With water at a density of \(999.8395\,kgm^{-3}\) at \(0\,^oC\),
\(v_{boom\,water}=3.4354*\cfrac{999.8395}{10}=343.48\,ms^{-1}\)
\(T_{water}=\cfrac{343.48^2*18.01528*10^{-3}}{3*8.3144}=85.21\,K\)
Since water is hydrogen bonded to 3.4 other molecules. We ignore hydrogen bonding beyond the first neighbor and apply kinetic theory for ideal gas to this hydrogen bonded macro-molecule, we have,
\(T_{water,H-bonded}=4.4*85.21=374.92\,K\) or \(101.78\,^oC\)
Which is a lot of data massaging because water at \(100\,^oC\) has a density of \(958.4\,kgm^{-3}\). This is not water that is boiling but ice water. However, water next to the surface of the container constrained to move along the surface of the container may be packed more closely like water at 0oC. Boiling then does not occur throughout the water, but just along the surface of the container.
Have a nice day.
