FIG. 13-38 McCabe-Thiele diagram for columns with and without an interre-boiler and an intercondenser.

is convenient for stepping off stages at extreme purities if it is plotted on log-log paper. The equilibrium curve at very low x1 values on ordinary graph paper can usually be assumed to be a straight line with an intercept term of zero which can be expressed as y = (y/x)x + 0.0

where the slope y/x is a constant. The necessity for knowing the slope is eliminated by taking the logarithm of both sides log y = log x + log (y/x)

and plotting y versus x on a log-log plot to give a straight line with a slope of unity. The slope y/x is now an intercept term which need not be known. One point from the equilibrium curve is sufficient, therefore, to locate the equilibrium curve on the log-log plot. The operating line will be curved on the log-log plot and is located by plotting the appropriate material-balance equation. Both the equilibrium and the operating lines can be extended to any purity desired.

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