly only applicable to ideal solutions since it assumes that there is no chemical interaction between the solute and solvent molecules. 

For a single fluid flowing through a section of reservoir rock, Darcy showed that the superficial velocity of the fluid (u) is proportional to the pressure drop applied (the hydrodynamic pressure gradient), and inversely proportional to the viscosity of the fluid. The constant of proportionality is called the absolute permeability which is a rock property, and is dependent upon the pore size distribution. The superficial velocity is the average flowrate... 

For this kind of case, a modification of the dilution method is being developed. Instead of using an external fixed-geometry measurement chamber, a suitable part of the process, e.g. a stretch of pipe, is used. A radiation detector is mounted on the outside of the pipe, and a tracer emitting sufficiently hard gamma radiation is used. As sufficient mixing can be achieved by injecting upstream the separator the radiation level found will be strictly proportional to the concentration and thus inversely proportional to the true flow rate. 

Some early observations on the catalytic oxidation of SO2 to SO3 on platinized asbestos catalysts led to the following observations (1) the rate was proportional to the SO2 pressure and was inversely proportional to the SO3 pressure (2) the apparent activation energy was 30 kcal/mol (3) the heats of adsorption for SO2, SO3, and O2 were 20, 25, and 30 kcal/mol, respectively. By using appropriate Langmuir equations, show that a possible explanation of the rate data is that there are two kinds of surfaces present, 5 and S2, and that the rate-determining step is... 

The time-dependent structure factor S k,t), which is proportional to the intensity I k,t) measured in an elastic scattering experiment, is a measure of the strength of the spatial correlations in the ordering system with wavenumber k at time t. It exliibits a peak whose position is inversely proportional to the average domain size. As the system phase separates (orders) the peak moves towards increasingly smaller wavenumbers (see figure A3.3.3. 

As is inversely proportional to solvent viscosity, in sufficiently viscous solvents the rate constant k becomes equal to k y. This concerns, for example, reactions such as isomerizations involving significant rotation around single or double bonds, or dissociations requiring separation of fragments, altiiough it may be difficult to experimentally distinguish between effects due to local solvent structure and solvent friction. 

As is the case for the double coincidence arrangement 8 is inversely proportional to the square root of... 

Figure BT2T4 illustrates the direct-space and reciprocal-space lattices for the five two-dimensional Bravais lattices allowed at surfaces. It is usefiil to realize that the vector a is always perpendicular to the vector b and that is always perpendicular to a. It is also usefiil to notice that the length of a is inversely proportional to the length of a, and likewise for b and b. Thus, a large unit cell in direct space gives a small unit cell in reciprocal space, and a wide rectangular unit cell in direct space produces a tall rectangular unit cell in reciprocal space. Also, the hexagonal direct-space lattice gives rise to another hexagonal lattice in reciprocal space, but rotated by 90° with respect to the direct-space lattice.

Hecaiise the repulsion interaction energy of two point charges is inversely proportional to the distance separating the two charges, Dewar and co-workers, for example, represent the (ssiss) two-ceri-ter two-electron integral by ... 

The limiting cases of greatest interest correspond to conditions in which the mean free path lengths are large and small, respectively, compared with the pore diameters. Recall from the discussion in Chapter 3 that the effective Knudsen diffusion coefficients are proportional to pore diameter and independent of pressure, while the effective bulk diffusion coefficients are independent of pore diameter and inversely proportional to pressure. 

It ls not surprising chat such a relation should hold at the Limit of Knudsen diffusion, since Che Knudsen diffusion coefficients are themselves inversely proportional to the square roots of molecular weights, but the pore diameters in Graham s stucco plugs were certainly many times larger chan the gaseous mean free path lengths at the experimental conditions. 

Now recall Chat la Inversely proportional to pressure, so that... 

With a given gas, plate and temperature difference, the pressure difference required to prevent flow is approximately inversely proportional to the density of the gas when the density is sufficiently high. However,... 

As the number of steps fj, in each block increases, so it would be expected that the block averages become uncorrelated. When this is the case, then the Vciriance of the block averages, will become inversely proportional to is calculated as follows ... 

By cooling the solution in a freezing mixture (ice and salt, ice and calcium chloride, or solid carbon dioxide and ether). It must be borne in mind that the rate of crystal formation is inversely proportional to the temperature cooling to very low temperatures may render the mass... 

This damping funetion s time seale parameter x is assumed to eharaeterize the average time between eollisions and thus should be inversely proportional to the eollision frequeney. Its magnitude is also related to the effeetiveness with whieh eollisions eause the dipole funetion to deviate from its unhindered rotational motion (i.e., related to the eollision strength). In effeet, the exponential damping eauses the time eorrelation funetion <( )j Eg ... 

If this electrostatic treatment of the substituent effect of poles is sound, the effect of a pole upon the Gibbs function of activation at a particular position should be inversely proportional to the effective dielectric constant, and the longer the methylene chain the more closely should the effective dielectric constant approach the dielectric constant of the medium. Surprisingly, competitive nitrations of phenpropyl trimethyl ammonium perchlorate and benzene in acetic anhydride and tri-fluoroacetic acid showed the relative rate not to decrease markedly with the dielectric constant of the solvent. It was suggested that the expected decrease in reactivity of the cation was obscured by the faster nitration of ion pairs. 

Frequency is inversely proportional to wavelength the greater the frequency the shorter the wavelength... 

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