Vapour pressure and liquid-surface curvature

Since surface tension is a manifestation of intermolecular forces, it is to be expected that the curvature of a liquid-vapour interface will affect the ease of evaporation and, therefore, the vapour pressure. A relationship between the vapour pressure over a curved surface and the curvature of the surface may be obtained as follows. 

Consider a closed volume containing only a one-component liquid and its vapour, as in Fig. 7.6(a). When a narrow bore tube is placed so as to dip in the liquid, the liquid rises or falls in the tube depending on the value of the angle of contact. 

For definiteness, consider the situation illustrated in Fig. 7.6(a), in which the liquid rises in the tube. Assume that the liquid wets the material of the tube and that the radius r of the tube is very small. Then the liquid surface in the tube is part of a sphere, also of radius r. 

Similarly, in moving a vertical distance dy through the liquid dp = -pgdy 

On passing through the meniscus there is a pressure drop of 2yjr (r is actually negative in Fig. 7.6(a), so that the pressure drop is negative, i.e. it is a pressure increase), p is also given by  

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