The classic penetration theory of gas-liquid mass transfer across a stationary interface (i.e., n = 0, k = 1) reveals /i dependence for the total number of moles of O2 that has been transported into the quiescent liquid. In general, the functional dependence of [moles(f)]A on time scales as /(2 /3)+i/2 -phe volume of the bubble must increase according to t, or its radius must increase as fC" to realize a linear increase in [moles(f)]A vs. time throughout the duration of the process. [Pg.327]

The constant of proportionality, Lk, is the linear phenomenological coefficient for diffusional flow. We have seen earlier that in an ideal fluid mixture the chemical potential can be written as p(p, T,Xk) = ii(p, T) + RThiXk, in which Xk is the mole fraction per unit volume of k, generally a function of position. If Utot is the total mole number density and n is the mole number density of [Pg.270]

This simply shows that there is a physical relationship between different quantities that one can measure in a gas system, so that gas pressure can be expressed as a function of gas volume, temperature and number of moles, n. In general, some relationships come from the specific properties of a material and some follow from physical laws that are independent of the material (such as the laws of thermodynamics). There are two different kinds of thermodynamic variables intensive variables (those that do not depend on the size and amount of the system, like temperature, pressure, density, electrostatic potential, electric field, magnetic field and molar properties) and extensive variables (those that scale linearly with the size and amount of the system, like mass, volume, number of molecules, internal energy, enthalpy and entropy). Extensive variables are additive whereas intensive variables are not. [Pg.62]

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