Kelvin equation

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,$p\_0$ is the saturated vapour pressure,$gamma$ is the surface tension, $V\_m$ 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 , then liquid evaporates from the droplets.

If $p\_0\; >\; p$, then the gas condenses onto thedroplets increasing their volumes.

As $r$ increases, $p$ decreases and thedroplets grow into bulk liquid.

If we now cool the vapour, then $T$ decreases, but so does $p\_0$. This means $p/p\_0$ increases as the liquid is cooled. We can treat $gamma$ 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.

ee also

* Condensation

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