If auto-ignition temperature is the temperature when the vapor molecules/atoms just achieve boom velocity, instantaneously as their vibration energy increases with temperature, then we have a good correspondence of temperature of the vapor given its molecular/atomic mass, and kinetic energy that was previously used to define temperature. As in
\(PV=nRT\)
we have instead,
\(T=density*f(v_{boom})\)
where \(T\) is temperature and \(f(v_{boom})\) is some function of \(v_{boom}\). Consider,
\(KE\equiv density*f(v_{boom})\)
so,
\(KE=\cfrac{1}{2}*density*v_{boom}^2\)
this would be kinetic energy per unit volume, but,
\(v_{boom}=3.4354*density*\cfrac{1}{particle\,count\,per\,type}\)
so,
\(KE=\cfrac{3.4354^2}{2}*density^3*\cfrac{1}{(particle\,count\,per\,type)^2}\)
And in the case of basic elements,
\(KE=density^3*\cfrac{5.901}{(atomic\,\,number)^2}\)
where the density (cubed) of the elements changes with \(T\). A plot of \(T\) vs \(v_{boom}\) of various density will give \(f(v_{boom})\) or the function f(x), from which we may then infer \(KE=g(T)\) where \(g(T)\) is a function of \(T\). Temperature \(T\) here then, as intended is a measure of the vibrational kinetic energy within the element.
This seemingly is a definition of temperature without the explicit involvement of temperature particles, derived from the vibrational kinetic energy of the atoms in an elements. A sentinel point in this definition is \(T_{boom}\), the temperature at which \(v_{boom}\) is achieved.
This is not melting, but it would be interesting if \(T_{boom}\) occurs before the melting point.
Or is it? Melting? \(v_{boom}\) changes density and could account for the energy released during phase change. There is a \(v_{boom}\) from solid to liquid, a different \(v_{boom}\) from liquid to gas and yet another value of \(v_{boom}\) for the gas as it disintegrate. Different \(v_{boom}\) values for different densities of the element/compound.
Is \(v_{boom}\) responsible for phase change? Phase change would then be nuclear. Boiling water for tea would then be nuclear.
