By Prigogine I.
Within the final a long time, Chemical Physics has attracted an ever expanding volume of curiosity. the range of difficulties, comparable to these of chemical kinetics, molecular physics, molecular spectros-copy, delivery techniques, thermodynamics, the learn of the country of topic, and the diversity of experimental equipment used, makes the nice improvement of this box comprehensible. however the final result of this breadth of material has been the scattering of the proper literature in a large number of guides.
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The degeneracies are g1 = 2 · (1/2) + 1 = 2 and g2 = 2 · (3/2) + 1 = 4. 93 A) ]. 96 A) = 36 K. Only at such an unreasonably low temperature could the minute energy difference that would favor the lower level of the 2 P doublet overcome the bias, due to its greater degeneracy, that favors the upper one. At any reasonable temperature ε2 − ε1 is so much less than kT that the population of the 2 P3/2 level is just twice as great as that of the 2 P1/2 level. 1 Thermodynamic preliminaries; the equilibrium constant One of the early applications of statistical mechanics to chemistry was in the calculation of the equilibrium constants of gas-phase reactions from spectroscopic data.
3). 1), only those levels within kT, or within a few kT, of the ε kT ε0 Fig. 1 20 2 The ideal gas ground state will be significantly populated. Thus, whether identical molecules’ being in the same state is or is not important depends entirely on whether the number of states in the range kT above ε0 shown in Fig. 1 is or is not much larger than the number of molecules. 6), would be essentially exact. 6) could be seriously in error. In that event one must distinguish the particles as bosons or fermions.
The approximation fails, however, for an electron gas at the typical density of the valence electrons in a metal, because of the exceptionally small mass of the electron. The Fermi–Dirac statistics is then essential. The condition fails also for helium at densities typical of that of the liquid because of the exceptionally low temperatures, only a few kelvin, at which one would be interested in it. 6) is a very good approximation to the partition function of a gas of non-interacting molecules. Sometimes the Boltzmann statistics is referred to as “classical,” as distinct from the Bose–Einstein and Fermi–Dirac statistics, which are called “quantum” statistics.