## Info

Mole fraction of C6H6 in liquid (x)

### The intersection of the operating lines

It is seen from the example shown in Figure 11.15 in which the feed enters as liquid at its boiling point that the two operating lines intersect at a point having an X-coordinate of x/. The locus of the point of intersection of the operating lines is of considerable importance since, as will be seen, it is dependent on the temperature and physical condition of the feed.

If the two operating lines intersect at a point with coordinates (xq,yq), then from equations 11.35 and 11.37:

or: yq(Vm - V„) = (Lm - L„)x^ - (Dxd + Wxw) (11.42)

A material balance over the feed plate gives:

To obtain a relation between Ln and Lm, it is necessary to make an enthalpy balance over the feed plate, and to consider what happens when the feed enters the column. If the feed is all in the form of liquid at its boiling point, the reflux Lm overflowing to the plate below will be Ln + F. If however the feed is a liquid at a temperature T/, that is less than the boiling point, some vapour rising from the plate below will condense to provide sufficient heat to bring the feed liquor to the boiling point.

If H/ is the enthalpy per mole of feed, and H/s is the enthalpy of one mole of feed at its boiling point, then the heat to be supplied to bring feed to the boiling point is F(H/s - H/), and the number of moles of vapour to be condensed to provide this heat is F(H/s - H/)/A, where A is the molar latent heat of the vapour.

The reflux liquor is then:

Ln F