Momentum monatomic gases

Classical mechanical formulas must agree with those obtained by taking the limit of quantum mechanical formulas as masses and energies become large (the correspondence limit). This limit does not affect the formula representing the equilibrium canonical probability density, so it must therefore be the same function of the energy as that of quantum statistical mechanics. For a one-component monatomic gas or liquid of N molecules without electronic excitation but with intermolecular forces, the classical energy (classical Hamiltonian function Jf) is expressed in terms of momentum components and coordinates ... 

Q, the partition function, is specific to the system under consideration. The analysis in Chapter 1 determined Q to within a proportionality constant, C, for ideal monatomic gas particles Q = C(2KmkTy according to Equation 1.34. The distribution law can give the average number of particles that possess a given discrete energy, but for fhe gas kinetic analysis needed here, fhe distribution needs to be expressed in terms of ofher values such as velocity components, momentum, or speed. 

The weak dependence of the rate of formation of the emission on the pressure of the bulk gas was attributed to a collisional momentum transfer process between the electron and the monatomic rare gas, i.e. 

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