The relative frequency of non-gleichberechtigt occurrences

The qualitative assumptions and ike first estimates of Clausius. On the basis of the assumptions about frequencies discussed above, Clausius gave a new derivation of the equation pv—RT and developed the first quantitative estimate for the diffusion velocity. 6 

At that time, however, Clausius had already expounded at least qualitatively the kinetic meaning of those phenomena whose quantitative treatment calls for much deeper assumptions about frequencies. Thus he showed, for instance, 7 that the equilibrium between a liquid and its saturated vapor at different temperatures depends on the fraction of the molecules in the liquid whose speed exceeds, at the temperature in question, the critical speed necessary to escape from the liquid. Therefore, in order to discuss the equilibrium in a quantitative manner, i.e., as a function of temperature, we need an assumption about the relative frequency of the various molecular speeds. 

Clausius, however, makes no attempt to give a quantitative estimate for the relative frequencies of obviously non-gleichberechiigt occurrences. As a consequence, in some cases he gives up the quantitative approach altogether. 6 In others he is satisfied with estimates he replaces the unknown relative frequency by an assumption which is intentionally schematic and which is chosen for convenience in calculation. He emphasizes, however, that he is presenting only an estimate. In his treatment of the velocity of diffusion, for instance, he carries through 

Maxwell s derivation of a law for the distribution of velocities. In order to elaborate further on the conclusions reached by Clausius, it became necessary to convert the qualitative statement about the smallness of the dispersion of the velocity distribution into some specific quantitative assumptions, which could then be used in calculations. This is where J. C. Maxwell entered the scene (1859).31 Considering the case of a monatomic gas at rest,33 in thermal equilibrium and in the absence of external forces, he postulated the following law for the distribution of velocities (the Maxwell distribution law )  

Here /( , v, w)AuAvAw is the number of molecules, the three velocity components of which are between the 

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