= Kelvin equation
{c}
{title2=$\ln(p/p_{\rm sat})\simeq2\Gamma v_l/(Rk_BT)$}
{wiki}
In the ideal-vapor, incompressible-liquid capillarity approximation, a spherical droplet of radius $R$ has the displayed equilibrium vapor-pressure relation. Here $v_l$ is liquid volume per molecule, $\Gamma$ is <surface tension>, and $p_{\rm sat}$ is the flat-interface saturation pressure at the same <temperature>. The <Young–Laplace equation> raises liquid pressure by $2\Gamma/R$, increasing its <chemical potential> by approximately $2\Gamma v_l/R$. Matching this with the ideal-vapor chemical-potential increase $k_BT\ln(p/p_{\rm sat})$ proves the formula. The liquid contribution from the vapor-pressure change itself is neglected relative to its curvature pressure, and bulk properties are taken independent of radius. A convex small drop therefore requires a higher ambient vapor pressure than a flat interface.
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