# Kelvin equation

Kelvin equation is named in honour of William Thomson, also known as Lord Kelvin. This equation is dependent upon thermodynamic principles. Kelvin equation describes how the vapour pressure of a liquid changes when it is on a curved surface, such as the surface of a droplet or capillaries.

Kelvin equation shows that the vapor pressure over a curved surface is higher than that over a plane surface due to the increased surface tension and the effects of curvature on the liquid-vapour interface. Smaller droplets with a higher curvature have higher vapor pressures leading to evaporate easily.

Kelvin equation is use to determine the pore size distribution of a porous medium using adsorption porosimetry.

The original form of the Kelvin equation, introduced by Lord Kelvin in 1871, is given as

Where, p(r) is vapor pressure at a curved interface of radius 'r', P is vapor pressure at a plane interface (where r = ∞), γ is surface tension, ρ_{vapor} is density of the vapor, ρ_{liquid} is density of the liquid, r_{1}, r_{2} is the principal radii of curvature of the surface.

This equation can also be expressed in a logarithmic form, known as the Ostwald–Freundlich equation

Where, p is actual vapor pressure, p_{sat} is saturated vapor pressure at flat surfaces, V_{m} is molar volume of the liquid, R is universal gas constant, r is radius of the droplet and T is the temperature.