F. Douglas Shields

Sound Absorption in the Halogen Gases

Apparatus has been constructed for measuring sound absorption by the tube method in corrosive gases at high temperatures. This apparatus has been used to measure sound absorption in chlorine, bromine, and iodine vapors at temperatures between 25 and 256°C. The measurements revealed vibrational relaxation absorption peaks in all the gases. In Cl2 the relaxation times varied from 4.90 μsec at 25°C to 1.55 μsec at 255°C. In Br2 the variation was from 0.854 μsec at 28°C to 0.460 μsec at 256°C. In I2 the relaxation time was almost independent of temperature, changing only from 0.106 to 0.102 μsec when the temperature changed from 112 to 253°C.The heights of the absorption peaks were adequately predicted by assuming the relaxing vibrational specific heat to be Cp−72R. Neither the Schwartz‐Herzfeld nor Cottrell‐Ream theoretical equations for the relaxation time accurately predict the measured variation with temperature, molecular mass and vibrational frequency.

Numerical Solution for Sound Velocity and Absorption in Cylindrical Tubes

A numerical solution of the Kirchhoff equation for the propagation constant of longitudinal sound waves in infinitely long cylindrical tubes has been obtained. The solution, which avoids the wide‐tube approximations, shows that the percentage errors in the von Helmholtz‐Kirchhoff tube velocity correction and tube absorption are both roughly equal to the percentage the velocity correction is of the free‐space velocity. The error in the von Helmholtz‐Kirchhoff equations can be plotted as a function of fD/a, pD/ηa, and γ. (f is the sound frequency, D the tube diameter, a the free‐space velocity, p the gas pressure, η the viscosity, and γ the ratio of specific heats.) Recent absorption measurements in Ar are in agreement with values calculated numerically, but measured velocities indicate the need for considering molecular slip at the tube wall. Thermal relaxation is introduced into Kirchhoffs basic equation by using the Eucken relation k/coηu2009−u2009(9γ −5)/4 and considering γ to be the ratio of complex relaxing ...

Vibrational Relaxation in CO2/D2O Mixtures

Sound absorption and velocity measurements have been made in CO2/D2O mixtures at 300°, 400°, and 500°K. The results show that D2O is from 13 to 15 as efficient as H2O in de‐exciting the bending‐mode vibration of CO2 in a molecular collision. The collision efficiency of D2O for de‐exciting CO2 decreases with temperature at an even greater rate than does that of H2O. The large difference between D2O and H2O invalidates the chemical affinity explanation of effect of H2O on CO2. An approximate semiclassical calculation of the transition probability indicates that it is possible to attribute the relaxation to an interchange between the vibration of the CO2 and the rotation of the H2O or D2O.

Absorption of sound in air: High‐frequency measurements

The absorption of sound in air at frequencies from 4 to 100 kHz in 1/12 octave intervals, for temperatures from 255.4°u2009K (0°u2009F) to 310.9°u2009K (100°u2009F) in 5.5°u2009K (10°u2009F) intervals, and at 10% relative‐humidity increments between 0% and saturation has been measured. The values of free‐field absorption have been analyzed to determine the relaxation frequency of oxygen for each of the 92 combinations of temperature and relative humidity studied and the results are compared to an empirical expression. The relaxation frequencies of oxygen have been analyzed to determine the microscopic energy‐transfer rates.

Thermal Relaxation in Carbon Dioxide as a Function of Temperature

Sound absorption and velocity measurements have been made in carbon dioxide between 0 and 200°C. The relaxation absorption was isolated by subtracting the tube and classical absorptions from the measured absorption. The Kirchhoff equations, which had been justified previously by measurements in A and N2 were used to make these corrections. From the relaxation absorption were determined the temperature variation of the thermal relaxation time, the transition probability, and the collision efficiency. The results indicate that for the frequencies and pressures here employed the relaxation absorption and velocity effects are a function of f/p. This means that only binary collisions are effective in transferring energy between the vibrational and translational modes. The relaxation theory with a single relaxation time for all the vibrational modes adequately predicts the observed absorption and velocity. It is estimated that a separation in the relaxation times of the two lowest modes by a factor of more than...

Thermal Relaxation in Fluorine

Sound absorption and velocity measurements in fluorine at 28° and 102°C indicate vibrational relaxation times of 20.7 and 10.7 μsec for these two temperatures, respectively. The measurements were made inside a glass tube 1.73 cm in diameter using progressive waves. These results when combined with earlier results in the other halogens indicate certain changes which improve the accuracy of the Slawsky, Schwartz, and Herzfeld theory.

Tube Corrections in the Study of Sound Absorption

The absorption and velocity of sound in argon, nitrogen, and carbon dioxide have been investigated over a range of frequency, pressure, and temperature conditions. Use was made of a movable sound source and a stationary microphone, both employing the principle of the ribbon microphone, located inside glass tubing 1.73 cm in diameter. It was found that Kirchhoffs equations correctly predicted the absorption and velocity as the temperature was varied from 0 to 200°C in the case of argon and from 0 to 150°C for N2. Not only did the tube absorption vary as a function of (f/p)12, but the factor incorporating the physical properties also appears to be valid. Certain earlier experiments have not agreed with the Kirchhoff predictions of the magnitude of the factor which depends on the physical properties, and the success in checking the theory is attributed to the use of improved data for the properties and to the use of precision bore tubing the apparatus.

On Obtaining Transition Rates from Sound Absorption and Dispersion Curves

The problem of obtaining transition rates from acoustic measurements of vibrational relaxation times is discussed. The error involved in using the Schafer equation, τ1u2009=u2009τC1/Σ1C1, to obtain the relaxation times for a single mode from the measured relaxation time is evaluated by calculating the sound absorption and dispersion from the reaction equations using the method of Tanczos. The analysis shows that the absorption and dispersion curves closely approximate the single‐relaxation‐time curve in a series relaxation process as long as the v‐v transfer is at least as fast as the v‐t transfer. The calculations rule out a v‐v process for the CO2/H2O interaction. [This work was supported by the U. S. Office of Naval Research.]

Measurements of Thermal Relaxation in CO2 Extended to 300°C

The tube method has been used to extend measurements of sound absorption in carbon dioxide to 300°C. Results indicate that all of the vibrational specific heat in CO2 relaxes with a single relaxation time. This relaxation time at 305°C was found to be 3.05 ×10−6 sec.

Sound Absorption in Pure D2S and CO2/D2S Mixtures

Sound absorption measurements in pure D2S at 300° and 400°K indicate a vibrational relaxation with a relaxation time of 4.8 × 10−8 sec⋅atm, which is independent of temperature. The mixture measurements, when compared with theoretical curves calculated for a series relaxation process, indicate that energy is exchanged between the excited vibrational levels of the two molecules. The results confirm the theory that the bending vibration in CO2 exchanges energy primarily with the rotational motion of the D2O molecule in a collision.