The Velocity of Sound in Hydrogen when Rotational Degrees of Freedom Fail to Be Excited

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Abstract
The velocity of sound in parahydrogen, normal hydrogen, and 50 percent para-50 percent orthohydrogen mixtures has been observed at several temperatures, and over a range of frequency to pressure ratio from one to 60 megacycles per atmosphere. Dispersion attributed to failure of the rotational degrees of freedom to follow the temperature associated with the translational degrees of freedom has been observed with all mixtures and at every temperature at which observations were made. Measurements at two different frequencies for similar samples at the same temperature indicate that frequency and pressure affect the velocity of sound only as the quotient, frequency/pressure, with the exception of small corrections that must be applied because hydrogen is not a perfect gas. Experiments indicate that the dispersion occupies a greater range of frequency to pressure than would be expected if the rotational specific heat behaved as a simple relaxation phenomenon. It is shown that a simple relaxation phenomenon is not to be expected, and that the dispersion in parahydrogen can be characterized, approximately, by two relaxation frequency to pressure ratios, one for the rotational transition 0-2, and another for the transition 2-4. An expression for these relaxation frequency to pressure ratios, that roughly fits the observations, is derived on the basis of some assumptions about the collision process.

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