Constant of proportionality

At pressures to a few bars, the vapor phase is at a relatively low density, i.e., on the average, the molecules interact with one another less strongly than do the molecules in the much denser liquid phase. It is therefore a common simplification to assume that all the nonideality in vapor-liquid systems exist in the liquid phase and that the vapor phase can be treated as an ideal gas. This leads to the simple result that the fugacity of component i is given by its partial pressure, i.e. the product of y, the mole fraction of i in the vapor, and P, the total pressure. A somewhat less restrictive simplification is the Lewis fugacity rule which sets the fugacity of i in the vapor mixture proportional to its mole fraction in the vapor phase the constant of proportionality is the fugacity of pure i vapor at the temperature and pressure of the mixture. These simplifications are attractive because they make the calculation of vapor-liquid equilibria much easier the K factors = i i ... 

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... 

The dielectric constant is a property of a bulk material, not an individual molecule. It arises from the polarity of molecules (static dipole moment), and the polarizability and orientation of molecules in the bulk medium. Often, it is the relative permitivity 8, that is computed rather than the dielectric constant k, which is the constant of proportionality between the vacuum permitivity so and the relative permitivity. 

The SI units of frequency are reciprocal seconds (s ) given the name hertz and the symbol Hz m honor of the nineteenth century physicist Heinrich R Hertz The constant of proportionality h is called Planck s constant and has the value... 

Friction and Adhesion. The coefficient of friction p. is the constant of proportionality between the normal force P between two materials in contact and the perpendicular force F required to move one of the materials relative to the other. Macroscopic friction occurs from the contact of asperities on opposing surfaces as they sHde past each other. On the atomic level friction occurs from the formation of bonds between adjacent atoms as they sHde past one another. Friction coefficients are usually measured using a sliding pin on a disk arrangement. Friction coefficients for ceramic fibers in a matrix have been measured using fiber pushout tests (53). For various material combinations (43) ... 

The constant of proportionality is based on nonnalizing the probability and establishing the size of the prior, that is, the number of data points that the prior represents. The advantage of the Dirichlet formalism is that it gives values for not only the modes of the probabilities but also the variances, covariances, etc. See Eq. (13). 

P = absolute pressure v = specific volume R = constant of proportionality T = absolute temperature... 

Planck s constant (Section 13.1) Constant of proportionality (A) in the equation E = hv, which relates the energy ( ) to the frequency (v) of electromagnetic radiation. 

The constant of proportionality is K/fx, where K is the permeability and is Newtonian viscosity. The dielectric properties of the resin are also measured using sensors. These measurements were correlated with viscosity and used as a part of the FRTM control system. 

In the region where the relationship between stress and strain is linear, the material is said to be elastic, and the constant of proportionality is E, Young s modulus, or the elastic modulus. 

For an elastic material the shear stress is related to the shear strain through a constant of proportionality G, railed the shear modulus. The shear strain is dimensionless, and the shear modulus has units of force per unit area. 

The constant of proportionality in the English system of units, g, which causes one pound of mass produces one pound of force under the acceleration of gravity, equal to 32.17 Ibm-ft/lbf-sec. ... 

The constant of proportionality between the force and the acceleration it produces is the mass, m ... 

When the constant of proportionality for the laws is written as R, this expression becomes the ideal gas law ... 

As explained in Section 6.5, the heat capacity of a substance is the constant of proportionality between the heat supplied to a substance and the temperature rise that results (q = CAT). However, the rise in temperature and therefore the heat capacity depend on the conditions under which the heating takes place because, at constant pressure, some of the heat is used to do expansion work rather than to raise the temperature of the system. We need to refine our definition of heat capacity. 

We have found that the initial rate of the reaction is proportional to the initial concentration of N205. If we were to follow the reaction rate in one of the flasks as the reaction proceeds we would also find that as the concentration of falls, the rate falls too. More specifically, we would find that the rate at any instant is directly proportional to the concentration of N205 at that instant, with the same constant of proportionality, k. We therefore conclude that, at any stage of the reaction. 

The expression for the ratio of cross-sections for the HeH + and HeD + products complete with the constants of proportionality (3) is given by ... 

For freely suspended bioparticles the most likely flow stresses are perceived to be either shear or normal (elongation) stresses caused by the local turbulent flow. In each case, there are a number of ways of describing mathematically the interactions between turbulent eddies and the suspended particles. Most methods however predict the same functional relationship between the prevailing turbulent flow stresses, material properties and equipment parameters, the only difference between them being the constant of proportionality in the equations. Typically, in the viscous dissipation subrange, theory suggests the following relationship for the mean stress [85] ... 

If termination were to occur in part by disproportionation, would still be proportional to v but the constant of proportionality would lie between one and two, its exact value depending on the fraction of termination which occurs by combination. The assumption that the reactions considered above suffice for the interpretation not only of the polymerization rate but also of the degree of polymerization requires in any case that Xn be proportional to v. 

In accordance with Pick s Law, diffusive flow always occurs in the direction of decreasing concentration and at a rate, which is proportional to the magnitude of the concentration gradient. Under true conditions of molecular diffusion, the constant of proportionality is equal to the molecular diffusivity of the component i in the system, D, (m /s). For other cases, such as diffusion in porous matrices and for turbulent diffusion applications, an effective diffusivity value is used, which must be determined experimentally. 

In diffusional mass transfer, the transfer is always in the direction of decreasing concentration and is proportional to the magnitude of the concentration gradient the constant of proportionality being the diffusion coefficient for the system. 

The energy of a photon is now recognized as being proportional to the frequency of the photon. The constant of proportionality relating the photon s frequency and energy is known as Planck s constant. It has a value of 6.626 x 10-34 J s, and is denoted by the letter h. In this activity, you will measure the value of Planck s constant by observing the photoelectric effect. 

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