Kelvin equation

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Kelvin equation describes the change of vapour pressure over liquid curved with a radius r (for example, in a capillary or over a droplet). The Kelvin equation is used for determination of pore size distribution of a porous medium using adsorption porosimetry.

The Kelvin equation may be written in the form

\ln {p \over p_0}= {2 \gamma V_m \over rRT}

where p is the actual vapour pressure, p0 is the saturated vapour pressure, γ is the surface tension, Vm is the molar volume, R is the universal gas constant, r is the radius of the droplet, and T is temperature.

Equilibrium vapor pressure depends on droplet size. If p0 < p, then liquid evaporates from the droplets.

If p0 > p, then the gas condenses onto the droplets increasing their volumes.

As r increases, p decreases and the droplets grow into bulk liquid.

If we now cool the vapour, then T decreases, but so does p0. This means p / p0 increases as the liquid is cooled. We can treat γ and V as approximately fixed, which means that the critical radius r must also decrease. The further a vapour is supercooled, the smaller the critical radius becomes. Ultimately it gets as small as a few molecules and the liquid undergoes homogeneous nucleation and growth.

[edit] See also

[edit] References

  • W. T. Thomson, Phil. Mag. 42, 448 (1871)
  • S. J. Gregg and K. S. W. Sing, Adsorption, Surface Area and Porosity, 2nd edition, Academic Press, New York, (1982) p.121
  • Adamson and Gast, Physical Chemistry of Surfaces, 6th edition, (1997) p.54