Two identical flat plates are held vertically a distance d $=0\mathrm{.}01$ mm apart and are partly dipped in

water at $25\backslash$deg C in a large water reservoir. The equilibrium contact angle at this temperature is $30\backslash$deg $.$ The meniscus of the water that rises in the gap between the plates can be assumed to be a portion of a cylindrical surface.

$($a$)$ Calculate the height the water will reach inside the plates above the free surface of the water in the reservoir.

$($b$)$ Calculate the vapor pressure of the water in the gap by application of the Kelvin equation.