For water at a pressure of 100 kPa and a temperature of 101 °C, estimate the minimum radius of a vapour bubble nucleus required to initiate boiling. I know you have to use pressure tables but not sure how to approach the question. Any help would be greatly appreciated.

This is a great question. I'm not able to answer it, but I think you are. I would approach this backwards. My first question would be what determines the radius of a vapor bubble? After I knew that I'd consult the tables.

You probably know that classically, most substances will begin to boil at a certain temperature, and will continue to vaporize at that temperature with the addition of heat energy. But there are other considerations. Freezing may be delayed in water, for instance (supercooling) if the sample is isolated from vibration. The same is true of boiling, that a nucleation site, whether a bubble in the liquid itself, or an imperfection in the wall of the vessel is necessary to determine exactly where/when the boiling will begin. Presumably, then, this microbubble would have to be of some finite size to produce the effect! Possibly the determining factor would be the thermodynamics at the interface from the interior of the bubble (gas) to its immediate exterior (liquid.) As the radius of the bubble rises, the curvature would decrease, and at some point the physics of the conditions would be right for boiling? Another way to view the situation would be from the standpoint of turbulance, as boiling on the surfaces of objects moving through any fluid is partially a function of roughness/surface texture. I'm not a Chemical Engineer, but I bet the Reynold's number of the liquid is a a factor, as R is important in determining the onset of turbulent flow. Possibly a recent ChemEng text would have some info, as many advances have been made in this field recently!

Here's how I'd do the problem. Assume the bubble is at a certain depth, probably near the surface. Then the pressure on a small bubble will be the pressure head (probably fairly small) plus atmospheric pressure (big). The vapor pressure of the vapor in the bubble will have to balance the pressure from the fluid. Write an expression for the surface area times the liquid's pressure; this must be equal to the same surface area times the vapor's pressure. Solve for the area and thus the radius. You'll probably have to do some interpolation in the steam tables.