By Arthur Adamson (Auth.)
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At r = Σ , the potential energy is just zero again; and for r < Σ , it is positive and very rapidly increasing. The average total energy of the pair of molecules can be written (1-67) Thus e t todiminishes to a minimum at r0 and then rises rapidly as r is decreased. In terms of the Boltzmann principle, the effect is to make separation distances around r = r0 relatively more probable and separation distances of r < σ rela tively less probable than for an ideal gas. A second effect of φ(ν) is on the ability of molecules to exert a pressure.
Benjamin, New York. CITED REFERENCES BENSON, S. , AND GOLDING, R. A. (1951). J. Chem. Phys. 1 9 , 1413. GLASSTONE, S. (1946). " Van Nostrand-Reinhold, Princeton, New Jersey. HIRSCHFELDER, J. , CURTISS, C. , AND BIRD, R. B . (1964). "Molecular Theory of Gases and Liquids," corrected ed. Wiley, New York. MACDOUGALL, F. H . (1936). / . Amer. Chem. Soc. 5 8 , 2585. WESTON, F. (1950). "An Introduction to Thermodynamics. " Addison-Wesley, Reading, Massachusetts. EXERCISES AND PROBLEMS As noted in the Preface, each section of this type is divided into three parts.
2 Equation (2-32) is plotted in Fig. 2-5 a n d looks much like the one for a twodimensional gas. The maximum or position of most probable velocity has moved outward, however. This most probable velocity cv may be evaluated analytically if dp(c)/dc is set equal to zero. On doing this, one obtains from Eq. (2-32) the con dition - wr N - w ) ] < * ' > + M - w - t W = 2 or 0 7kT c p* = ^ - . (2-33) As a final comment on the general character of these distribution laws, we note that the probability of a given velocity rapidly decreases with increasing c owing to the exponential term.
A Textbook of Physical Chemistry by Arthur Adamson (Auth.)