System in a Centrifugal Field

Near the surface of the earth, the gravitational acceleration g is essentially constant. For contrast, let us turn our attention next to a centrifugal field, where the acceleration is very sensitive to the distance from the center of rotation. 

The centrifugal force at a distance r from the axis of rotation (Fig. 21.2) is 

The negative sign on the right-hand side occurs because the Gibbs function decreases as r increases that is, work would have to be performed on the sedimenting particle to bring it back from an axial position at large r to a position at small r. 

If we now examine a cell (Fig. 21.2) containing a pure hquid (rather than a solution as shown), then again (as in the case of a gravitational field) we can show that the pressure in the pure fluid varies with position in the centrifugal field. Starting with Equation (21.8) we obtain 

We consider a transfer at constant temperature of an infinitesimal amount of any single solute i from a position r in the cell in the centrifugal field to a second position r + dr. For this transfer at equilibrium, at constant T and external P, dG = 0, so we write in place of Equation (21.12), 

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