Scientia Sinica

42 SCIENTIA SINICA Vol, V

If the equation of state or the second virial coefficient of the gas is known, Br is known and y and y,, can be calculated from f, and B. by using (20) and (21). We shall then find that in addition to the well-known dependence of yp on molecular structure, the difference between y, and y,, allows more definite conclusions to be made at once as will be illustrated below. Knowing yo and y.,, ome can calculate the heat capacities C,, C,, and C” from

Crp =—“_ TV aBr, Cv = Colo, Yo—l

EO — EG — ¥o) (a — 1) ~ (35)

From the value of C™ thus calculated together with available spectroscopic data one can make judgment as to what internal states of excitation effectively participate in the relaxation, e.g., what modes of vibration are sonically activated. C‘’ having been obtained, the thermal relaxation time can be computed from (11), viz.,

Tn = Ea oe (36)

Since, when the energy of excitation E in question is, as actually the case, much larger than RT so that the concentration of excited molecules is much less than that of unexcited ones, T,, is the mean lifetime of the excited state of the molecule responsible for the relaxation process, and the average number of molecular collisions necessary for a molecule to lose its energy of excitation will be Z t,,, where Z is the average number of collisions a molecule encounters per unit time, being equal to the average molecular speed divided by mean free path. From kinetic theory, this may be calculated from the coefficient of shearing viscosity and Sutherland’s constant'’”!. Thus, the effective probability, P=1/Z 7,, of de-excitation per collision may be calculated. Since under normal conditions Z is of the order of 10”, P= ti x NO.

These calculations have been made from available sound absorption and dispersion data for various gases and vapours which appear to be sufficiently accurate and the results are given in Tables I and II respectively. In these illustrations we have for the sake of simplicity disregarded the effect of the intermolecular forces by putting Bry=1/p and C,—C,=R..

In Table I are tabulated the results of calculations from ultrasonic absorption data. The values of e and v» are taken from the Handbook of Chemistry and Physics, and from the International Critical Tables, corrections having been made for differences in temperature. In the case of hydrogen, data for 25°C and 25.63°C, both under atmospheric pressure, are those of Stewart!) and Zartmen™! respectively. They both give y=7/5 and y,=5/3. These