Pressure reciprocal theorem

As already noted, the reciprocal theorem does not include specifically conditions where sliding between particles takes place. Geometrical alterations between granular material affect reciprocity of pressure and displacement. 

Closely related to the preceding is the problem of calculating the pressure drop due to Stokes flow through a cylinder of arbitrary (but constant) cross section for arbitrary boundary conditions on the surfaces bounding the cylinder. A simple application of the Reciprocal theorem (B18) permits one to express this pressure drop directly in terms of the prescribed velocity field on the cylinder walls, top, and bottom. If (v, n) and denote the velocity... 

First Theorem of Gibbs and Konovalow.—Under a canr slant pressure cause the composition of the liquid mixture to vary in a wdl-defined way the boiling-point of this mixture changes] if, for a certain composition of the liquid mixture, the boUing-point passes through a maximum or minimum, this liquid mixture gives off a saturated vapor of the same composition, and reciprocally. 

The reciprocal of this theorem is also true namely, if the temperature of coexistence passes, at constant pressure, through an extremum, then the two phases must have the same composition. This follows immediately for from (18.46) and (18.47), (dT/dx ) and dTjdx f), can only be zero if the phases are of the same composition. 

This theorem may be applied for example to the equilibrium at constant pressure between a binary solution and vapour. The reciprocals of the differential coefficients in (18.46) and (18.47) are the slopes... 

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