开尔文方程的推导及表达

Study on the Derivation and Expression of Kelvin Equation

目前物理化学教材及相关文献中有关开尔文方程的推导方法有多种。但是推导方程的出发点基本上可归于两类,一类是考虑液体变液滴,表面积增加,增加表面吉布斯自由能,从而引起液滴的蒸气压较平面液体蒸气压变大。另一类认为液滴具有弯曲液面,产生的附加压力使得液滴的吉布斯自由能增大,从而使得液滴的蒸气压较平面液体蒸气压变大。对两类推导方法进行了分析研究,认为第1类推导方法,出发点是正确的,但推导过程不够严谨;对于第2类推导方法,推导的出发点并不合理。提出了推导开尔文方程新思路,推导出的结果表明,开尔文方程应将原表达式做一修正,即将原表达式中系数2修正为3,具体表达式应为RTlnpr/p=3γ/r·M/ρ=3γ/r·Vm。

At present,there are many derivation methods of Kelvin equation in physical chemistry textbooks and related literature.However,the starting point of deriving the equation can be basically divided into two categories.One is to consider that the liquid changes into droplets,the surface area increases,and the surface Gibbs free energy increases,resulting in the increase of the vapor pressure of droplets.The other is that the droplet has a curved liquid surface,and the additional pressure increases the Gibbs free energy of the droplet,which makes the vapor pressure of the droplet larger than that of the flat liquid.Two kinds of derivation methods are analyzed and studied.It is considered that the starting point of the first kind of derivation method is correct,but the derivation process is not rigorous enough.For the second kind of derivation method,the starting point of derivation is unreasonable.This paper puts forward a new idea of deriving Kelvin equation.The derived results show that the original expression of Kelvin equation should be modified,that is,the coefficient 2 in the original expression should be modified to 3,and specifically the expression should be RTlnpr/p=3γ/r·M/ρ=3γ/r·Vm.