Further comparisons of the multi- and single-point methods

3 Further comparisons of the multi- and single-point methods 

The analysis immediately above discloses that, when the BET C value is 100, the single-point method using a relative pressure more than three 

Using the method of partial fractions the right side of equation (5.12) can be written as 

Equation (5.14) is the BET equation expressed as the difference between two rectangular hyperbola. If the value of C is taken as infinity then equation (5.14) immediately reduces to equation (5.3), the single point BET equation. The hyperbola referred to above are shown in Fig. 5.1. 

As indicated in Fig. 5.1, curve Y which is the BET curve for an arbitrary C value, approaches curve X, the single-point curve, as the value of C increases. In the limiting case of C equal to infinity the BET curve is coincident with the single-point curve. For all other C values the single point curve lies above the BET curve and their difference vanishes as the relative pressure approaches unity. Thus, as the value of C increases the knee of the isotherm becomes sharper and moves toward lower relative pressures. For lower C values, curves X and Y diverge and higher relative pressures must be used to make single-point surface areas conform to those obtained by the multipoint method. 

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