Collision Lifetimes and the Thermodynamics of Real Gases

The perfect gas law p/kT=n=Σini (where ni is in molecules per cm3) is inadequate for describing real gases because of the interactions during collisions. By a simple intuitive argument, these interactions can be taken into account exactly if you know the collision lifetimes. The product of collision rate and lifetime gives the concentration of transient collision complexes, which must be considered in the perfect gas law along with the stable species. As a result, the complete virial expansion is obtained, in both quantal and classical mechanics. The argument leads further to a new form for the partition function which includes the continuum as well as bound states. From this all the thermodynamic functions can be obtained.