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An equation giving the increase in vapor pressure of a substance which accompanies an increase in curvature of its surface; the equation describes the greater rate of evaporation of a small liquid droplet as compared to that of a larger one, and the greater solubility of small solid particles as compared to that of larger particles. source: http://encyclopedia2.thefreedictionary.com/Kelvin+Equation 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, 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. source: http://en.wikipedia.org/wiki/Kelvin_equation

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <apply> <and/> <apply> <eq/> <apply> <divide/> <ci>p</ci> <ci> <msub> <mi>p</mi> <mn>0</mn> </msub> </ci> </apply> <apply> <divide/> <ci>c</ci> <ci> <msub> <mi>c</mi> <mn>0</mn> </msub> </ci> </apply> </apply> <apply> <eq/> <apply> <divide/> <ci>c</ci> <ci> <msub> <mi>c</mi> <mn>0</mn> </msub> </ci> </apply> <apply> <exp/> <apply> <divide/> <apply> <times/> <cn>2</cn> <ci>&sigma;</ci> <ci>v</ci> </apply> <apply> <times/> <ci>r</ci> <ci>R</ci> <ci>T</ci> </apply> </apply> </apply> </apply> </apply> </math>

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mrow> <mfrac> <mi>p</mi> <msub> <mi>p</mi> <mn>0</mn> </msub> </mfrac> <mo>=</mo> <mfrac> <mi>c</mi> <msub> <mi>c</mi> <mn>0</mn> </msub> </mfrac> <mo>=</mo> <mrow> <mi>exp</mi> <mo>&ApplyFunction;</mo> <mfenced close=")" open="("> <mfrac> <mrow> <mn>2</mn> <mo>&InvisibleTimes;</mo> <mi>&sigma;</mi> <mo>&InvisibleTimes;</mo> <mi>v</mi> </mrow> <mrow> <mi>r</mi> <mo>&InvisibleTimes;</mo> <mi>R</mi> <mo>&InvisibleTimes;</mo> <mi>T</mi> </mrow> </mfrac> </mfenced> </mrow> </mrow> </math>

\frac {p}{p_0} = \frac{c}{c_0} = \exp (\frac{2 \sigma v}{rRT})

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <semantics> <mrow> <mfrac> <mi>p</mi> <msub> <mi>p</mi> <mn>0</mn> </msub> </mfrac> <mo>=</mo> <mfrac> <mi>c</mi> <msub> <mi>c</mi> <mn>0</mn> </msub> </mfrac> <mo>=</mo> <mi>exp</mi> <mfenced close=")" open="("> <mfrac> <mrow> <mn>2</mn> <mi>&sigma;</mi> <mi>v</mi> </mrow> <mrow> <mi>r</mi> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> </mfenced> </mrow> <annotation encoding="SnuggleTeX">\[ \frac {p}{p_0} = \frac{c}{c_0} = \exp (\frac{2 \sigma v}{rRT}) \]</annotation> </semantics> </math>