Mass expansion coefficient

With mixtures of ideal gases the mass expansion coefficient can be found from the thermal equation of state... 

D=mass diffumsion coefficient Z)T=fiiermal diffusion coefficient /=friction coefficient G=(oh (centrifugal acceleration) / =Boltzniann constant meff=particle effective mass r=radius of centrifuge basket s=sedimentation coefficient T = absolute temperature =geometric volume of die channel w=channel thickness y=diermal expansion coefficient p=electrophoretic... 

Mo+ and Mc>2+ one may resort to a multinomial expansion coefficient analysis. Let us represent the fractional abundances of the 7 Mo isotopes by a, b, c, d, e, f and g. The calculated and experimental fractional abundances of the 15 mass lines in Mo + are listed in Table 2.4. When the calculated abundances are compared with the experimental abundances, one reaches the conclusion that the spectrum shown in Fig. 2.17 contains few if any Mo+ ions. If on the other hand, a fraction of the ions are Mo+, say p, then the relative abundances of each mass line can also be calculated. For example, that of Min = 92 should be [pa + (1 — p)a2], and that of M/n = 94 should be [pb + (1 — p)(b2 + 2ad), etc. Thus the fraction p can be obtained by best fit of theoretical abundances and experimental abundances of different Min mass lines. 

The conditions (a), (b), (c), and (d) are met since we have the experimental value of the gas-liquid mass transfer coefficient, the wetting efficiency is given to be 100%, plug-flow condition is assumed in the original study, and the expansion factor is zero as the oxygen concentration has been taken as constant. 

The thermal expansion coefficient governs the influence of temperature on density and therefore it is necessary to specify temperature when discussing density or specific gravity. The density of milk is of consequence since fluid milk is normally retailed by volume rather than by mass. Measurement of the density of milk using a hydrometer (lactometer) has also been used to estimate its total solids content. 

The high pressures shewn here are produced by thermal expansion of the specimen at constant volume. At these pressures, the generated gas is completely dissolved in the gel-like mass. The volume expansion coefficient,... 

Here, the subscript (c) is short for the set of expansion parameters (c) = (2i, 22, A, L, oi, u2) r, is the vibrational coordinate of the molecule i R is the separation between the centers of mass of the molecules the Q, are the orientations (Euler angles a, jS y,) of molecule i Q specifies the direction of the separation / the C(2i22A M[M2Ma), etc., are Clebsch-Gordan coefficients the DxMt) are Wigner rotation matrices. The expansion coefficients A(C) = A2i22Al u1u2(ri,r2, R) are independent of the coordinate system these will be referred to as multipole-induced or overlap-induced dipole components - whichever the case may be. 

Variables 2 and Zj are charges of ions i and j Ay is the Pauling factor defined as Ay = (1 + zjnx + z-Jn i, where nK and nj represent the numbers of electrons in the outermost shell of ions i and j, respectively Cy = (3/2) aiajEiEj/(Ei + Ej) and dy = (9/4e2)Cy(a, 1/Ar1 + atjE/Nj), where a denotes the polarizability of ions, N is the number of the total electrons of an ion, and E is the first ionization potential, evaluated from the Equation Ef = Nle2h2I Tr2mai for ion i, where h and m are the Planck constant and the mass of the ion, respectively. Values of p, b, and cr are estimated from isothermal compressibilities and thermal expansion coefficients of 17 rock-salt-type crystals of alkali halides by Fumi and Tosi (15). 

Table 6. 1/n expansion coefficients bi for the Bethe logarithms of helium. The coefficients di and da give the finite mass correction due to mass polarization effects on the wave function. See Eqs. (16) and (17)... 

The following symbols are used in the definitions of the dimensionless quantities mass (m), time (t), volume (V area (A density (p), speed (u), length (/), viscosity (rj), pressure (p), acceleration of free fall (p), cubic expansion coefficient (a), temperature (T surface tension (y), speed of sound (c), mean free path (X), frequency (/), thermal diffusivity (a), coefficient of heat transfer (/i), thermal conductivity (/c), specific heat capacity at constant pressure (cp), diffusion coefficient (D), mole fraction (x), mass transfer coefficient (fcd), permeability (p), electric conductivity (k and magnetic flux density ( B) ... 

The plot of a master curve of the thermal variations of rio for various molecular weights and temperatmes (Fig. 23) shows that the expansion coefficient Uf can be considered as a constant in a wide range of temperatures. The vertical and horizontal shift factors respectively describe the mass dependence of the radius of gyration and temperature T . 

Figure 1 Structural (left column) and dynamical (right column) properties of the systems investigated. Upper left centre-of-mass radial pair distribution function gooo( ) lower left spherical harmonic expansion coefficient g2oo(r) upper right angular velocity correlation function lower right orientational correlation function. Dotted lines CO, 80 K, 1 bar thin lines CS2, 293 K, 1 bar thick lines CS2, 293 K, 10 kbar.

---