## 4aPAa6. Speed of sound in real gases. I. Theory.

### Session: Thursday Morning, December 5

### Time: 9:15

**Author: Allan J. Zuckerwar**

**Location: NASA Langley Res. Ctr., M.S. 236, Hampton, VA 23681-0001**

**Abstract:**

The simple Laplace formula for the speed of sound in gases is corrected to
account for three real-gas effects: molecular degrees of freedom which in
equilibrium are not fully excited, deviations from the ideal-gas law, and
dispersion due to relaxation processes. These are called the specific-heat,
virial, and relaxation corrections, respectively. The specific-heat correction
is based on a power-series expansion of C[inf p0] (specific heat at zero
pressure) with respect to temperature. The virial correction is based on a
three-parameter formula by Kaye and Laby for the second virial coefficient and a
new five-parameter empirical formula for the third virial coefficient. Both are
used to derive the corresponding acoustic virial coefficients. The relaxation
correction is based on both Landau--Teller and Arrhenius temperature
dependencies and inverse-pressure scaling. Using independent handbook data to
obtain values for the above three corrections, the theory is capable of yielding
sound-speed estimates to high accuracy over a wide range of temperatures and
pressures. The theoretical uncertainty is due to the uncertainty in the original
data, smoothing process, and truncation error; these are discussed in detail.

ASA 132nd meeting - Hawaii, December 1996