Equivalency of mercury porosimetry and gas adsorption

Lowell and Shields have shown that vapor condensation-evaporation and mercury intrusion-extrusion into and out of pores are thermodynamically equivalent processes. 

A vapor will condense into pores of radius r according to the Kelvin equation, namely 

The molar free-energy change associated with the isothermal vapor-pressure change from Pq to P is given by 

The process of mercury intrusion requires the application of hydraulic pressure, P, to force mercury into pores for which the molar free-energy change is given by 

Equating the molar free-energy terms in (12.24) and (12.25) affords an expression which relates the hydraulic pressure P required to force mercury into pores to the relative pressure, PJPq, exerted by the liquid with radius of curvature, r. That is. 

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A significant aspect of the equivalency of mercury porosimetry and gas adsorption is the implication that mercury can fill pores by either liquid or vapor transport. 

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