Problem 2.192

If an additional pressure \(\Delta p\) of a saturated vapour over a convex spherical surface of a liquid is considerably less than the vapour pressure over a plane surface, then \(\Delta p=\left(\rho_{v} / \rho_{l}\right) 2 \alpha / r,\) where \(\rho_{v}\) and \(\rho_{l}\) are the densities of the vapour and the liquid, \(\alpha\) is, the surface tension, and \(r\) is the radius of curvature of the surface. Using this formula, find the diameter of water droplets at which the saturated vapour pressure exceeds the vapour pressure over the plane surface by \(\eta=1.0 \%\) at a temperature \(t=27^{\circ} \mathrm{C.}\) The vapour is assumed to be an ideal gas.