There are a number of ways of stating this. A mole is [[Avogadro's number]] (6.022x10<sup>23</sup>) of molecules. The gas law can be restated in terms of the number of molecules:
:<math>PV = nkT\,</math>
where <math>n\,</math> is the number of molecules and <math>k\,</math> is ''Boltzmann's constant'' (1.38x10<sup>-23</sup> joules per kelvin). It is just the universal gas constant <math>R\,</math> scaled by Avogadro's number. Since it makes no reference to artificial units like grams, physicists consider it to be more theoretically significant than the gas constant, and it shows up in many physical formulas (quantum mechanics and statistical mechanics, for example) that are not related to gas behavior.
Scientists were now fairly close to figuring out thermodynamics. They just needed the kinetic theory and statistical mechanics. They still didn't know why heat only flows "downhill"—it was still just an observed fact. And they didn't know why "heat engines", that is, things that turn heat (e.g. steam) into mechanical energy, aren't very efficient.