Expressions for

Equations (4.5) to (4.7) can now be solved to give expressions for the vapor- and liquid-phase compositions leaving the separator ... 

There is now a simple explicit expression for the vapor rate in a single column in terms of the feed to the column. In order to use this expression to screen column sequences, the vapor rate in each column must be calculated according to Eq. (5.8), assuming a sharp separation in each column, and the individual vapor rates summed. 

Expression for the Minimum Number of 1-2 Shell-and-Tube Heat Exchangers for a... 

Equation (F.7) may be split stream-wise to obtain an expression for the modified h value h of either stream in the match ... 

For petroleum fractions, there is a problem of coherence between the expression for liquid enthalpy and that of an ideal gas. When the reduced temperature is greater than 0.8, the liquid enthalpy is calculated starting with the enthalpy of the ideal gas. On the contrary, when the reduced temperature is less than 0.8, it is preferable to calculate the enthalpy of the ideal gas starting with the enthalpy of the liquid (... 

In the expression for heating value, it is useful to define the physical state of the motor fuel for conventional motor fuels such as gasoline, diesei fuel, and jet fuels, the liquid state is chosen most often as the reference. Nevertheless, if the material is already in its vapor state before entering the combustion system because of mechanical action like atomization or thermal effects such as preheating by exhaust gases, an increase of usefui energy resufts that is not previously taken into consideration. 

For a rough estimation of the optimum excitation frequency for a given test object, one can use the well known expression for the skin penetration depth S ... 

For each frequency 100 points were taken along a line running from the surface of the conductor into a depth of 30 mm in that region below the coil, where the maximum eddy currents are located (dashed vertical lines in the sketch). These data are fitted by appropriate polynomials to obtain an analytical expression for s (to, z) in the frequency and depth interval mentioned above. 

Most of the situations encountered in capillarity involve figures of revolution, and for these it is possible to write down explicit expressions for and R2 by choosing plane 1 so that it passes through the axis of revolution. As shown in Fig. II-7n, R then swings in the plane of the paper, i.e., it is the curvature of the profile at the point in question. R is therefore given simply by the expression from analytical geometry for the curvature of a line... 

If the surface is to be in mechanical equilibrium, the two work terms as given must be equal, and on equating them and substituting in the expressions for dx and dy, the final result obtained is... 

The method is a very old one, remarks on it having been made by Tate in 1864 (33), and a simple expression for the weight W of a drop is given by what... 

Application of the exact continuum analysis of dispersion forces requires significant calculations and the knowledge of the frequency spectmm of the material dielectric response over wavelengths X = 2irc/j/ around 10-10 nm. Because of these complications, it is common to assume that a primary absorption peak at one frequency in the ultraviolet, j/uv. dominates the dielectric spectrum of most materials. This leads to an expression for the dielectric response... 

Derive the expression for the electric field around a point dipole, Eq. VI-5, by treating the dipole as two charges separated by a distance d, then moving to distances X d. 

The full equation for I is obtained by substituting into Eq. IX-8 the expression for AGmax and the gas kinetic expression for Z ... 

Both the kinetics and the equilibrium aspects of ion exchange involve more than purely surface chemical considerations. Thus, the formal expression for the exchange... 

Derive from Eq. XU-24 an expression for the maximum work of adhesion involving only and 7c. Calculate this maximum work for 7c = 22 dyn/cm and 0 = 0.030, as well as 7/. for this case, and the contact angle. 

These concluding chapters deal with various aspects of a very important type of situation, namely, that in which some adsorbate species is distributed between a solid phase and a gaseous one. From the phenomenological point of view, one observes, on mechanically separating the solid and gas phases, that there is a certain distribution of the adsorbate between them. This may be expressed, for example, as ria, the moles adsorbed per gram of solid versus the pressure P. The distribution, in general, is temperature dependent, so the complete empirical description would be in terms of an adsorption function ria = f(P, T). 

The two expressions for bo may be brought into formal identity as follows. On adsorption, the three degrees of translational freedom can be supposed to appear as two degrees of translational motion within the confines of a two-... 

The expressions for and g now have the same appearance as those for H and G in a bulk system. 

One serious issue is the detemihiation of the exchange energy per particle, e, or the corresponding exchange potential, V The exact expression for either of these quantities is miknown, save for special cases. If one... 

This expression for the conductivity is consistent with experimental trends. 

If the long-range mteraction between a pair of molecules is treated by quantum mechanical perturbation theory, then the electrostatic interactions considered in section Al.5.2.3 arise in first order, whereas induction and dispersion effects appear in second order. The multipole expansion of the induction energy in its fill generality [7, 28] is quite complex. Here we consider only explicit expressions for individual temis in the... 

The Chapman-Enskog solution of the Boltzmaim equation [112] leads to the following expressions for the transport coefficients. The viscosity of a pure, monatomic gas can be written as... 

---