**C1.** For Example 4-4 (open steam), show that the x intercept (y = 0) is at x = x_{B}.

**C2.** Derive the bottom operating line for a column with a total reboiler. Show that this is the same result as is obtained with a partial reboiler.

**C3.** Derive Eqs. (4-51) and (4-52).

**C4.** For a side stream below the feed:

**a.** Draw a sketch corresponding to Figure 4-22A.

**b.** Derive the operating equation and y = x intercept.

**c.** Sketch the McCabe-Thiele diagram.

**C5.** Derive the operating equations for the two middle operating sections when an intermediate reboiler is used (see Figures 4-23A and 4-23B). Show that the operating line with slope of L′/V′ goes through the point y = x = x_{B}.

**C6.** Show that the total amount of cooling needed is the same for a column ...

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