This graph shows the relationship between the average kinetic energy of molecules [½(mass)(velocity)²] at two different temperatures. For any given sample of molecules, there is a range of kinetic energies possible; some will have higher kinetic energy, some lower, with the majority of the molecules falling in the middle range.

 

The graph shows that at a second, higher temperature, the molecules in the sample not only have a greater range of kinetic energies, but they also have an overall higher AVERAGE kinetic energy.

 

E_min  is the temperature at which the molecules of a liquid contain enough kinetic energy to change phase, from a liquid to a gas. At the lower temperature, very few molecules have sufficient energy to change phase, but at the higher temperature, all of the molecules in the KE range above E_min contain enough energy to change phase.