Pole point

Draw a line from e through / and extend it to cross the line drawn in step 6, at the pole point, P. 

Find the composition of the raffinate leaving the first stage, n by judging the position of the tie-line from e. Draw a line from the pole point, P, through r to cut the curve at e2, the extract leaving stage 2. 

If an extended tie-line passes through the pole point P, an infinite number of stages will be needed. This condition sets the minimum flow of extraction-solvent required. It is analogous to a pinch point in distillation. 

Draw a line through from the pole point P through r, to find the point on the curve giving the extract composition leaving the second stage, e2. 

The pole point A is obtained where yn+ xn+ and yi xi extended meet and the construction described in Chapter 10 is then followed. 

The enthalpy-composition approach may also be used for multiple feeds and sidestreams for binary systems. For the condition of constant molar overflow, each additional sidestream or feed adds a further operating line and pole point to the system. 

The upper pole point N is located as before. The effect of removing a sidestream S from the system is to produce an effective feed F, where F = F — S and where F S /F F = F/S. Thus, once S and F have been located in the diagram, the position of F may also be determined. The position of the lower pole point M, which must lie on the intersection of x = xw and the straight line drawn through NF, may then be found. N relates to the section of the column above the sidestream and M to that part below the feed plate. A third pole point must be defined to handle that part of the column between the feed and the sidestream. 

The pole point for the intermediate section must be on the limiting operating line for the upper part of the column, that is NS. This must also lie on the limiting operating line for the lower part of the column, that is MF or its extension. Thus the intersection of NS and MF extended gives the position of the intermediate pole point O. 

The number of stages required is determined in the same manner as before, using the upper pole point N for that part of the column between the sidestream and the top, the intermediate pole point O between the feed and the sidestream, and the lower pole point M between the feed and the bottom. 

From the enthalpy data and the reflux ratio, the upper pole point M may be located as shown in Figure 11.32. Points F and S are located on the liquid line, and the position of the effective feed, such that F S /F F = 10. NF is joined and extended to cut x = xw at M, the lower pole point. 

MF is Joined and extended to cut NS at O, the immediate pole point. The number of stages required is then obtained from the figure and... 

In practice a molecule with a dipole moment is often mobile. If the dipole is free to rotate and close to a positive charge it tends to rotate until its negative pole points towards the positive charge. On the other hand, thermal fluctuations drive it away from a perfect orientation. On average, a net preferential orientation remains and the dipole is attracted by the monopole. The average potential energy is... 

Another possible explanation was recently offered by Zwietering (151), who discusses the possibility that type-A adsorption is due to hydrogen atoms having a dipole with the negative pole pointing away from the surface, and that type-B represents the type where the dipole has a reversed direction. Type-A adsorption is comparable to chemisorption on pure-metal surfaces in the form of wires or of films obtained by sublimation the sign of the dipoles of the hydrogen chemisorption at very low... 

It takes 84 years — a human lifetime — for Uranus and its 15 moons to travel through the zodiac. Like Jupiter, Saturn, and Neptune, Uranus is a gas giant. But while every other planet rotates on its axis in a more-or-less upright fashion, unconventional Uranus seems to roll around on its side with its north pole pointing to the Sun. As a result, the Uranian day is 42 years long, and the night is the same length. 

A permanent bar magnet with its north pole pointing upward... 

A solenoid of n turns per meter, through which a current i flows so as to produce a magnetic field intensity that is in the same direction as that of the permanent magnet (i.e., with the north pole pointing up)... 

Countercun ent extraction according to the pole point construction... 

Fig. 5.7 shows how the reboiler operating point is shifted by changing the Damkohler number. All reboiler operating lines for the different Da numbers meet in the pole point Tt eh whose coordinates are given by... 

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